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Express your answer as a single numerical value.", "answer_preview": "0", "source": "big_math" }, { "sample_id": 2514, "sample_count": 7, "error_ema": 0.02061430551111698, "priority_score": 0.7202249765396118, "sampling_probability": 2.1606998416245915e-05, "seen": 1, "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 ", "answer_preview": "156", "source": "orca_math" }, { "sample_id": 2523, "sample_count": 7, "error_ema": 0.017627079039812088, "priority_score": 0.7183240056037903, "sampling_probability": 2.1566420400631614e-05, "seen": 1, "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 $9$ . 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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", "source": "olympiads" }, { "sample_id": 3835, "sample_count": 7, "error_ema": 0.04836041480302811, "priority_score": 0.737881600856781, "sampling_probability": 2.19875782931922e-05, "seen": 1, "prompt_preview": "What number times (1/6)^2 will give a certain value? The answer is 7776. What is the value?", "answer_preview": "279936", "source": "orca_math" }, { "sample_id": 4430, "sample_count": 7, "error_ema": 0.0027808286249637604, "priority_score": 0.708876371383667, "sampling_probability": 2.1365873180911876e-05, "seen": 1, "prompt_preview": "a number when divided by 296 leaves 75 as remainder . when the same number is divided by 37 , the remainder will be :", "answer_preview": "1", "source": "orca_math" }, { "sample_id": 5102, "sample_count": 7, "error_ema": 0.014456501230597496, "priority_score": 0.7163063883781433, "sampling_probability": 2.1523432224057615e-05, "seen": 1, "prompt_preview": "A pet store has 9 bird cages. In each cage, there are 2 parrots, 3 parakeets, and 1 cockatiel. However, to ensure bird compatibility, every third cage has only parakeets, with 5 parakeets in each of those cages. How many birds does the pet ", "answer_preview": "51", "source": "orca_math" }, { "sample_id": 5538, "sample_count": 7, "error_ema": 0.27569612860679626, "priority_score": 0.8825497627258301, "sampling_probability": 2.5369241484440863e-05, "seen": 1, "prompt_preview": "What is the molecular weight of Acetic acid?", "answer_preview": "60.052", "source": "orca_math" }, { "sample_id": 5575, "sample_count": 7, "error_ema": 0.03312796354293823, "priority_score": 0.7281882166862488, "sampling_probability": 2.1777819711132906e-05, "seen": 1, "prompt_preview": "There are a few integers \\( n \\) such that \\( n^{2}+n+1 \\) divides \\( n^{2013}+61 \\). 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What is Tim's in", "answer_preview": "12", "source": "aops_forum" }, { "sample_id": 8399, "sample_count": 7, "error_ema": 0.01490426529198885, "priority_score": 0.7165912985801697, "sampling_probability": 2.1529500372707844e-05, "seen": 1, "prompt_preview": "Simplify first, then evaluate: $(2y+3x^{2})-(x^{2}-y)-x^{2}$, where $x=-2$ and $y=\\frac{1}{3}$.", "answer_preview": "5", "source": "cn_k12" }, { "sample_id": 9025, "sample_count": 7, "error_ema": 0.015967808663845062, "priority_score": 0.7172681093215942, "sampling_probability": 2.1543912225752138e-05, "seen": 1, "prompt_preview": "Given that $f(x) = x^{3} + 3ax^{2} + bx + a^{2}$ has an extremum of $0$ at $x = -1$, calculate the value of $a - b$. Express your answer as a single numerical value.", "answer_preview": "-7", "source": "big_math" }, { "sample_id": 9282, "sample_count": 7, "error_ema": 0.008875182829797268, "priority_score": 0.7127546072006226, "sampling_probability": 2.1447971448651515e-05, "seen": 1, "prompt_preview": "the least number which must be subtracted from 509 to make it exactly divisible by 9 is :", "answer_preview": "5", "source": "orca_math" }, { "sample_id": 9647, "sample_count": 7, "error_ema": 0.008214923553168774, "priority_score": 0.7123344540596008, "sampling_probability": 2.1439062038552947e-05, "seen": 1, "prompt_preview": "Given that the sum of all the coefficients of the binomial $({2{x^2}-\\frac{1}{x}})^n$ is $128$, find the coefficient of the term containing $\\frac{1}{x}$ in its expansion.", "answer_preview": "-84", "source": "cn_k12" }, { "sample_id": 9761, "sample_count": 7, "error_ema": 0.026890583336353302, "priority_score": 0.7242189645767212, "sampling_probability": 2.1692507289117202e-05, "seen": 1, "prompt_preview": "There exists a unique strictly increasing arithmetic sequence $\\{a_i\\}_{i=1}^{100}$ of positive integers such that \\[a_1+a_4+a_9+\\cdots+a_{100}=\\text{1000},\\] where the summation runs over all terms of the form $a_{i^2}$ for $1\\leq i\\l", "answer_preview": "123", "source": "aops_forum" }, { "sample_id": 9867, "sample_count": 7, "error_ema": 0.03255616873502731, "priority_score": 0.727824330329895, "sampling_probability": 2.1769985323771834e-05, "seen": 1, "prompt_preview": "Let $a$ and $b$ be rational numbers, and $|a| > 0$. 