9624 lines
397 KiB
JSON
9624 lines
397 KiB
JSON
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|
||
|
|
"answer_preview": "6",
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||
|
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|
||
|
|
"answer_preview": "30.06",
|
||
|
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"source": "orca_math",
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||
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||
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||
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||
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||
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||
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||
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||
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||
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|
{
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||
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|
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||
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||
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||
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||
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||
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||
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||
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||
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||
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"prompt_preview": "Given the parabola $y^2 = 8x$ with focus $F$, a line passing through point $F$ intersects the parabola at points $A$ and $B$. If the midpoint $E$ of segment $AB$ is 3 units away from the y-axis, then the length of $AB$ is ___.",
|
||
|
|
"answer_preview": "10",
|
||
|
|
"source": "cn_k12",
|
||
|
|
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||
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||
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||
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||
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||
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||
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|
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||
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|
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||
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||
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||
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||
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||
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||
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||
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||
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|
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||
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|
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||
|
|
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||
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||
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|
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||
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|
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||
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||
|
|
{
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||
|
|
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||
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|
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||
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|
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||
|
|
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||
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||
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||
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||
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||
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||
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|
||
|
|
"answer_preview": "25",
|
||
|
|
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||
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|
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||
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||
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||
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|
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||
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|
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||
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|
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||
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|
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
|
|
{
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||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
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|
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||
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||
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||
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||
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||
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|
"prompt_preview": "James decides to cut down some trees. In the first 2 days, he cuts down 20 trees each day. For the next 3 days, his 2 brothers help him cut down trees. They cut 20% fewer trees per day than James. Then, their cousin joins them for the follo",
|
||
|
|
"answer_preview": "1021",
|
||
|
|
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||
|
|
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||
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||
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||
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||
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||
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|
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||
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|
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||
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|
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||
|
|
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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|
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||
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||
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},
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||
|
|
{
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||
|
|
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||
|
|
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||
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|
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||
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|
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||
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|
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||
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|
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||
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||
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||
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||
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|
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||
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|
"prompt_preview": "a and b together can do a piece of work in some days, and a alone can do it in 11 days. b alone can do it in 13.2 days. In how many days can a and b together do the work?",
|
||
|
|
"answer_preview": "6",
|
||
|
|
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|
||
|
|
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||
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|
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||
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||
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||
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|
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||
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||
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|
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||
|
|
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||
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|
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||
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|
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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|
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||
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||
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|
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||
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|
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||
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},
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||
|
|
{
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||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
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|
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||
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|
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||
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||
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||
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|
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||
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|
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||
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|
"prompt_preview": "How many real number solutions exist for the equation $\\sqrt{x-1} \\cdot \\sqrt{x+1}=-\\sqrt{x^{2}-1}$, given that $x \\geq 1$? Express your answer as a single integer.",
|
||
|
|
"answer_preview": "1",
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||
|
|
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||
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|
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||
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||
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|
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||
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|
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||
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|
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||
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|
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||
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|
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||
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||
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||
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|
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||
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|
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||
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|
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||
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|
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||
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|
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||
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||
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},
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||
|
|
{
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||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
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|
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||
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|
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||
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|
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||
|
|
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||
|
|
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||
|
|
"prompt_preview": "The circumference of the front wheel of a cart is 30 ft long and that of the back wheel is 33 ft long. What is the distance traveled by the cart when the front wheel has done five more revolutions than the rear wheel?",
|
||
|
|
"answer_preview": "1650",
|
||
|
|
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||
|
|
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|
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||
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||
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|
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||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
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||
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|
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||
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|
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"prompt_preview": "Some squirrels collected 575 acorns. If each squirrel needs 130 acorns to get through the winter, each squirrel needs to collect 15 more acorns. How many squirrels are there?",
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||
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"answer_preview": "5",
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|
||
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|
"answer_preview": "246",
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||
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"prompt_preview": "Suppose that \\( x \\) and \\( y \\) are real numbers with \\( -4 \\leq x \\leq -2 \\) and \\( 2 \\leq y \\leq 4 \\). Find the greatest possible value of \\( \\frac{x+y}{x} \\). Express your answer as a single numerical value.",
|
||
|
|
"answer_preview": "0",
|
||
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||
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||
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{
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||
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||
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||
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"prompt_preview": "With one mighty blow, Maria cracked open the pinata, and countless candies spilled all over the floor. There were 50 red candies, 35 less than three times as many yellow candies as red candies, and a third as many blue candies as twice the ",
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||
|
|
"answer_preview": "156",
|
||
|
|
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||
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||
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||
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||
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||
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|
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{
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||
|
|
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||
|
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||
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||
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||
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||
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||
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"prompt_preview": "The number $123454321$ is written on a blackboard. Evan walks by and erases some (but not all) of the digits, and notices that the resulting number (when spaces are removed) is divisible by $9$ . What is the fewest number of digits he co",
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||
|
|
"answer_preview": "2",
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||
|
|
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||
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||
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||
|
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||
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|
|
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||
|
|
{
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||
|
|
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||
|
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||
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|
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||
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|
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||
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||
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||
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||
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||
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||
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"prompt_preview": "In an arithmetic sequence, the third term is 14 and the eighteenth term is 23. Determine how many terms in the first 2010 terms of this sequence are integers.",
|
||
|
|
"answer_preview": "402",
|
||
|
|
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||
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|
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||
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|
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||
|
|
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||
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||
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||