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What is the sum?", "answer_preview": "880", "source": "orca_math" }, { "sample_id": 10083, "sample_count": 7, "error_ema": 0.001304257777519524, "priority_score": 0.7079367637634277, "sampling_probability": 2.1346031644497998e-05, "seen": 1, "prompt_preview": "In an isosceles triangle, if the lengths of two sides are $2$ and $4$, then the perimeter of the isosceles triangle is ______.", "answer_preview": "10", "source": "cn_k12" }, { "sample_id": 10131, "sample_count": 7, "error_ema": 0.058497555553913116, "priority_score": 0.744332492351532, "sampling_probability": 2.2128289856482297e-05, "seen": 1, "prompt_preview": "Two students in a class are preparing to register for the independent admission tests of Zhejiang University, Fudan University, and Shanghai Jiao Tong University, with the requirement that each student can choose up to two schools. Find the", "answer_preview": "36", "source": "big_math" }, { "sample_id": 10382, "sample_count": 7, "error_ema": 0.002286745933815837, "priority_score": 0.7085619568824768, "sampling_probability": 2.1359230231610127e-05, "seen": 1, "prompt_preview": "A total of 1252 students participated in a knowledge competition, and a systematic sampling method is used to select a sample of size 50. How many individuals should be randomly removed from the population to ensure divisibility? Express yo", "answer_preview": "2", "source": "big_math" }, { "sample_id": 11019, "sample_count": 7, "error_ema": 0.006071188487112522, "priority_score": 0.7109702229499817, "sampling_probability": 2.14101564779412e-05, "seen": 1, "prompt_preview": "Given the functional equation \\( f(a+b) = f(a) \\cdot f(b) \\) and \\( f(1) = 1 \\), calculate the sum: \\[ \\frac{f(2)}{f(1)} + \\frac{f(3)}{f(2)} + \\frac{f(4)}{f(3)} + \\cdots + \\frac{f(1988)}{f(1987)} \\] Express your answer as a single integer.", "answer_preview": "1987", "source": "big_math" }, { "sample_id": 11211, "sample_count": 7, "error_ema": 0.011617450043559074, "priority_score": 0.7144997119903564, "sampling_probability": 2.1485015167854726e-05, "seen": 1, "prompt_preview": "In an arithmetic sequence $\\{a_n\\}$, $a_2 + a_5 = 19$, and the sum of the first five terms, $S_5 = 40$. Find the value of $a_{10}$.", "answer_preview": "29", "source": "cn_k12" }, { "sample_id": 11345, "sample_count": 7, "error_ema": 0.004640929866582155, "priority_score": 0.7100600600242615, "sampling_probability": 2.1390897018136457e-05, "seen": 1, "prompt_preview": "There are 30 players on a football team. The coach has 8 liters of water. She pours some milliliters of water for every player so they can get hydrated. Unfortunately, there was a water spill and 250ml of water was spilled. There was 1750ml", "answer_preview": "200", "source": "orca_math" }, { "sample_id": 11403, "sample_count": 7, "error_ema": 0.010100610554218292, "priority_score": 0.713534414768219, "sampling_probability": 2.1464516976266168e-05, "seen": 1, "prompt_preview": "Given the real numbers \\( a \\) and \\( b \\) satisfying \\(\\frac{4}{a^{4}}-\\frac{2}{a^{2}}-3=0\\) and \\(b^{4}+b^{2}-3=0\\), respectively, calculate the value of the algebraic expression \\(\\frac{a^{4} b^{4}+4}{a^{4}}\\). Express your answer as a s", "answer_preview": "7", "source": "big_math" }, { "sample_id": 11724, "sample_count": 7, "error_ema": 0.01764737069606781, "priority_score": 0.7183369398117065, "sampling_probability": 2.1566693249042146e-05, "seen": 1, "prompt_preview": "Define a new operation \"$*$\" within the range of positive integers, where $k*n$ represents the sum of $n$ consecutive positive integers starting from $k$. Given the equation $3*n=150$, calculate the value of $n$ that satisfies this equation", "answer_preview": "15", "source": "big_math" }, { "sample_id": 11888, "sample_count": 7, "error_ema": 0.030322570353746414, "priority_score": 0.7264029383659363, "sampling_probability": 2.1739406292908825e-05, "seen": 1, "prompt_preview": "Three builders build a single floor of a house in some days. Each builder is paid $100 for a single day\u2019s work. It would cost $270000 to hire 6 builders to build 5 houses with 6 floors each. How many days does it take for three builders to ", "answer_preview": "30", "source": "orca_math" }, { "sample_id": 12067, "sample_count": 7, "error_ema": 0.005254401359707117, "priority_score": 0.7104504704475403, "sampling_probability": 2.1399158868007362e-05, "seen": 1, "prompt_preview": "Abby is building 2 raised beds to grow vegetables. The beds are both 8 feet long, 4 feet wide and have a certain height. Each bag of soil has 4 cubic feet. She will need 16 bags of soil. How high are the beds?", "answer_preview": "1", "source": "orca_math" }, { "sample_id": 12726, "sample_count": 7, "error_ema": 0.1408858448266983, "priority_score": 0.7967613935470581, "sampling_probability": 2.3305812646867707e-05, "seen": 1, "prompt_preview": "Given the function $y= \\frac {x-b}{x+2}$, if its range on the interval $(a,a+6)$ $(b < -2)$ is $(2,+\u221e)$, then $a+b=$ _____ .", "answer_preview": "-10", "source": "cn_k12" }, { "sample_id": 12770, "sample_count": 7, "error_ema": 0.022244073450565338, "priority_score": 0.7212620973587036, "sampling_probability": 2.162917189707514e-05, "seen": 1, "prompt_preview": "a small company reduced its faculty by approximately 13 percent to 195 employees . what was the original number of employees ?", "answer_preview": "224", "source": "orca_math" }, { "sample_id": 13132, "sample_count": 7, "error_ema": 0.01570822298526764, "priority_score": 0.7171028852462769, "sampling_probability": 2.154039430024568e-05, "seen": 1, "prompt_preview": "Given that \\( x \\) and \\( y \\) are positive real numbers that satisfy \\( xy + x + y = 71 \\) and \\( x^2 y + xy^2 = 880 \\), find the value of \\( x^2 + y^2 \\).", "answer_preview": "146", "source": "olympiads" }, { "sample_id": 13136, "sample_count": 7, "error_ema": 0.017954645678400993, "priority_score": 0.7185324430465698, "sampling_probability": 2.1570864191744477e-05, "seen": 1, "prompt_preview": "Given $a=(-1,3)$, $b=(1,t)$, if $(a-2b) \\perp a$, then the real number $t=$ ?", "answer_preview": "2", "source": "cn_k12" }, { "sample_id": 13568, "sample_count": 7, "error_ema": 0.011974742636084557, "priority_score": 0.7147270441055298, "sampling_probability": 2.148984458472114e-05, "seen": 1, "prompt_preview": "In a class of 50 students, it is required to select 10 students using systematic sampling. The 50 students are randomly assigned numbers from 1 to 50 and grouped, with group one containing numbers 1 to 5, group two containing numbers 6 to 1", "answer_preview": "37", "source": "cn_k12" }, { "sample_id": 14619, "sample_count": 7, "error_ema": 0.00434482004493475, "priority_score": 0.7098716497421265, "sampling_probability": 2.1386911612353288e-05, "seen": 1, "prompt_preview": "In a geometric sequence $\\{a_n\\}$ where each term is positive, if $a_5a_6=81$, calculate the value of $\\log_{3}a_1+\\log_{3}a_2+\\ldots+\\log_{3}a_{10}$. Express your answer as a single numerical value.", "answer_preview": "20", "source": "big_math" }, { "sample_id": 14810, "sample_count": 7, "error_ema": 0.0017319017788395286, "priority_score": 0.7082088589668274, "sampling_probability": 2.1351774194044992e-05, "seen": 1, "prompt_preview": "Given vectors $\\overrightarrow{a} = \\left( \\frac{1}{2}, \\frac{\\sqrt{3}}{2} \\right)$ and $\\overrightarrow{b} = \\left( -\\frac{\\sqrt{3}}{2}, \\frac{1}{2} \\right)$, calculate the dot product of $\\overrightarrow{a} + \\overrightarrow{b}$ and $\\ove", "answer_preview": "1", "source": "big_math" }, { "sample_id": 14988, "sample_count": 7, "error_ema": 0.0055033317767083645, "priority_score": 0.7106088995933533, "sampling_probability": 2.1402509446488693e-05, "seen": 1, "prompt_preview": "Given a geometric sequence \\(\\{a_n\\}\\) where each term is a positive number, the sum of the first two terms is 6, and the sum of the first six terms is 126, calculate the sum of the first four terms. Express your answer as a single integer.", "answer_preview": "30", "source": "big_math" }, { "sample_id": 15783, "sample_count": 7, "error_ema": 0.013715759851038456, "priority_score": 0.7158349752426147, "sampling_probability": 2.1513402316486463e-05, "seen": 1, "prompt_preview": "There are 4 different books, among which there are 2 Chinese books and 2 math books. If they are randomly placed side by side on the same shelf, the number of ways to place them such that books of the same subject are not adjacent to each o", "answer_preview": "8", "source": "cn_k12" }, { "sample_id": 15792, "sample_count": 7, "error_ema": 0.015205483883619308, "priority_score": 0.7167829871177673, "sampling_probability": 2.1533580365939997e-05, "seen": 1, "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?", "answer_preview": "10", "source": "orca_math" }, { "sample_id": 15817, "sample_count": 7, "error_ema": 0.0314333513379097, "priority_score": 0.7271097898483276, "sampling_probability": 2.1754607587354258e-05, "seen": 1, "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: ", "answer_preview": "6", "source": "math" }, { "sample_id": 16095, "sample_count": 7, "error_ema": 0.018035490065813065, "priority_score": 0.718583881855011, "sampling_probability": 2.1571962861344218e-05, "seen": 1, "prompt_preview": "Given the function $f(x) = \\ln(x + \\sqrt{x^2 + 1}) + ax^7 + bx^3 - 4$, where $a$ and $b$ are constants. If $f(-3) = 4$, then $f(3) = \\_\\_\\_\\_\\_\\_$.", "answer_preview": "-12", "source": "cn_k12" }, { "sample_id": 16103, "sample_count": 7, "error_ema": 0.017583398148417473, "priority_score": 0.718296229839325, "sampling_probability": 2.156582922907546e-05, "seen": 1, "prompt_preview": "63 men working some hours per day dig 30 m deep. To dig to a depth of 50 m working 6 hours per day, 77 extra men should be put to work. How many hours per day were the initial men working?", "answer_preview": "8", "source": "orca_math" }, { "sample_id": 16150, "sample_count": 7, "error_ema": 0.016217511147260666, "priority_score": 0.7174270153045654, "sampling_probability": 2.1547297365032136e-05, "seen": 1, "prompt_preview": "There are 2013 colored lights numbered 1, 2, 3, 4, \u2026, 2013, all turned on, each controlled by a switch. If the first time you press the switch of all lights numbered with multiples of 2, the second time you press the switch of lights number", "answer_preview": "1006", "source": "cn_k12" }, { "sample_id": 16853, "sample_count": 7, "error_ema": 0.002917038043960929, "priority_score": 0.7089630365371704, "sampling_probability": 2.1367703084251843e-05, "seen": 1, "prompt_preview": "A pet store had 1700 puppies. In one week they sold 621 of them and put the rest into cages with 26 in each cage. How many cages did they use?", "answer_preview": "42", "source": "orca_math" }, { "sample_id": 17114, "sample_count": 7, "error_ema": 0.03232692554593086, "priority_score": 0.7276784181594849, "sampling_probability": 2.1766845748061314e-05, "seen": 1, "prompt_preview": "A seven-digit number, where the sum of every two adjacent digits from left to right is 9, 7, 9, 2, 8, 11. What is this seven-digit number?", "answer_preview": "9072083", "source": "olympiads" }, { "sample_id": 17371, "sample_count": 7, "error_ema": 0.015112492255866528, "priority_score": 0.7167237997055054, "sampling_probability": 2.153231980628334e-05, "seen": 1, "prompt_preview": "There are 80 cable cars traveling in a circular route between ski resorts A and B, all moving in the same