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||
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||
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||
|
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||
|
|
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||
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||
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||
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||
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||
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||
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"prompt_preview": "A railway freight station decided to organize and dispatch 8 coal freight trains into two groups, each containing 4 trains, with the conditions that trains A and B cannot be in the same group, train A departs first, and train B departs last",
|
||
|
|
"answer_preview": "720",
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||
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|
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||
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||
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|
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||
|
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||
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||
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||
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||
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||
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||
|
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|
|
{
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||
|
|
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||
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|
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||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
|
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||
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||
|
|
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||
|
|
"prompt_preview": "Let \\( a, b \\), and \\( c \\) be positive real numbers. Determine the largest total number of real roots that the following three polynomials may have among them: \\( ax^2 + bx + c \\), \\( bx^2 + cx + a \\), and \\( cx^2 + ax + b \\).",
|
||
|
|
"answer_preview": "4",
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||
|
|
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||
|
|
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|
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||
|
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|
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||
|
|
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||
|
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|
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||
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||
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||
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||
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||
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|
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||
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||
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||
|
|
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||
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|
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{
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||
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||
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||
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|
||
|
|
"answer_preview": "36",
|
||
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|
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||
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},
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||
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|
{
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||
|
|
"sample_id": 7242,
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||
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||
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||
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||
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||
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||
|
|
"answer_preview": "1",
|
||
|
|
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||
|
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||
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||
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||
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||
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||
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||
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||
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||
|
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||
|
|
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||
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||
|
|
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||
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||
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|
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||
|
|
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||
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},
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||
|
|
{
|
||
|
|
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|
||
|
|
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||
|
|
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||
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|
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||
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||
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||
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||
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||
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||
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||
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|
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|
||
|
|
"answer_preview": "12",
|
||
|
|
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|
||
|
|
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||
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||
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||
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||
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||
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||
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||
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|
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||
|
|
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||
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||
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||
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||
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||
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||
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||
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||
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||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
|
|
},
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||
|
|
{
|
||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
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||
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||
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||
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||
|
|
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||
|
|
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||
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|
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|
||
|
|
"answer_preview": "5",
|
||
|
|
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||
|
|
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||
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||
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||
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||
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|
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||
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||
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||
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||
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||
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||
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||
|
|
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||
|
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||
|
|
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||
|
|
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||
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|
},
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||
|
|
{
|
||
|
|
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|
||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
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|
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||
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|
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|
||
|
|
"answer_preview": "-7",
|
||
|
|
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|
||
|
|
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||
|
|
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||
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||
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||
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|
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||
|
|
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||
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|
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|
||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
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|
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||
|
|
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||
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|
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||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
|
|
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|
||
|
|
},
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||
|
|
{
|
||
|
|
"sample_id": 9282,
|
||
|
|
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|
||
|
|
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|
||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
|
|
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|
||
|
|
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||
|
|
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||
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|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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||
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|
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||
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||
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||
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|
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||
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||
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|
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||
|
|
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||
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|
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||
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||
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|
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||
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|
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||
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||
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|
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||
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|
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||
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||
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|
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||
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||
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|
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||
|
|
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||
|
|
},
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||
|
|
{
|
||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
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|
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||
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|
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||
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|
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||
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|
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||
|
|
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||
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|
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||
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|
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|
||
|
|
"answer_preview": "-84",
|
||
|
|
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||
|
|
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||
|
|
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|
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|
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|
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||
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|
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||
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|
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||
|
|
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||
|
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||
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||
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|
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||
|
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||
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|
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||
|
|
{
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||
|
|
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||
|
|
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||
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|
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||
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|
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||
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|
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||
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|
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||
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|
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||
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||
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||
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||
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||
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||
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||
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|
"answer_preview": "1",
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||
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||
|
|
"answer_preview": "-10",
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||
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||
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||
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{
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||
|
|
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||
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||
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||
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||
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||
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||
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|
||
|
|
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||
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|
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||
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||
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||
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||
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||
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||
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|
||
|
|
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||
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|
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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"prompt_preview": "Given $a=(-1,3)$, $b=(1,t)$, if $(a-2b) \\perp a$, then the real number $t=$ ?",
|
||
|
|
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||
|
|
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||
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||
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{
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||
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|
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||
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|
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||