direction. The distance between two adjacent cable cars is the same. Xiaoming, who is sitting in one of the cable cars, encounters an ", "answer_preview": "20", "source": "olympiads" }, { "sample_id": 17500, "sample_count": 7, "error_ema": 0.040935028344392776, "priority_score": 0.7331563234329224, "sampling_probability": 2.1885074602323584e-05, "seen": 1, "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 2)$.", "answer_preview": "0.1", "source": "cn_k12" }, { "sample_id": 20133, "sample_count": 7, "error_ema": 0.03259235620498657, "priority_score": 0.7278473377227783, "sampling_probability": 2.1770478269900195e-05, "seen": 1, "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" }, { "sample_id": 20179, "sample_count": 7, "error_ema": 0.003454261925071478, "priority_score": 0.709304928779602, "sampling_probability": 2.1374928110162728e-05, "seen": 1, "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" }, { "sample_id": 20258, "sample_count": 7, "error_ema": 0.04922666400671005, "priority_score": 0.7384328246116638, "sampling_probability": 2.199956725235097e-05, "seen": 1, "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", "source": "orca_math" }, { "sample_id": 20316, "sample_count": 7, "error_ema": 0.008223098702728748, "priority_score": 0.7123396396636963, "sampling_probability": 2.143917117791716e-05, "seen": 1, "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", "source": "cn_k12" }, { "sample_id": 20800, "sample_count": 7, "error_ema": 0.0027252391446381807, "priority_score": 0.7088410258293152, "sampling_probability": 2.1365127395256422e-05, "seen": 1, "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", "source": "orca_math" }, { "sample_id": 21002, "sample_count": 7, "error_ema": 0.024944648146629333, "priority_score": 0.7229806184768677, "sampling_probability": 2.1665960957761854e-05, "seen": 1, "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", "source": "cn_k12" }, { "sample_id": 21022, "sample_count": 7, "error_ema": 0.0035646501928567886, "priority_score": 0.7093752026557922, "sampling_probability": 2.1376414224505424e-05, "seen": 1, "prompt_preview": "In the expansion of $(x^{2}+ \\frac{1}{2x})^{8}$, the coefficient of $x^{7}$ is __________.", "answer_preview": "7", "source": "cn_k12" }, { "sample_id": 21037, "sample_count": 7, "error_ema": 0.21271392703056335, "priority_score": 0.8424701690673828, "sampling_probability": 2.438342198729515e-05, "seen": 1, "prompt_preview": "In a vast garden, there are 500 plants. On the first day, hungry bugs devoured 300 plants. The next day, they were still hungry and ate 5/7 of the remaining plants. After that, they consumed 12 more plants. How many plants remain?", "answer_preview": "45", "source": "orca_math" }, { "sample_id": 21157, "sample_count": 7, "error_ema": 0.04006636142730713, "priority_score": 0.7326035499572754, "sampling_probability": 2.1873116565984674e-05, "seen": 1, "prompt_preview": "I run a 15-mile route which consists of 5 miles at a pace of 7 minutes per mile, then 6 miles at a pace of 8 minutes per mile, and finally 4 miles at a pace of 6 minutes per mile. What is my average speed in kilometers per hour for the enti", "answer_preview": "13.54", "source": "orca_math" }, { "sample_id": 21183, "sample_count": 7, "error_ema": 0.005645943805575371, "priority_score": 0.7106996178627014, "sampling_probability": 2.1404428480309434e-05, "seen": 1, "prompt_preview": "In a geometric sequence where all terms are positive, if $6a_{1}$, $a_{3}$, and $4a_{2}$ form an arithmetic sequence, then find the value of the expression $\\frac{a_{11}+a_{13}+a_{16}+a_{20}+a_{21}}{a_{8}+a_{10}+a_{13}+a_{17}+a_{18}}$.", "answer_preview": "27", "source": "cn_k12" }, { "sample_id": 21556, "sample_count": 7, "error_ema": 0.0, "priority_score": 0.7071067690849304, "sampling_probability": 2.132851477654185e-05, "seen": 1, "prompt_preview": "In the diagram below, \\( D \\) and \\( E \\) lie on the side \\( AB \\), and \\( F \\) lies on the side \\( AC \\) such that \\( DA = DF = DE \\), \\( BE = EF \\), and \\( BF = BC \\). It is given that \\(\\angle ABC = 2 \\angle ACB\\). Find \\( x \\), where \\(", "answer_preview": "108", "source": "olympiads" }, { "sample_id": 21642, "sample_count": 7, "error_ema": 0.002164690289646387, "priority_score": 0.7084842920303345, "sampling_probability": 2.1357591322157532e-05, "seen": 1, "prompt_preview": "Skylar started donating 8k to an organization on Skylar's birthday when Skylar turned 17. Yesterday, Skylar turned a certain age. Skylar has donated 440k till now. How old is Skylar now?", "answer_preview": "72", "source": "orca_math" }, { "sample_id": 21805, "sample_count": 7, "error_ema": 0.009020831435918808, "priority_score": 0.7128472924232483, "sampling_probability": 2.1449935957207344e-05, "seen": 1, "prompt_preview": "In a football tournament, each team meets exactly twice with every other team. There are no draws, a victory earns two points and a defeat earns no points. One team won the tournament with 26 points, and there are two teams tied for last pl", "answer_preview": "12", "source": "olympiads" } ], "top_by_probability": [ { "sample_id": 42, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12" }, { "sample_id": 177, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "prompt_preview": "sum of 49 odd numbers is ?", "answer_preview": "2401", "source": "orca_math" }, { "sample_id": 185, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "prompt_preview": "On the first day, Barry Sotter used his magic wand to make an object's length increase by $\\frac{1}{2}$, meaning that if the length of the object was originally $x,$ then it is now $x + \\frac{1}{2} x.