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||
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{
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||
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"prompt_preview": "Rahul can complete a work in 5 days, and Meena can complete the same work in some days. When they work together, they can complete the work in 3.333333333333333 days. In how many days can Meena complete the work alone?",
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||
|
|
"answer_preview": "10",
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||
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|
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||
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||
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||
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||
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"prompt_preview": "Let $(a_1, b_1),$ $(a_2, b_2),$ $\\dots,$ $(a_n, b_n)$ be the real solutions to \\begin{align*} a + \\frac{17a + 6b}{a^2 + b^2} &= 6, \\\\ b + \\frac{6a - 17b}{a^2 + b^2} &= 0. \\end{align*}Find $a_1 + b_1 + a_2 + b_2 + \\dots + a_n + b_n.$ Hint: ",
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||
|
|
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||
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||
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||
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"answer_preview": "1006",
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{
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||
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|
||
|
|
"answer_preview": "10",
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||
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|
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||
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{
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||
|
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||
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||
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||
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||
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||
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|
||
|
|
"answer_preview": "42",
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||
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|
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||
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||
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||
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||
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{
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||
|
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||
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||
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||
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||
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||
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||
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|
||
|
|
"answer_preview": "9072083",
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||
|
|
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||
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||
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||
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||
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||
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||
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||
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||
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|
||
|
|
"answer_preview": "20",
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||
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|
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||
|
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||
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||
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||
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||
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||
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||
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||
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"prompt_preview": "Given the function \\(f(x)=\\sin ^{4} \\frac{k x}{10}+\\cos ^{4} \\frac{k x}{10}\\), where \\(k\\) is a positive integer, if for any real number \\(a\\), it holds that \\(\\{f(x) \\mid a<x<a+1\\}=\\{f(x) \\mid x \\in \\mathbb{R}\\}\\), find the minimum value o",
|
||
|
|
"answer_preview": "16",
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||
|
|
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|
"previous_priority_score": 0.7600964307785034,
|
||
|
|
"previous_sampling_probability": 2.2486257876153104e-05,
|
||
|
|
"global_step": 994,
|
||
|
|
"feedback_mode": "best_reward",
|
||
|
|
"occurrences": 1,
|
||
|
|
"raw_rows": 32,
|
||
|
|
"valid_rows": 32,
|
||
|
|
"priority_error": 0.0024999999999999988,
|
||
|
|
"mean_completion_error": 0.015937500000000004,
|
||
|
|
"mean_confidence": 0.5656250000000003,
|
||
|
|
"mean_correctness": 0.4375,
|
||
|
|
"selected_reward": 1.495008945465088,
|
||
|
|
"selected_confidence": 0.9,
|
||
|
|
"selected_correctness": 1.0,
|
||
|
|
"selected_overconfidence_error": 0.0,
|
||
|
|
"selected_underconfidence_error": 0.009999999999999995,
|
||
|
|
"sample_count": 7,
|
||
|
|
"error_ema": 0.006501176860183477,
|
||
|
|
"priority_score": 0.7112438678741455,
|
||
|
|
"sampling_probability": 2.1476864276337437e-05,
|
||
|
|
"probability_ratio_vs_uniform": 0.6443059282901231
|
||
|
|
}
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"sample_id": 17912,
|
||
|
|
"sample_count": 7,
|
||
|
|
"error_ema": 0.0011402327800169587,
|
||
|
|
"novelty_component": 0.7071067690849304,
|
||
|
|
"risk_component": 0.0007256026729010046,
|
||
|
|
"count_shrinkage_multiplier": 0.6363636255264282,
|
||
|
|
"priority_score": 0.707832396030426,
|
||
|
|
"sampling_probability": 2.1480265786522068e-05,
|
||
|
|
"probability_ratio_vs_uniform": 0.644407973595662,
|
||
|
|
"seen": 1,
|
||
|
|
"prompt_preview": "Find the number of sets A that satisfy the condition {0, 1} \u222a A = {0, 1}. Express your answer as a whole number.",
|
||
|
|
"answer_preview": "4",
|
||
|
|
"source": "big_math",
|
||
|
|
"last_feedback": {
|
||
|
|
"previous_sample_count": 6,
|
||
|
|
"previous_error_ema": 0.0009891475783661008,
|
||
|
|
"previous_priority_score": 0.7565224766731262,
|
||
|
|
"previous_sampling_probability": 2.1218402252998203e-05,
|
||
|
|
"global_step": 696,
|
||
|
|
"feedback_mode": "best_reward",
|
||
|
|
"occurrences": 1,
|
||
|
|
"raw_rows": 32,
|
||
|
|
"valid_rows": 32,
|
||
|
|
"priority_error": 0.0024999999999999988,
|
||
|
|
"mean_completion_error": 0.002500000000000001,
|
||
|
|
"mean_confidence": 0.8999999999999995,
|
||
|
|
"mean_correctness": 1.0,
|
||
|
|
"selected_reward": 1.495008945465088,
|
||
|
|
"selected_confidence": 0.9,
|
||
|
|
"selected_correctness": 1.0,
|
||
|
|
"selected_overconfidence_error": 0.0,
|
||
|
|
"selected_underconfidence_error": 0.009999999999999995,
|
||
|
|
"sample_count": 7,
|
||
|
|
"error_ema": 0.0011402327800169587,
|
||
|
|
"priority_score": 0.707832396030426,
|
||
|
|
"sampling_probability": 2.0441428205231205e-05,
|
||
|
|
"probability_ratio_vs_uniform": 0.6132428461569361
|
||
|
|
}
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"sample_id": 17998,
|
||
|
|
"sample_count": 7,
|
||
|
|
"error_ema": 0.0011713975109159946,
|
||
|
|
"novelty_component": 0.7071067690849304,
|
||
|
|
"risk_component": 0.0007454347796738148,
|
||
|
|
"count_shrinkage_multiplier": 0.6363636255264282,
|
||
|
|
"priority_score": 0.7078521847724915,
|
||
|
|
"sampling_probability": 2.1480680516106077e-05,
|
||
|
|
"probability_ratio_vs_uniform": 0.6444204154831823,
|
||
|
|
"seen": 1,
|
||
|
|
"prompt_preview": "He wanted to make sure that he is protected from the cold evenings in the forest so he decided to build a fireplace made of cement. If he bought 215 lbs of cement and his son brought another 137 lbs, how much cement did he have originally i",
|
||
|
|
"answer_preview": "98",
|
||
|
|
"source": "orca_math",
|
||
|
|
"last_feedback": {
|
||
|
|
"previous_sample_count": 6,
|
||
|
|
"previous_error_ema": 0.001023775083012879,
|
||
|
|
"previous_priority_score": 0.7565432786941528,
|
||
|
|
"previous_sampling_probability": 2.2440803149947897e-05,
|
||
|
|
"global_step": 1001,
|
||
|
|
"feedback_mode": "best_reward",
|
||
|
|
"occurrences": 1,
|
||
|
|
"raw_rows": 32,
|
||
|
|
"valid_rows": 32,
|
||
|
|
"priority_error": 0.0024999999999999988,
|
||
|
|
"mean_completion_error": 0.0032031250000000007,
|
||
|
|
"mean_confidence": 0.8906249999999996,
|
||
|
|
"mean_correctness": 1.0,
|
||
|
|
"selected_reward": 1.495008945465088,
|
||
|
|
"selected_confidence": 0.9,
|
||
|
|
"selected_correctness": 1.0,
|
||
|
|
"selected_overconfidence_error": 0.0,
|
||
|
|
"selected_underconfidence_error": 0.009999999999999995,
|
||
|
|
"sample_count": 7,
|
||
|
|
"error_ema": 0.0011713975109159946,
|
||
|
|
"priority_score": 0.7078521847724915,
|
||
|
|
"sampling_probability": 2.142495577572845e-05,
|
||
|
|
"probability_ratio_vs_uniform": 0.6427486732718535
|
||
|
|
}
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"sample_id": 18156,
|
||
|
|
"sample_count": 7,
|
||
|
|
"error_ema": 0.0017028384609147906,
|
||
|
|
"novelty_component": 0.7071067690849304,
|
||
|
|
"risk_component": 0.0010836244327947497,
|
||
|
|
"count_shrinkage_multiplier": 0.6363636255264282,
|
||
|
|
"priority_score": 0.708190381526947,
|
||
|
|
"sampling_probability": 2.1487790945684537e-05,
|
||
|
|
"probability_ratio_vs_uniform": 0.6446337283705361,
|
||
|
|
"seen": 1,
|
||
|
|
"prompt_preview": "If the perimeter of a rectangle is 6, and its area is 1, and two squares are constructed with the sides of the rectangle as their sides, then find the sum of the areas of these two squares. Express your answer as a whole number.",
|
||
|
|
"answer_preview": "7",
|
||
|
|
"source": "big_math",
|
||
|
|
"last_feedback": {
|
||
|
|
"previous_sample_count": 6,
|
||
|
|
"previous_error_ema": 0.0016142649110406637,
|
||
|
|
"previous_priority_score": 0.7568975687026978,
|
||
|
|
"previous_sampling_probability": 2.2457470549852587e-05,
|
||
|
|
"global_step": 1005,
|
||
|
|
"feedback_mode": "best_reward",
|
||
|
|
"occurrences": 1,
|
||
|
|
"raw_rows": 32,
|
||
|
|
"valid_rows": 32,
|
||
|
|
"priority_error": 0.0024999999999999988,
|
||
|
|
"mean_completion_error": 0.002500000000000001,
|
||
|
|
"mean_confidence": 0.8999999999999995,
|
||
|
|
"mean_correctness": 1.0,
|
||
|
|
"selected_reward": 1.495008945465088,
|
||
|
|
"selected_confidence": 0.9,
|
||
|
|
"selected_correctness": 1.0,
|
||
|
|
"selected_overconfidence_error": 0.0,
|
||
|
|
"selected_underconfidence_error": 0.009999999999999995,
|
||
|
|
"sample_count": 7,
|
||
|
|
"error_ema": 0.0017028384609147906,
|
||
|
|
"priority_score": 0.708190381526947,
|
||
|
|
"sampling_probability": 2.1440153432195075e-05,
|
||
|
|
"probability_ratio_vs_uniform": 0.6432046029658522
|
||
|
|
}
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"sample_id": 18158,
|
||
|
|
"sample_count": 7,
|
||
|
|
"error_ema": 0.0026377809699624777,
|
||
|
|
"novelty_component": 0.7071067690849304,
|
||
|
|
"risk_component": 0.0016785878688097,
|
||
|
|
"count_shrinkage_multiplier": 0.6363636255264282,
|
||
|
|
"priority_score": 0.708785355091095,
|
||
|
|
"sampling_probability": 2.1500305592780933e-05,
|
||
|
|
"probability_ratio_vs_uniform": 0.645009167783428,
|
||
|
|
"seen": 1,
|
||
|
|
"prompt_preview": "Find the number of different values of the expression $C_{10}^{r+1} + C_{10}^{17-r}$, where $r$ is a positive integer satisfying the system of inequalities: $$ \\begin{cases} 0 \\leq r+1 \\leq 10 \\\\ 0 \\leq 17-r \\leq 10 \\end{cases} $$ Express y",
|
||
|
|
"answer_preview": "2",
|
||
|
|
"source": "big_math",
|
||
|
|
"last_feedback": {
|
||
|
|
"previous_sample_count": 6,
|
||
|
|
"previous_error_ema": 0.002653090050444007,
|
||
|
|
"previous_priority_score": 0.757520854473114,
|
||
|
|
"previous_sampling_probability": 2.2464619178208522e-05,
|
||
|
|
"global_step": 1008,
|
||
|
|
"feedback_mode": "best_reward",
|
||
|
|
"occurrences": 1,
|
||
|
|
"raw_rows": 32,
|
||
|
|
"valid_rows": 31,
|
||
|
|
"priority_error": 0.0024999999999999988,
|
||
|
|
"mean_completion_error": 0.0026612903225806455,
|
||
|
|
"mean_confidence": 0.8838709677419351,
|
||
|
|
"mean_correctness": 0.967741935483871,
|
||
|
|
"selected_reward": 1.495008945465088,
|
||
|
|
"selected_confidence": 0.9,
|
||
|
|
"selected_correctness": 1.0,
|
||
|
|
"selected_overconfidence_error": 0.0,
|
||
|
|
"selected_underconfidence_error": 0.009999999999999995,
|
||
|
|
"sample_count": 7,
|
||
|
|
"error_ema": 0.0026377809699624777,
|
||
|
|
"priority_score": 0.708785355091095,
|
||
|
|
"sampling_probability": 2.143671918020118e-05,
|
||
|
|
"probability_ratio_vs_uniform": 0.6431015754060354
|
||
|
|
}
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"sample_id": 18367,
|
||
|
|
"sample_count": 7,
|
||
|
|
"error_ema": 0.0017028384609147906,
|
||
|
|
"novelty_component": 0.7071067690849304,
|
||
|
|
"risk_component": 0.0010836244327947497,
|
||
|
|
"count_shrinkage_multiplier": 0.6363636255264282,
|
||
|
|
"priority_score": 0.708190381526947,
|
||
|
|
"sampling_probability": 2.1487790945684537e-05,
|
||
|
|
"probability_ratio_vs_uniform": 0.6446337283705361,
|
||
|
|
"seen": 1,
|
||
|
|
"prompt_preview": "The total weight of 9 apples of the same weight is 4.5 kilograms (kg). Several melons weighing 850 grams (g) and two apples were placed on one side of the pan balance scale, and five watermelons weighing 1050 grams (g) were placed on the ot",
|
||
|
|
"answer_preview": "5",
|
||
|
|
"source": "orca_math",
|
||
|
|
"last_feedback": {
|
||
|
|
"previous_sample_count": 6,
|
||
|
|
"previous_error_ema": 0.0016142649110406637,
|
||
|
|
"previous_priority_score": 0.7568975687026978,
|
||
|
|
"previous_sampling_probability": 2.2532540242536925e-05,
|
||
|
|
"global_step": 1035,
|
||
|
|
"feedback_mode": "best_reward",
|
||
|
|
"occurrences": 1,
|
||
|
|
"raw_rows": 32,
|
||
|
|
"valid_rows": 32,
|
||
|
|
"priority_error": 0.0024999999999999988,
|
||
|
|
"mean_completion_error": 0.0027343750000000007,
|
||
|
|
"mean_confidence": 0.8968749999999995,
|
||
|
|
"mean_correctness": 1.0,
|
||
|
|
"selected_reward": 1.495008945465088,
|
||
|
|
"selected_confidence": 0.9,
|
||
|
|
"selected_correctness": 1.0,
|
||
|
|
"selected_overconfidence_error": 0.0,
|
||
|
|
"selected_underconfidence_error": 0.009999999999999995,
|
||
|
|
"sample_count": 7,
|
||
|
|
"error_ema": 0.0017028384609147906,
|
||
|
|
"priority_score": 0.708190381526947,
|
||
|
|
"sampling_probability": 2.1487790945684537e-05,
|
||
|
|
"probability_ratio_vs_uniform": 0.6446337283705361
|
||
|
|
}
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"sample_id": 18674,
|
||
|
|
"sample_count": 7,
|
||
|
|
"error_ema": 0.002653090050444007,
|
||
|
|
"novelty_component": 0.7071067690849304,
|
||
|
|
"risk_component": 0.0016883299686014652,
|
||
|
|
"count_shrinkage_multiplier": 0.6363636255264282,
|
||
|
|
"priority_score": 0.7087950706481934,
|
||
|
|
"sampling_probability": 2.150050931959413e-05,
|
||
|
|
"probability_ratio_vs_uniform": 0.6450152795878239,
|
||
|
|
"seen": 1,
|
||
|
|
"prompt_preview": "Find the minimum value of the function $f(x) = -x^2 + 4x + 5$ within the closed interval $[1, 4]$. Express your answer as a single number.",
|
||
|
|
"answer_preview": "5",
|
||
|
|
"source": "big_math",
|
||
|
|
"last_feedback": {
|
||
|
|
"previous_sample_count": 6,
|
||
|
|
"previous_error_ema": 0.0026701001916080713,
|
||
|
|
"previous_priority_score": 0.7575310468673706,
|
||
|
|
"previous_sampling_probability": 2.04920579562895e-05,
|
||
|
|
"global_step": 580,
|
||
|
|
"feedback_mode": "best_reward",
|
||
|
|
"occurrences": 1,
|
||
|
|
"raw_rows": 32,
|
||
|
|
"valid_rows": 32,
|
||
|
|
"priority_error": 0.0024999999999999988,
|
||
|
|
"mean_completion_error": 0.002500000000000001,
|
||
|
|
"mean_confidence": 0.8999999999999995,
|
||
|
|
"mean_correctness": 1.0,
|
||
|
|
"selected_reward": 1.495008945465088,
|
||
|
|
"selected_confidence": 0.9,
|
||
|
|
"selected_correctness": 1.0,
|
||
|
|
"selected_overconfidence_error": 0.0,
|
||
|
|
"selected_underconfidence_error": 0.009999999999999995,
|
||
|
|
"sample_count": 7,
|
||
|
|
"error_ema": 0.002653090050444007,
|
||
|
|
"priority_score": 0.7087950706481934,
|
||
|
|
"sampling_probability": 1.9785908079938963e-05,
|
||
|
|
"probability_ratio_vs_uniform": 0.5935772423981689
|
||
|
|
}
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"sample_id": 18855,
|
||
|
|
"sample_count": 7,
|
||
|
|
"error_ema": 0.003797437297180295,
|
||
|
|
"novelty_component": 0.7071067690849304,
|
||
|
|
"risk_component": 0.0024165508802980185,
|
||
|
|
"count_shrinkage_multiplier": 0.6363636255264282,
|
||
|
|
"priority_score": 0.7095233201980591,
|
||
|
|
"sampling_probability": 2.1515836124308407e-05,
|
||
|
|
"probability_ratio_vs_uniform": 0.6454750837292522,
|
||
|
|
"seen": 1,
|
||
|
|
"prompt_preview": "Distribute 100 apples among several children, with each child receiving at least one apple and each child receiving a different number of apples. What is the maximum number of children that can receive apples? Express your answer as a whole",
|
||
|
|
"answer_preview": "13",
|
||
|
|
"source": "big_math",
|
||
|
|
"last_feedback": {
|
||
|
|
"previous_sample_count": 6,
|
||
|
|
"previous_error_ema": 0.0039415969513356686,
|
||
|
|
"previous_priority_score": 0.7582939267158508,
|
||
|
|
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|
||
|
|
"global_step": 838,
|
||
|
|
"feedback_mode": "best_reward",
|
||
|
|
"occurrences": 1,
|
||
|
|
"raw_rows": 32,
|
||
|
|
"valid_rows": 32,
|
||
|
|
"priority_error": 0.0024999999999999988,
|
||
|
|
"mean_completion_error": 0.017265625000000003,
|
||
|
|
"mean_confidence": 0.7531250000000003,
|
||
|
|
"mean_correctness": 1.0,
|
||
|
|
"selected_reward": 1.495008945465088,
|
||
|
|
"selected_confidence": 0.9,
|
||
|
|
"selected_correctness": 1.0,
|
||
|
|
"selected_overconfidence_error": 0.0,
|
||
|
|
"selected_underconfidence_error": 0.009999999999999995,
|
||
|
|
"sample_count": 7,
|
||
|
|
"error_ema": 0.003797437297180295,
|
||
|
|
"priority_score": 0.7095233201980591,
|
||
|
|
"sampling_probability": 2.1028494302299805e-05,
|
||
|
|
"probability_ratio_vs_uniform": 0.6308548290689941
|
||
|
|
}
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"sample_id": 18869,
|
||
|
|
"sample_count": 7,
|
||
|
|
"error_ema": 0.0010696251410990953,
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|
||
|
|
"answer_preview": "7425",
|
||
|
|
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||
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||
|
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||
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||
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||
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|
||
|
|
"answer_preview": "0.1",
|
||
|
|
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|
||
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||
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||
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||
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||
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||
|
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||
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||
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||
|
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||
|
|
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||
|
|
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||
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|
},
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||
|
|
{
|
||
|
|
"sample_id": 20133,
|
||
|
|
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|
||
|
|
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|
||
|
|
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||
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||
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||
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||
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||
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|
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||
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|
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||
|
|
"prompt_preview": "Tim spends 1 hour a day meditating and twice as much time reading. He also spends half the time he meditates exercising and one-third of his reading time practicing a musical instrument. How much time a week does he spend on all these activ",
|
||
|
|
"answer_preview": "29.17",
|
||
|
|
"source": "orca_math",
|
||
|
|
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|
||
|
|
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||
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||
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|
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||
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|
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||
|
|
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||
|
|
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|
||
|
|
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||
|
|
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||
|
|
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||
|
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||
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||
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||
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||
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||
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|
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||
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||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
|
|
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|
||
|
|
},
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||
|
|
{
|
||
|
|
"sample_id": 20179,
|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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||
|
|
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||
|
|
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||
|
|
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|
||
|
|
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|
||
|
|
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||
|
|
"prompt_preview": "Given that the coefficient of the $x^3$ term in the expansion of $((ax-1)^{5})$ is $80$, find the coefficient of the $x^2$ term in the expansion.",
|
||
|
|
"answer_preview": "-40",
|
||
|
|
"source": "cn_k12",
|
||
|
|
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|
||
|
|
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||
|
|
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||
|
|
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||
|
|
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|
||
|
|
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||
|
|
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|
||
|
|
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|
||
|
|
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||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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||
|
|
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|
||
|
|
},
|
||
|
|
{
|
||
|
|
"sample_id": 20258,
|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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||
|
|
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||
|
|
"prompt_preview": "Southton buries their time capsule some feet underground. Northton buries their time capsule 12 feet higher than 4 times the depth of the Southton time capsule. Northton's time capsule is buried 48 feet deep. How deep is Southton's time cap",
|
||
|
|
"answer_preview": "9",
|
||
|
|
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|
||
|
|
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|
||
|
|
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||
|
|
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||
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|
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||
|
|
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||
|
|
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||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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||
|
|
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|
||
|
|
},
|
||
|
|
{
|
||
|
|
"sample_id": 20316,
|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
"prompt_preview": "A certain unit has a total of 600 employees, of whom 250 are young employees, 200 are middle-aged employees, and 150 are elderly employees. A stratified sampling method is used to select a sample, and the sample contains 5 young employees. ",
|
||
|
|
"answer_preview": "12",
|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
},
|
||
|
|
{
|
||
|
|
"sample_id": 20800,
|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
"prompt_preview": "Two trains, each a certain length, moving in opposite directions, cross each other in 20 sec. If one is moving twice as fast as the other, and the speed of the faster train is 24 m/s, what is the length of each train?",
|
||
|
|
"answer_preview": "360",
|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
}
|
||
|
|
},
|
||
|
|
{
|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
"prompt_preview": "There are a total of 9 seats in a row. Three people, A, B, and C, are to be seated in such a way that each person has empty seats on both sides, and A must be seated between B and C. How many different seating arrangements are there? (Answe",
|
||
|
|
"answer_preview": "20",
|
||
|
|
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|
||
|
|
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||
|
|
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|
||
|
|
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|
||
|
|
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||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
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||
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||
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"answer_preview": "198",
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"answer_preview": "50",
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||
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"source": "big_math",
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"prompt_preview": "Let \\(d\\) and \\(f\\) be positive integers and \\(a_{1} = 0.9\\). If \\(a_{i+1} = a_{i}^{2}\\) and \\(\\prod_{i=1}^{4} a_{i} = \\frac{3^{d}}{f}\\), determine the smallest possible value of \\(d\\).",
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"answer_preview": "30",
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"source": "olympiads",
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"prompt_preview": "At a monthly meeting, 3/5 of the attendees were males and 7/8 of the male attendees arrived on time. Some fraction of the female attendees arrived on time, and 0.115 fraction of the attendees did not arrive on time. What fraction of the fem",
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|
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"answer_preview": "0.9",
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"prompt_preview": "During the holiday, a school organizes a trip for 360 teachers and students. A bus rental company offers two types of buses for hire: Type A buses have 40 seats each and a rental fee of 400 yuan; Type B buses have 50 seats each and a rental",
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"answer_preview": "3520",
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"prompt_preview": "What is the value of y in the expression ( ( 2 ^ 5 ) * ( y ) ) / ( ( 8 ^ 2 ) * ( 3 ^ 5 ) ) if the result is 0.16666666666666666?",
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"answer_preview": "81",
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"answer_preview": "141",
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"prompt_preview": "The greatest number that divides 178340 and 253785 leaving remainders 20 and 35 respectively, and also divides 375690 leaving a remainder of 50 is:",
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"answer_preview": "8",
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"prompt_preview": "Suppose that $x, y$, and $z$ are non-negative real numbers such that $x+y+z=1$. What is the maximum possible value of $x+y^{2}+z^{3}$ ?",
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"answer_preview": "1",
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"source": "omnimath",
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"prompt_preview": "A driver goes on a trip of 70 kilometers, the first 35 kilometers at a certain speed and the remaining distance at 24 kilometers per hour. The average speed of the entire trip in kilometers per hour is 32. What is the speed of the first par",
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"answer_preview": "48",
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"source": "orca_math",
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"prompt_preview": "Jackson buys a computer game for $66 and three movie tickets for $12 each. How much did he spend on entertainment total?",
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"answer_preview": "102",
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"source": "openmath",
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"sample_id": 828,
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"prompt_preview": "There are 11 males & 12 females in the orchestra and twice that number in the band. There are 12 males & some females in the choir. There are 98 musicians total in the orchestra, the band, and the choir. How many females are there in the ch",
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|
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"answer_preview": "17",
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"source": "orca_math",
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"prompt_preview": "Convex quadrilateral $A B C D$ has right angles $\\angle A$ and $\\angle C$ and is such that $A B=B C$ and $A D=C D$. The diagonals $A C$ and $B D$ intersect at point $M$. Points $P$ and $Q$ lie on the circumcircle of triangle $A M B$ and seg",
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"answer_preview": "36",
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"source": "omnimath",
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"sample_id": 946,
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"probability_ratio_vs_uniform": 2.281994093209505,
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"prompt_preview": "In an arithmetic sequence $\\{a_n\\}$ where each term is a positive number, it is given that $3a_6 - a_7^2 + 3a_8 = 0$. Find the value of $a_7$. Express your answer as a single number.",
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"answer_preview": "6",
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|
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"source": "big_math",
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"sample_id": 976,
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"probability_ratio_vs_uniform": 2.281994093209505,
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"prompt_preview": "Given the expression \\(2 - 0 - 1 - 9\\), find the largest possible value that can be obtained by inserting exactly one pair of brackets into the expression. Provide your answer as a single integer.",
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|
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"answer_preview": "10",
|
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|
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"source": "big_math",
|
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"last_feedback": null
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"sample_id": 979,
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"prompt_preview": "Determine the least possible value of the natural number $n$ such that $n!$ ends in exactly $1987$ zeros. <details><summary>Note</summary>Note. Here (and generally in MathLinks) natural numbers supposed to be positive.</details>",
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|
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"answer_preview": "7960",
|
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"source": "aops_forum",
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},
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{
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"sample_id": 1014,
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"prompt_preview": "It takes 1 hour for refrigerated dough to come to room temperature, 15 minutes to shape the dough, 2 hours to proof, and 30 minutes to bake. The head baker needs a certain amount of time for the bread to cool. If the bakery opens at 6:00 am",
|
||
|
|
"answer_preview": "15",
|
||
|
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"source": "orca_math",
|
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|
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"last_feedback": null
|
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|
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},
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{
|
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|
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"sample_id": 1114,
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|
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"sampling_probability": 7.606646977365017e-05,
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|
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"probability_ratio_vs_uniform": 2.281994093209505,
|
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|
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"seen": 0,
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|
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"prompt_preview": "In triangle PQR, the angle Q = 90 degrees, PQ = 2 cm, QR = 8 cm. X is a variable point on PQ. The line through X parallel to QR intersects PR at Y, and the line through Y parallel to PQ intersects QR at Z. What is the least possible length ",
|
||
|
|
"answer_preview": "2",
|
||
|
|
"source": "orca_math",
|
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|
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"last_feedback": null
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},
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{
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|
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"sample_id": 1121,
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"probability_ratio_vs_uniform": 2.281994093209505,
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"seen": 0,
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|
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"prompt_preview": "There is food for 760 men for 22 days. After two days, 2280 more men join. How many additional days does the same food last after the new men join?",
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|
|
"answer_preview": "5",
|
||
|
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"source": "orca_math",
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|
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"last_feedback": null