$ On the second day he increased the ob", "answer_preview": "198", "source": "math" }, { "sample_id": 298, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "prompt_preview": "Given vectors $\\overrightarrow{v} = \\left(a_{n+1} - \\frac{a_n}{2}, \\frac{a_{n+1}^2}{2a_n}\\right)$ and $\\overrightarrow{\\mu} = (3, 3)$, and $\\overrightarrow{v}$ is parallel to $\\overrightarrow{\\mu}$, if $a_1 = 5$, find the sum of the first 1", "answer_preview": "50", "source": "big_math" }, { "sample_id": 405, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "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\\).", "answer_preview": "30", "source": "olympiads" }, { "sample_id": 453, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "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", "answer_preview": "0.9", "source": "orca_math" }, { "sample_id": 463, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "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", "answer_preview": "3520", "source": "cn_k12" }, { "sample_id": 493, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "prompt_preview": "What is the value of y in the expression ( ( 2 ^ 5 ) * ( y ) ) / ( ( 8 ^ 2 ) * ( 3 ^ 5 ) ) if the result is 0.16666666666666666?", "answer_preview": "81", "source": "orca_math" }, { "sample_id": 632, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "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:", "answer_preview": "10", "source": "orca_math" }, { "sample_id": 662, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "prompt_preview": "I should have added 32 to a number and multiply it by 12 but I accidently multiplied it by 3 and subtracted 45, and 159 came out as a result. If you calculate this correctly, how much is it?", "answer_preview": "1200", "source": "orca_math" }, { "sample_id": 687, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "prompt_preview": "At a math conference, the following exchange rates are used: $$ \\begin{aligned} 1 \\text { calculator } & =100 \\text { rulers } \\\\ 10 \\text { rulers } & =30 \\text { compasses } \\\\ 25 \\text { compasses } & =50 \\text { protractors } \\end{alig", "answer_preview": "600", "source": "big_math" }, { "sample_id": 729, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "prompt_preview": "There is a piece of colored paper in the shape of a square with a side length of 4 centimeters (cm). The four sides of this colored paper were cut into diamond shapes by connecting the two equally divided dots. Find the area of this rhombus", "answer_preview": "8", "source": "orca_math" }, { "sample_id": 748, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "prompt_preview": "If $(2x+ \\sqrt{3})^{4}={a}_{0}+{a}_{1}x+{a}_{2}{x}^{2}+{a}_{3}{x}^{3}+{a}_{4}{x}^{4}$, calculate the value of $({a}_{0}+{a}_{2}+{a}_{4})^{2}-({a}_{1}+{a}_{3})^{2}$. Express your answer as a single number.", "answer_preview": "1", "source": "big_math" }, { "sample_id": 754, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "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}$ ?", "answer_preview": "1", "source": "omnimath" }, { "sample_id": 771, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "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", "answer_preview": "48", "source": "orca_math" }, { "sample_id": 779, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "prompt_preview": "Jackson buys a computer game for $66 and three movie tickets for $12 each. How much did he spend on entertainment total?", "answer_preview": "102", "source": "openmath" }, { "sample_id": 828, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "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", "answer_preview": "17", "source": "orca_math" }, { "sample_id": 891, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "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", "answer_preview": "36", "source": "omnimath" }, { "sample_id": 946, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "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.", "answer_preview": "6", "source": "big_math" }, { "sample_id": 976, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "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.", "answer_preview": "10", "source": "big_math" }, { "sample_id": 979, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "prompt_preview": "Determine the least possible value of the natural number $n$ such that $n!$ ends in exactly $1987$ zeros.
NoteNote. Here (and generally in MathLinks) natural numbers supposed to be positive.