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},
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"prompt_preview": "A group of ten people went to the cinema. They received tickets for 5 adjacent seats in two different rows. \u00c1bel and Bendeg\u00faz want to sit next to each other, while Zsuzsi and Anik\u00f3 want to sit separately. In how many ways can they be seated",
|
||
|
|
"answer_preview": "518400",
|
||
|
|
"source": "olympiads",
|
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|
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"prompt_preview": "If the focus of the parabola $y^{2}=2px$ coincides with the right focus of the hyperbola $\\frac{x^{2}}{6}-\\frac{y^{2}}{3}=1$, then the value of $p$ is $\\boxed{6}$.",
|
||
|
|
"answer_preview": "6",
|
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|
|
"source": "cn_k12",
|
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|
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"prompt_preview": "Given the function f(x) = x^2 - 3x, calculate the limit of [f(2) - f(2-3t)]/t as t approaches 0. Express your answer as a single number.",
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|
|
"answer_preview": "3",
|
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|
|
"source": "big_math",
|
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|
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"prompt_preview": "A cuckoo clock chimes \"cuckoo\" as many times as the hour indicated by the hour hand (e.g., at 19:00, it chimes 7 times). One morning, Maxim approached the clock at 9:05 and started turning the minute hand until the clock advanced by 7 hours",
|
||
|
|
"answer_preview": "43",
|
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|
|
"source": "olympiads",
|
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|
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|
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},
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|
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"seen": 0,
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"prompt_preview": "Yvette wants to frame a new picture. When she goes to her local frame shop, she finds out that the frame she wanted is 20% more expensive than her budget of $60. If she paid for a smaller frame at 3/4 the new price of the frame she initiall",
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||
|
|
"answer_preview": "6",
|
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|
|
"source": "openmath",
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|
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|
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"prompt_preview": "Given a moving circle with its center C on the parabola $x^2=2py$ ($p>0$), the circle passes through point A $(0, p)$, and intersects the x-axis at two points M and N, the maximum value of $\\sin\\angle MCN$ is \\_\\_\\_\\_\\_\\_.",
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|
|
"answer_preview": "1",
|
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|
|
"source": "cn_k12",
|
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|
|
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|
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},
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|
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"sample_id": 1429,
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|
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|
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"seen": 0,
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|
|
"prompt_preview": "90 students represent x percent of the boys at Jones Elementary School. The boys at Jones Elementary make up 30% of the total school population of x students. What is the value of x?",
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||
|
|
"answer_preview": "300",
|
||
|
|
"source": "orca_math",
|
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|
|
"last_feedback": null
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|
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},
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{
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|
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"sample_id": 1612,
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|
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|
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"probability_ratio_vs_uniform": 2.281994093209505,
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|
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"seen": 0,
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|
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"prompt_preview": "In a $5 \\times 5$ square, some cells have been painted black as shown in the figure. Consider all possible smaller squares within this grid whose sides align with the grid lines. In how many of these smaller squares is the number of black c",
|
||
|
|
"answer_preview": "16",
|
||
|
|
"source": "olympiads",
|
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|
|
"last_feedback": null
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|
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},
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|
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"sample_id": 1629,
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|
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"probability_ratio_vs_uniform": 2.281994093209505,
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|
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"seen": 0,
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|
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"prompt_preview": "A certain item is priced at $1.5$ times its cost price, and after a discount of $20$ yuan, it is sold with a profit of $40\\%$. Find the cost price of each item.",
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|
|
"answer_preview": "200",
|
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|
|
"source": "cn_k12",
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|
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|
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"sample_id": 1741,
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"sample_count": 0,
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"prompt_preview": "Teena is driving at 55 miles per hour and is currently 7.5 miles behind Poe, who is driving at a certain speed in the same direction. In 90 minutes, Teena will be 15 miles ahead of Poe. What is Poe's speed in miles per hour?",
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||
|
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"answer_preview": "40",
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|
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"source": "orca_math",
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"sample_id": 1841,
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"probability_ratio_vs_uniform": 2.281994093209505,
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"prompt_preview": "In the Cartesian coordinate system, for the ellipse C: $$\\frac {x^{2}}{25} + \\frac {y^{2}}{9} = 1$$, the left and right foci are denoted as F<sub>1</sub> and F<sub>2</sub>, respectively. Let P be a point on the ellipse C such that line segm",
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"answer_preview": "9",
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|
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"source": "cn_k12",
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{
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"sample_id": 1902,
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"risk_component": 0.0,
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"priority_score": 2.0,
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"sampling_probability": 7.606646977365017e-05,
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"probability_ratio_vs_uniform": 2.281994093209505,
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"prompt_preview": "Caleb visited a rectangular park which also had 3 rectangular shaped flower beds inside it. He noted down the number of 90 \\degree angles he could find from the layout. Then he went to a square-shaped football field which had 4 square-shape",
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|
|
"answer_preview": "36",
|
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|
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"source": "orca_math",
|
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|
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"last_feedback": null
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{
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"sample_id": 1903,
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"probability_ratio_vs_uniform": 2.281994093209505,
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"prompt_preview": "How many total days were there in the years 2001 through 2004?",
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||
|
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"answer_preview": "1461",
|
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"source": "math",
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"sample_id": 1919,
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"probability_ratio_vs_uniform": 2.281994093209505,
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"prompt_preview": "Among the following propositions: \u2460 February 14, 2010, is both Chinese New Year and Valentine's Day; \u2461 A multiple of 10 is definitely a multiple of 5; \u2462 A trapezoid is not a rectangle. Count the number of propositions that use logical c",
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|
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"answer_preview": "2",
|
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|
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"source": "big_math",
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},
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{
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"sample_id": 1996,
|
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|
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|
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"sampling_probability": 7.606646977365017e-05,
|
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|
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"probability_ratio_vs_uniform": 2.281994093209505,
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"seen": 0,
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"prompt_preview": "Let $f(x)$ be an odd function defined on $\\mathbb{R}$ with a period of 4. When $-2 \\leq x < 0$, $f(x) = 3x + 1$. Calculate the value of $f(5)$. Express your answer as a single integer.",
|
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|
|
"answer_preview": "2",
|
||
|
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"source": "big_math",
|
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|
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"last_feedback": null
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},
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{
|
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|
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"sample_id": 2009,
|
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|
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|
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"error_ema": 0.0,
|
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|
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|
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|
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"priority_score": 2.0,
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"sampling_probability": 7.606646977365017e-05,
|
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|
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"probability_ratio_vs_uniform": 2.281994093209505,
|
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|
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"seen": 0,
|
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|
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"prompt_preview": "If some men can do a piece of work in 25 hours, then 10 men can do it in 90 hours. How many men were in the first group?",
|
||
|
|
"answer_preview": "36",
|
||
|
|
"source": "orca_math",
|
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|
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"last_feedback": null
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},
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{
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"sample_id": 2040,
|
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|
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"sample_count": 0,
|
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"error_ema": 0.0,
|
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|
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"sampling_probability": 7.606646977365017e-05,
|
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|
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"probability_ratio_vs_uniform": 2.281994093209505,
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|
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"seen": 0,
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"prompt_preview": "Find the smallest positive integer $n$ that satisfies the inequality $\\sqrt{n} - \\sqrt{n-1} < 0.01$. Express your answer as a single integer.",
|
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|
|
"answer_preview": "2501",
|
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|
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"source": "big_math",
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"last_feedback": null
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},
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{
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"sample_id": 2050,
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"sample_count": 0,
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"error_ema": 0.0,
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"probability_ratio_vs_uniform": 2.281994093209505,
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"seen": 0,
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"prompt_preview": "Find the constant term in the expansion of $$( \\sqrt[4]{x}- \\frac {3}{x})^{5}$$.",
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|
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"answer_preview": "-15",
|
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|
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"source": "cn_k12",
|
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|
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"last_feedback": null
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},
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{
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"sample_id": 2081,
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|
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"probability_ratio_vs_uniform": 2.281994093209505,
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"seen": 0,
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"prompt_preview": "Given a geometric sequence with 10 terms, where the product of the odd terms is 2, and the product of the even terms is 64, find the common ratio. Express your answer as a single value.",
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|
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"answer_preview": "2",
|
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|
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"source": "big_math",
|
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"last_feedback": null
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},
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{
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"sample_id": 2084,
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"prompt_preview": "Given that the arithmetic sequence $\\{a\\_n\\}$ is an increasing sequence, if $a\\_1 > 0$ and $2(a\\_n+a_{n+2})=5a_{n+1}$, then the common ratio of the sequence $\\{a\\_n\\}$ is $q=$ _____ .",
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||
|
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"answer_preview": "2",
|
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|
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"source": "cn_k12",
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"last_feedback": null
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{
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"sample_id": 2095,
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"prompt_preview": "To pave a rectangular courtyard 20 m long and 16 1/2 m wide, a certain number of paving stones, each measuring a specific length * 2 m, are required. If 66 paving stones are needed, what is the length of each paving stone?",
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|
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"answer_preview": "2.5",
|
||
|
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"source": "orca_math",
|
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|
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"last_feedback": null
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},
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{
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"sample_id": 2141,
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"sample_count": 0,
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"probability_ratio_vs_uniform": 2.281994093209505,