", "answer_preview": "7960", "source": "aops_forum" }, { "sample_id": 1014, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "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", "source": "orca_math" }, { "sample_id": 1114, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "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" }, { "sample_id": 1121, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "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?", "answer_preview": "5", "source": "orca_math" }, { "sample_id": 1125, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "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" }, { "sample_id": 1212, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "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", "source": "cn_k12" }, { "sample_id": 1250, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "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.", "answer_preview": "3", "source": "big_math" }, { "sample_id": 1262, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "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", "source": "olympiads" }, { "sample_id": 1306, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "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", "answer_preview": "6", "source": "openmath" }, { "sample_id": 1388, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "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 \\_\\_\\_\\_\\_\\_.", "answer_preview": "1", "source": "cn_k12" }, { "sample_id": 1429, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "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?", "answer_preview": "300", "source": "orca_math" }, { "sample_id": 1612, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "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" }, { "sample_id": 1629, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "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.", "answer_preview": "200", "source": "cn_k12" }, { "sample_id": 1741, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "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?", "answer_preview": "40", "source": "orca_math" }, { "sample_id": 1841, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "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 F1 and F2, respectively. Let P be a point on the ellipse C such that line segm", "answer_preview": "9", "source": "cn_k12" }, { "sample_id": 1902, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "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", "answer_preview": "36", "source": "orca_math" }, { "sample_id": 1903, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "prompt_preview": "How many total days were there in the years 2001 through 2004?", "answer_preview": "1461", "source": "math" }, { "sample_id": 1919, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "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", "answer_preview": "2", "source": "big_math" }, { "sample_id": 1996, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "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.", "answer_preview": "2", "source": "big_math" }, { "sample_id": 2009, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "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" }, { "sample_id": 2040, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "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.", "answer_preview": "2501", "source": "big_math" }, { "sample_id": 2050, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "prompt_preview": "Find the constant term in the expansion of $$( \\sqrt[4]{x}- \\frac {3}{x})^{5}$$.", "answer_preview": "-15", "source": "cn_k12" }, { "sample_id": 2081, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "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.", "answer_preview": "2", "source": "big_math" }, { "sample_id": 2084, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "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=$ _____ .", "answer_preview": "2", "source": "cn_k12" }, { "sample_id": 2095, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "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?", "answer_preview": "2.5", "source": "orca_math" }, { "sample_id": 2141, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "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 ______.", "answer_preview": "2", "source": "cn_k12" }, { "sample_id": 2186, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "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" }, { "sample_id": 2187, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "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" }, { "sample_id": 2236, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "prompt_preview": "Given that $\\sqrt{102.01}=10.1$, find the value of $\\sqrt{1.0201}$. Express your answer as a decimal number.", "answer_preview": "1.01", "source": "big_math" }, { "sample_id": 2262, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "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 ?", "answer_preview": "34", "source": "orca_math" }, { "sample_id": 2277, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "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" }, { "sample_id": 2314, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "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.", "answer_preview": "1", "source": "big_math" }, { "sample_id": 2316, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "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.", "answer_preview": "45", "source": "orca_math" }, { "sample_id": 2323, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "prompt_preview": "When $x=$______, the value of the algebraic expression $\\frac{1}{x-1}+\\frac{3}{1-{x}^{2}}$ is zero.", "answer_preview": "2", "source": "cn_k12" }, { "sample_id": 2467, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "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.", "answer_preview": "2", "source": "big_math" }, { "sample_id": 2704, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "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?", "answer_preview": "5", "source": "orca_math" }, { "sample_id": 