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"seen": 0,
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"prompt_preview": "A cone has a surface area of $3\\pi$. Its lateral surface unfolds into a semicircle. The diameter of the base of the cone is ______.",
|
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|
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"answer_preview": "2",
|
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|
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"source": "cn_k12",
|
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|
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"last_feedback": null
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},
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{
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"sample_id": 2186,
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"probability_ratio_vs_uniform": 2.281994093209505,
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"seen": 0,
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"prompt_preview": "There are ten horses numbered from 1 to 10. The \\( k \\)-th horse (\\( k = 1, 2, \\cdots, 10 \\)) takes exactly \\( k \\) minutes to run one lap on a circular track. Initially, all horses start at the starting point of the track at the same time,",
|
||
|
|
"answer_preview": "3",
|
||
|
|
"source": "big_math",
|
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|
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"last_feedback": null
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},
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{
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"sample_id": 2187,
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"probability_ratio_vs_uniform": 2.281994093209505,
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"seen": 0,
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"prompt_preview": "Given an arithmetic sequence ${{a_n}}$, let ${S_n}$ denote the sum of its first $n$ terms. If ${a_4 + a_6 + a_8 = 15}$, find the value of ${S_{11}}$. Express your answer as a single number.",
|
||
|
|
"answer_preview": "55",
|
||
|
|
"source": "big_math",
|
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|
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"last_feedback": null
|
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|
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},
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{
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|
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"sample_id": 2236,
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"prompt_preview": "Given that $\\sqrt{102.01}=10.1$, find the value of $\\sqrt{1.0201}$. Express your answer as a decimal number.",
|
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|
|
"answer_preview": "1.01",
|
||
|
|
"source": "big_math",
|
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|
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"last_feedback": null
|
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},
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{
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|
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"sample_id": 2262,
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"probability_ratio_vs_uniform": 2.281994093209505,
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|
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"seen": 0,
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|
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"prompt_preview": "the average of 11 numbers is 22 . average of the first 6 of them is 19 and that of the last 6 is 27 . find the 6 th number ?",
|
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|
|
"answer_preview": "34",
|
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|
|
"source": "orca_math",
|
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|
|
"last_feedback": null
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},
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{
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|
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"sample_id": 2273,
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|
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"probability_ratio_vs_uniform": 2.281994093209505,
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"seen": 0,
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|
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"prompt_preview": "Among the expressions $2x^{2}$, $1-2x=0$, $ab$, $a>0$, $\\frac{1}{a}$, $\\pi$, and $m=\\frac{1}{2}$, how many do not qualify as polynomials? Provide your answer as a single integer.",
|
||
|
|
"answer_preview": "4",
|
||
|
|
"source": "big_math",
|
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|
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"last_feedback": null
|
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|
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},
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{
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|
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"sample_id": 2277,
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|
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"sampling_probability": 7.606646977365017e-05,
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|
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"probability_ratio_vs_uniform": 2.281994093209505,
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|
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"seen": 0,
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|
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"prompt_preview": "A person bought 118 glass bowls at a certain rate per bowl. He sold 102 of them at Rs. 15 and the remaining broke. The percentage gain for him is 8.050847457627118%. What was the rate at which he bought the glass bowls?",
|
||
|
|
"answer_preview": "12",
|
||
|
|
"source": "orca_math",
|
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|
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"last_feedback": null
|
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{
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|
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"sample_id": 2314,
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"probability_ratio_vs_uniform": 2.281994093209505,
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"seen": 0,
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|
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"prompt_preview": "Given $i$ is the imaginary unit, $\\overline{z}$ is the conjugate of $z$, and $(2-i) \\overline{z}=3-4i$, find the imaginary part of $z$. Express your answer as a single number.",
|
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|
|
"answer_preview": "1",
|
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|
|
"source": "big_math",
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"prompt_preview": "Father's age is three times the sum of the ages of his two children. After 5 years his age will be twice the sum of age of two children. Find the age of father.",
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"answer_preview": "45",
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"prompt_preview": "When $x=$______, the value of the algebraic expression $\\frac{1}{x-1}+\\frac{3}{1-{x}^{2}}$ is zero.",
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"answer_preview": "2",
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"prompt_preview": "Given the circle equation $x^{2}+y^{2}+2x-2y-2=0$, find the coordinates of the center and the radius of the circle. Express the center as an ordered pair (x, y) and the radius as a numerical value.",
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"answer_preview": "2",
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"prompt_preview": "Tom bought 10 packages of miniature racing cars. Each package contains five cars. He gave a certain number of nephews 1/5 of the cars. Tom has 30 miniature racing cars left. How many nephews did Tom give cars to?",
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"answer_preview": "5",
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"prompt_preview": "Triassic Discoglossus tadpoles have five legs each, and Sabertooth Frog tadpoles grow several tails (each has the same number). A Jurassic Park employee scooped up a few tadpoles along with some water. It turned out that the captured tadpol",
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"answer_preview": "3",
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"sample_id": 2780,
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"prompt_preview": "There were sweets on the table. Jack came and took half of all the candies and 4 more candies. Then Paul came and took some sweets. There were 22 sweets on the table at first. How many sweets did Paul take?",
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"answer_preview": "7",
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"source": "orca_math",
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"prompt_preview": "On the circle $C:x^2+y^2=4$, there are two points $A(x_1,y_1)$ and $B(x_2,y_2)$. If $|\\vec{AB}|=2\\sqrt{3}$, then $x_1x_2+y_1y_2=$ ?",
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"answer_preview": "-2",
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"prompt_preview": "Find the greatest common divisor of $10! + 2$ and $11! + 8$.",
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"answer_preview": "2",
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"source": "math",
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"prompt_preview": "In the convex quadrilateral \\(ABCD\\), the midpoints of sides \\(BC\\) and \\(CD\\) are \\(E\\) and \\(F\\) respectively. The segments \\(AE\\), \\(EF\\), and \\(AF\\) divide the quadrilateral into four triangles whose areas are four consecutive integers.",
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"answer_preview": "6",
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"source": "olympiads",
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"answer_preview": "72",
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"source": "olympiads",
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"prompt_preview": "Shelly writes down a vector $v=(a, b, c, d)$, where $0<a<b<c<d$ are integers. Let $\\sigma(v)$ denote the set of 24 vectors whose coordinates are $a, b, c$, and $d$ in some order. For instance, $\\sigma(v)$ contains $(b, c, d, a)$. Shelly not",
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"answer_preview": "6",
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"source": "omnimath",
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"prompt_preview": "Given two non-zero vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$ with an angle of $60^{\\circ}$ between them, and satisfying $|\\overrightarrow{a} - 2\\overrightarrow{b}| = 2$, determine the maximum value of $\\overrightarrow{a} \\cdot \\",
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"answer_preview": "1",
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"prompt_preview": "If \\( S = \\frac{1}{1 + 1^{2} + 1^{4}} + \\frac{2}{1 + 2^{2} + 2^{4}} + \\frac{3}{1 + 3^{2} + 3^{4}} + \\ldots + \\frac{200}{1 + 200^{2} + 200^{4}} \\), find the value of \\( 80402 \\times S \\).",
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|
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"answer_preview": "40200",
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"prompt_preview": "If $2^x = 9$, and $\\log_{2} \\frac {8}{3} = y$, then $x + 2y = \\_\\_\\_\\_\\_\\_$.",
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"answer_preview": "6",
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"prompt_preview": "If the integer part of $\\sqrt[3]{a}$ is $2$, then the number of odd numbers $a$ that satisfy this condition is ____.",
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"answer_preview": "9",
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|
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"answer_preview": "160",
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"prompt_preview": "How many parts at most can three planes divide space into?",
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|
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"answer_preview": "8",
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"prompt_preview": "A woman is not good at weaving cloth, and the amount of cloth she weaves decreases by the same amount every day. She weaves 5 feet on the first day and 1 foot on the last day. Calculate the total amount of cloth she weaves in 30 days. Expre",
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|
|
"answer_preview": "90",
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"source": "big_math",
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"seen": 0,
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|
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"prompt_preview": "jenny can divide her sweets equally to 5 people and also to 6 people equally but not to 12 people . what could be the number ?",
|
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|
|
"answer_preview": "90",
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|
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"source": "orca_math",
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"probability_ratio_vs_uniform": 2.281994093209505,
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"prompt_preview": "the ratio of numbers is 4 : 5 and their h . c . f is 4 . their l . c . m is :",
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|
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"answer_preview": "80",
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|
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"source": "orca_math",
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"probability_ratio_vs_uniform": 2.281994093209505,
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"prompt_preview": "The product of 6 consecutive odd numbers greater than zero is 135135. What is the largest of these 6 numbers? $\\qquad$",
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|
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"answer_preview": "13",
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|
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"source": "olympiads",
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"prompt_preview": "Li Jiang's average score for 5 math tests is 90, the median is 91, and the mode is 93. What is the sum of his lowest two test scores?",
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"answer_preview": "173",
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"source": "cn_k12",
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"prompt_preview": "Sylvia chose positive integers \\( a, b \\) and \\( c \\). Peter determined the value of \\( a+\\frac{b}{c} \\) and got an answer of 101. Paul determined the value of \\( \\frac{a}{c}+b \\) and got an answer of 68. Mary determined the value of \\( \\fr",
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"answer_preview": "13",
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"source": "big_math",
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"sample_id": 3822,
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"prompt_preview": "Nicholas bought six times as much fabric as Kenneth. If Kenneth paid $40 for an oz of fabric and bought 700oz, calculate the amount of money that Nicholas paid more than Kenneth for the fabric he bought.",
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"answer_preview": "140000",
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|
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"source": "openmath",
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"prompt_preview": "Two trains of equal length are running on parallel inclined tracks in the same direction. The tracks have a uniform incline of 5 degrees. The trains initially have speeds of 47 km/hr and 36 km/hr while moving uphill. Considering the effects",
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"answer_preview": "55",
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"source": "orca_math",
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"prompt_preview": "In the complex plane, given a complex number $z$ satisfies $|z|=1$, where $i$ is the imaginary unit, then the maximum value of $|z-3-4i|$ is ____.",
|
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|
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"answer_preview": "6",
|
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"source": "cn_k12",
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"last_feedback": null
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{
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"probability_ratio_vs_uniform": 2.281994093209505,
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"prompt_preview": "Lion Alex decided to count the stripes on Marty the zebra (black and white stripes alternate). It turned out that there is one more black stripe than white stripes. Alex also noted that all white stripes are of the same width, while black s",
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|
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"answer_preview": "8",
|
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|
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"source": "olympiads",
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"prompt_preview": "The first term of the arithmetic sequence $\\left\\{ a_n \\right\\}$ is $a_1=-5$, and the sum of its first $11$ terms equals $55$. If one term is removed, leaving the average of the remaining $10$ terms as $4.6$, then the removed term is the $\\",