2759, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "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", "answer_preview": "3", "source": "olympiads" }, { "sample_id": 2780, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "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?", "answer_preview": "7", "source": "orca_math" }, { "sample_id": 2808, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "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=$ ?", "answer_preview": "-2", "source": "cn_k12" }, { "sample_id": 2823, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "prompt_preview": "Find the greatest common divisor of $10! + 2$ and $11! + 8$.", "answer_preview": "2", "source": "math" }, { "sample_id": 2866, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "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.", "answer_preview": "6", "source": "olympiads" }, { "sample_id": 2988, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "prompt_preview": "A triangle has two medians of lengths 9 and 12. Find the largest possible area of the triangle. (Note: A median is a line segment joining a vertex of the triangle to the midpoint of the opposite side.)", "answer_preview": "72", "source": "olympiads" }, { "sample_id": 3014, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "prompt_preview": "Shelly writes down a vector $v=(a, b, c, d)$, where $0 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 ", "answer_preview": "0.8", "source": "big_math" }, { "sample_id": 4078, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "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?", "answer_preview": "3", "source": "olympiads" }, { "sample_id": 4083, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "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=$ \\_\\_\\_\\_\\_\\_.", "answer_preview": "10", "source": "cn_k12" }, { "sample_id": 4127, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "prompt_preview": "If the sum of three real numbers is $0$ and their product is $17$, then what is the sum of their cubes?", "answer_preview": "51", "source": "math" }, { "sample_id": 4143, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "prompt_preview": "Determine the coefficient of $x$ in the binomial expansion of $(2x^{2}- \\frac{1}{x})^{5}$ (Answer with a number)", "answer_preview": "-40", "source": "cn_k12" }, { "sample_id": 4344, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "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.", "answer_preview": "6", "source": "big_math" }, { "sample_id": 4369, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "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", "answer_preview": "200", "source": "orca_math" }, { "sample_id": 4382, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "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", "answer_preview": "22", "source": "big_math" }, { "sample_id": 4415, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "prompt_preview": "Find the value of $\\log_{4}\\cos\\frac{\\pi}{5}+\\log_{4}\\cos\\frac{2\\pi}{5}$.", "answer_preview": "-1", "source": "cn_k12" }, { "sample_id": 4517, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "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" }, { "sample_id": 4518, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "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" }, { "sample_id": 4600, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "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?", "answer_preview": "60", "source": "orca_math" }, { "sample_id": 4626, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "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.", "answer_preview": "-9", "source": "big_math" }, { "sample_id": 4697, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "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", "answer_preview": "0.216", "source": "cn_k12" }, { "sample_id": 4886, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "prompt_preview": "Calculate the sum of \\(0.001 + 1.01 + 0.11\\). Express your answer as a decimal number, including all significant digits.", "answer_preview": "1.121", "source": "big_math" }, { "sample_id": 4895, "sample_count": 0, "error_ema": 0.0, "priority_score": 2.0, "sampling_probability": 7.659749098820612e-05, "seen": 0, "prompt_preview": "It takes a certain number of days to fill a laboratory dish with bacteria. If the size of the bacteria doubles each day, it took 24 days for the bacteria to fill 1/64 of the dish. How many days does it take to fill the entire dish?", "answer_preview": "30", "source": "orca_math" } ], "top_by_error": [ { "sample_id": 5538, "sample_count": 7, "error_ema": 0.27569612860679626, "priority_score": 0.8825497627258301, "sampling_probability": 2.5369241484440863e-05, "seen": 1, "prompt_preview": "What is the molecular weight of Acetic acid?", "answer_preview": "60.052", "source": "orca_math" }, { "sample_id": 9618, "sample_count": 6, "error_ema": 0.25845763087272644, "priority_score": 0.911003589630127, "sampling_probability": 2.6093204724020325e-05, "seen": 1, "prompt_preview": "In the arithmetic sequence $\\{a_n\\}$, $a_1 = 142$, and $d = -2$. Starting from the first term, every other term is selected to form a new sequence $\\{b_n\\}$. Find the value of $n$ when the sum of the first $n$ terms of this new sequence rea", "answer_preview": "24", "source": "big_math" }, { "sample_id": 