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|
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"answer_preview": "8",
|
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|
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"source": "cn_k12",
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{
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"sample_id": 4011,
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"prompt_preview": "Cora started reading a 158-page book on Monday, and she decided she wanted to finish it by the end of Friday. She read 23 pages on Monday, 38 pages on Tuesday, and some pages on Wednesday. She knows she will have time to read twice as much ",
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|
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"answer_preview": "61",
|
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|
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"source": "orca_math",
|
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|
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},
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"sample_id": 4039,
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"prompt_preview": "A monkey starts climbing up a tree that is 51 ft tall. Each hour, it hops up 7 ft but slips back 4 ft. How much time would it take the monkey to reach the top?",
|
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|
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"answer_preview": "15",
|
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|
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"source": "orca_math",
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},
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"sample_id": 4040,
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"prompt_preview": "Excluding stoppages, the average speed of a bus is 50 km/hr, and including stoppages, the average speed of the bus is 40 km/hr. For how many minutes does the bus stop per hour?",
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||
|
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"answer_preview": "12",
|
||
|
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"source": "orca_math",
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"prompt_preview": "Given the set A={x|y= $\\sqrt {(x-1)(5-x)}$, x\u2208Z}, calculate the number of elements in set A. Express your answer as a single integer.",
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|
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"answer_preview": "5",
|
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|
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"source": "big_math",
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},
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{
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|
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"prompt_preview": "Given that the measurement result \u03be follows a normal distribution N(1, \u03c3^2) (\u03c3 > 0), and the probability of \u03be falling within the interval (0, 1) is 0.4, calculate the probability of \u03be taking a value within the interval (0, 2). Express your ",
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|
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"answer_preview": "0.8",
|
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|
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"source": "big_math",
|
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|
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"prompt_preview": "Arrange the natural numbers that are divisible by both 5 and 7 in ascending order starting from 105. Take the first 2013 numbers. What is the remainder when the sum of these 2013 numbers is divided by 12?",
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|
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"answer_preview": "3",
|
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|
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"source": "olympiads",
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"prompt_preview": "If the coefficient of $x^{6}$ in the expansion of $(x^{2}-a)(x+ \\frac {1}{x})^{10}$ is $30$, then $\\int _{ 0 }^{ a }(3x^{2}+1)dx=$ \\_\\_\\_\\_\\_\\_.",
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|
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"answer_preview": "10",
|
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"source": "cn_k12",
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"sample_id": 4127,
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"prompt_preview": "If the sum of three real numbers is $0$ and their product is $17$, then what is the sum of their cubes?",
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"answer_preview": "51",
|
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|
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"source": "math",
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{
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"sample_id": 4143,
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"prompt_preview": "Determine the coefficient of $x$ in the binomial expansion of $(2x^{2}- \\frac{1}{x})^{5}$ (Answer with a number)",
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|
|
"answer_preview": "-40",
|
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|
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"source": "cn_k12",
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|
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},
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{
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|
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"sample_id": 4344,
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"probability_ratio_vs_uniform": 2.281994093209505,
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"prompt_preview": "Find the number of monomials that satisfy the following conditions simultaneously: (1) contains the letters x, y, z; (2) coefficient is -3; (3) degree is 5. Express your answer as a whole number.",
|
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|
|
"answer_preview": "6",
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|
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"source": "big_math",
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{
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|
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"sample_id": 4369,
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"probability_ratio_vs_uniform": 2.281994093209505,
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"prompt_preview": "A crow leaves its nest, and flies back and forth from its nest to a nearby ditch to gather worms. The distance between the nest and the ditch is unknown. In one and a half hours, the crow manages to bring worms to its nest 15 times, and its",
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|
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"answer_preview": "200",
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"source": "orca_math",
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"last_feedback": null
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|
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"prompt_preview": "Jones's four cousins have ages that are four different single-digit positive integers. The product of the ages of two of them is 24, and the product of the ages of the other two is 30. What is the sum of the ages of the four cousins? Expres",
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||
|
|
"answer_preview": "22",
|
||
|
|
"source": "big_math",
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|
|
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},
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{
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|
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"sample_id": 4415,
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"prompt_preview": "Find the value of $\\log_{4}\\cos\\frac{\\pi}{5}+\\log_{4}\\cos\\frac{2\\pi}{5}$.",
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||
|
|
"answer_preview": "-1",
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|
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{
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"sample_id": 4517,
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|
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|
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||
|
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"prompt_preview": "The total number of students in Changhyeon's school is 32 fewer than eight times the number of fourth-year students. Of the fourth-year students, there are 10 more students who wear glasses than those who do not wear glasses. If the total n",
|
||
|
|
"answer_preview": "69",
|
||
|
|
"source": "orca_math",
|
||
|
|
"last_feedback": null
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||
|
|
},
|
||
|
|
{
|
||
|
|
"sample_id": 4518,
|
||
|
|
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|
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|
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|
||
|
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|
||
|
|
"risk_component": 0.0,
|
||
|
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"count_shrinkage_multiplier": 0.0,
|
||
|
|
"priority_score": 2.0,
|
||
|
|
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|
||
|
|
"probability_ratio_vs_uniform": 2.281994093209505,
|
||
|
|
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||
|
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"prompt_preview": "The school plans to select 3 students from 5 applicants to serve as volunteers for the track and field, swimming, and ball games at the 2011 World University Games. It is known that student A cannot serve as a volunteer for the swimming com",
|
||
|
|
"answer_preview": "48",
|
||
|
|
"source": "big_math",
|
||
|
|
"last_feedback": null
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||
|
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},
|
||
|
|
{
|
||
|
|
"sample_id": 4600,
|
||
|
|
"sample_count": 0,
|
||
|
|
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|
||
|
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|
||
|
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"risk_component": 0.0,
|
||
|
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|
|
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|
||
|
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|
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|
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"probability_ratio_vs_uniform": 2.281994093209505,
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|
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|
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"prompt_preview": "How many liters of pure hydrochloric acid must be added to a certain amount of solution that is 10% hydrochloric acid to get a solution that is 15% hydrochloric acid, if 3.52941176471 liters of pure hydrochloric acid is added?",
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||
|
|
"answer_preview": "60",
|
||
|
|
"source": "orca_math",
|
||
|
|
"last_feedback": null
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||
|
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},
|
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|
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{
|
||
|
|
"sample_id": 4626,
|
||
|
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|
||
|
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|
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|
||
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|
||
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|
||
|
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|
||
|
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|
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|
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||
|
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|
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"prompt_preview": "Solve for x in the equation: x(x(x+1)+2)+3 = x^3 + x^2 + x - 6. Express your answer as a single integer.",
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||
|
|
"answer_preview": "-9",
|
||
|
|
"source": "big_math",
|
||
|
|
"last_feedback": null
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||
|
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},
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|
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{
|
||
|
|
"sample_id": 4697,
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||
|
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|
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"prompt_preview": "Blind boxes are a new type of product. Merchants package different styles of products from the same series in boxes with the same appearance, so that consumers do not know which style of product they are buying. A merchant has designed thre",
|
||
|
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"answer_preview": "0.216",
|
||
|
|
"source": "cn_k12",
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|
|
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|
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}
|
||
|
|
],
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||
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|
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||
|
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"answer_preview": "3",
|
||
|
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|
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||
|
|
"answer_preview": "4",
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|
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"source": "cn_k12",
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|
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{
|
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|
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"sample_id": 880,
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||
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||
|
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"prompt_preview": "A can finish a work in 9 days and B can do the same work in some days. B worked for 10 days and left the job. A alone can finish the remaining work in 3 days. In how many days can B finish the work?",
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||
|
|
"answer_preview": "10.33",
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||
|
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|
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|
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"prompt_preview": "Given that the function $f(x)$ is an odd function, and when $x < 0$, $f(x) = x^2 + a \\cdot \\cos(\\pi x)$. If $f(1) = 2$, then the real number $a = \\ $.",
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||
|
|
"answer_preview": "-3",
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||
|
|
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|
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|
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||
|
|
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||
|
|
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||
|
|
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|
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||
|
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|
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|
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|
|
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},
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|
|
{
|
||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
|
|
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|
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|
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||
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|
"prompt_preview": "How much time will it take for a man to travel some distance across the floor if he is traveling at 2 m/s and it takes him 39 seconds to complete the journey?",
|
||
|
|
"answer_preview": "78",
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||
|
|
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|
|
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||
|
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|
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|
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|
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||
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"answer_preview": "0795",
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||
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"answer_preview": "23",
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||
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||
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||
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||
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||
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|
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||
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||
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|
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|
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|
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||
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|
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||
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||
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||
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|
"answer_preview": "4",
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||
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||
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||
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||
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"prompt_preview": "Convert the decimal number 365 to an octal number.",
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||
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|
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||
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|
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||
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|
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||
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|
"prompt_preview": "how many pieces of 85 cm length can be cut from a rod of 17 meters long ?",
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||
|
|
"answer_preview": "17",
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||
|
|
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||
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|
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|
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||
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||
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|
||
|
|
"answer_preview": "2",
|
||
|
|
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||
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|
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|
|
{
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||
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|
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||
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||
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||
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||
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||
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|
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||
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||
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||
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||
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|
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||
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|
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||
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|
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|
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|
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|
|
{
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||
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|
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||
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|
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||
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||
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||
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||
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|
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||
|
|
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||
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|
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||
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|
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||
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|
||
|
|
"answer_preview": "2",
|
||
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"prompt_preview": "in 7 given numbers , the average of first 4 numbers is 4 and that of last 4 numbers is also 4 . if the average of these 7 numbers is 3 , the fourth number is ?",
|
||
|
|
"answer_preview": "5.5",
|
||
|
|
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
|
|
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||
|
|
{
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||
|
|
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||
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||
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||
|
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||
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||
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||
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||
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||
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||
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|
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||
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|
"prompt_preview": "One student on a field trip counted some squirrels. Another student counted a third more squirrels than the first student. Both students counted 28 squirrels combined. How many squirrels did the first student count?",
|
||
|
|
"answer_preview": "21",
|
||
|
|
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|
||
|
|
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|
||
|
|
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||
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||
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||
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||
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|
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||
|
|
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||
|
|
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||
|
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||
|
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||
|
|
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||
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||
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||
|
|
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||
|
|
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||
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||
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||
|
|
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||
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|
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||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
|
|
},
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||
|
|
{
|
||
|
|
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|
||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
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||
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||
|
|
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||
|
|
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||
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|
"prompt_preview": "Find the value of 72516 x 9999. What is the product of these two numbers?",
|
||
|
|
"answer_preview": "724987484",
|
||
|
|
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||
|
|
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||
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||
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||
|
|
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||
|
|
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||
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||
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||
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||
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||
|
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||
|
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||
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||
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||
|
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||
|
|
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||
|
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||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
|
|
},
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||
|
|
{
|
||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
|
|
"prompt_preview": "find the value of a from ( 15 ) ^ 2 x 8 ^ 3 \u00e3 \u00b7 256 = a .",
|
||
|
|
"answer_preview": "29491200",
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||
|
|
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||
|
|
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||
|
|
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||
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||
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||
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||
|
|
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||
|
|
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||
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||
|
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||
|
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||
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||
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||
|
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||
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||
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||
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||
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||
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||
|
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||
|
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||
|
|
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||
|
|
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||
|
|
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||
|
|
},
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||
|
|
{
|
||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
|
|
"prompt_preview": "Johny traveled South 40 miles, then turned East and traveled for some more miles than the distance he took to travel to the south. He turned North and traveled twice the distance he had traveled to the East. His total journey took 220 miles",
|
||
|
|
"answer_preview": "40",
|
||
|
|
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||
|
|
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||
|
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||
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|
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||
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||
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|
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||
|
|
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||
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||
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||
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||
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||
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||
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||
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||
|
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||
|
|
},
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||
|
|
{
|
||
|
|
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||
|
|
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||
|
|
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||
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||
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|
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||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
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|
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||
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|
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|
||
|
|
"answer_preview": "2048",
|
||
|
|
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||
|
|
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||
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||
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||
|
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||
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||
|
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||
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|
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||
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||
|
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||
|
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||
|
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||
|
|
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||
|
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||
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||
|
|
{
|
||
|
|
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|
||
|
|
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||
|
|
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|
||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
|
|
"prompt_preview": "A shopkeeper bought 600 oranges and some bananas. He found that 15% of oranges and 8% of bananas were rotten. The percentage of fruits in good condition was 87.8%. How many bananas did the shopkeeper buy?",
|
||
|
|
"answer_preview": "448",
|
||
|
|
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|
||
|
|
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||
|
|
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||
|
|
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|
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||
|
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||
|
|
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||
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|
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||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
|
|
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||
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||
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|
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||
|
|
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||
|
|
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|
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||
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||
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||
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||
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||
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||
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||
|
|
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||
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|
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||
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||
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||
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||
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||
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||
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||
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|
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||
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||
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||
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||
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||
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||
|
|
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||
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|
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||
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|
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||
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||
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||
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||
|
|
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||
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||
|
|
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||
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}
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},
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{
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"sample_id": 18398,
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|
||
|
|
"answer_preview": "3188",
|
||
|
|
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}
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},
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{
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||
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|
"sample_id": 18858,
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||
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||
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||
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||
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|
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||
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"prompt_preview": "a certain number of men complete a piece of work in 60 days . if there were 8 men more , the work could be finished in 10 days less . how many men were originally there ?",
|
||
|
|
"answer_preview": "48",
|
||
|
|
"source": "orca_math",
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||
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|
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||
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||
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||
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||
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||
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|
}
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||
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|
}
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||
|
|
]
|
||
|
|
}
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