12083, "sample_count": 6, "error_ema": 0.2544912099838257, "priority_score": 0.9086236953735352, "sampling_probability": 2.603186840133276e-05, "seen": 1, "prompt_preview": "Jack will have twenty times more handball trophies than Michael has right now in seven years. If Michael has 100 trophies right now, and the number of his trophies increases by 200 each year for the next seven years, what's the total number", "answer_preview": "5000", "source": "orca_math" }, { "sample_id": 27688, "sample_count": 6, "error_ema": 0.2501737177371979, "priority_score": 0.9060332179069519, "sampling_probability": 2.596526792331133e-05, "seen": 1, "prompt_preview": "In a mathematics competition, 1000 students are numbered as follows: 0001, 0002, 0003, ..., 1000. It is planned to draw a sample of size 50 by dividing into 50 parts using systematic sampling. If the first part includes the numbers 0001, 00", "answer_preview": "0795", "source": "cn_k12" }, { "sample_id": 28729, "sample_count": 6, "error_ema": 0.24764886498451233, "priority_score": 0.9045183062553406, "sampling_probability": 2.5926401576725766e-05, "seen": 1, "prompt_preview": "Valerie needs to buy new light bulbs for her room. She needs 3 small light bulbs and some large light bulbs. She has $60 to spend. Small light bulbs cost $8 and large light bulbs cost $12. After buying the light bulbs, Valerie will have $24", "answer_preview": "3", "source": "orca_math" }, { "sample_id": 21753, "sample_count": 5, "error_ema": 0.23887455463409424, "priority_score": 0.9492046236991882, "sampling_probability": 2.709776526899077e-05, "seen": 1, "prompt_preview": "Megan baked 71 cupcakes for her school's bake sale. Her brother, Todd, ate some of them. She could make 4 packages with 7 cupcakes in each package. How many cupcakes did Todd eat?", "answer_preview": "28", "source": "orca_math" }, { "sample_id": 20834, "sample_count": 5, "error_ema": 0.2303493618965149, "priority_score": 0.9444684386253357, "sampling_probability": 2.6971150873578154e-05, "seen": 1, "prompt_preview": "Given $M = \\{a \\,|\\, |a| \\geq 2\\}$, $A = \\{a \\,|\\, (a - 2)(a^2 - 3) = 0, a \\in M\\}$, then the number of subsets of set $A$ is $\\_\\_\\_\\_\\_\\_\\_\\_$.", "answer_preview": "4", "source": "cn_k12" }, { "sample_id": 880, "sample_count": 5, "error_ema": 0.22778645157814026, "priority_score": 0.9430446028709412, "sampling_probability": 2.6933199478662573e-05, "seen": 1, "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?", "answer_preview": "10.33", "source": "orca_math" }, { "sample_id": 18483, "sample_count": 5, "error_ema": 0.21817561984062195, "priority_score": 0.9377052187919617, "sampling_probability": 2.6791365598910488e-05, "seen": 1, "prompt_preview": "a reduction of 10 % in the price of oil enables a house wife to obtain 5 kgs more for rs . 800 , what is the reduced price for kg ?", "answer_preview": "16.00", "source": "orca_math" }, { "sample_id": 24775, "sample_count": 5, "error_ema": 0.21755072474479675, "priority_score": 0.9373580813407898, "sampling_probability": 2.6782172426464967e-05, "seen": 1, "prompt_preview": "walking at 3 / 4 of his usual place , a man reaches his office 20 minute late . find his usual time ?", "answer_preview": "80", "source": "orca_math" }, { "sample_id": 21037, "sample_count": 7, "error_ema": 0.21271392703056335, "priority_score": 0.8424701690673828, "sampling_probability": 2.438342198729515e-05, "seen": 1, "prompt_preview": "In a vast garden, there are 500 plants. On the first day, hungry bugs devoured 300 plants. The next day, they were still hungry and ate 5/7 of the remaining plants. After that, they consumed 12 more plants. How many plants remain?", "answer_preview": "45", "source": "orca_math" }, { "sample_id": 20870, "sample_count": 5, "error_ema": 0.212409108877182, "priority_score": 0.9345016479492188, "sampling_probability": 2.6706629796535708e-05, "seen": 1, "prompt_preview": "What is the units digit of 33 * 219^89 + 89^19? Express your answer as a single digit.", "answer_preview": "8", "source": "big_math" }, { "sample_id": 21847, "sample_count": 5, "error_ema": 0.21146783232688904, "priority_score": 0.9339786767959595, "sampling_probability": 2.6692820028983988e-05, "seen": 1, "prompt_preview": "how many pieces of 85 cm length can be cut from a rod of 17 meters long ?", "answer_preview": "17", "source": "orca_math" }, { "sample_id": 5439, "sample_count": 5, "error_ema": 0.21130919456481934, "priority_score": 0.9338905811309814, "sampling_probability": 2.669049717951566e-05, "seen": 1, "prompt_preview": "Milan has two phone lines for his long-distance phone service. For the first phone line, he pays a 3 dollar monthly fee plus 15 cents per minute, and for the second phone line, he pays a 4 dollar monthly fee plus 10 cents per minute. Last m", "answer_preview": "252", "source": "orca_math" }, { "sample_id": 3903, "sample_count": 5, "error_ema": 0.20792406797409058, "priority_score": 0.9320099353790283, "sampling_probability": 2.6640902433427982e-05, "seen": 1, "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 = \\ $.", "answer_preview": "-3", "source": "cn_k12" }, { "sample_id": 11477, "sample_count": 6, "error_ema": 0.20318952202796936, "priority_score": 0.8778427243232727, "sampling_probability": 2.52514273597626e-05, "seen": 1, "prompt_preview": "In a plane, some parallel lines are intersected by a family of another 8 parallel lines. There are 280 parallelograms in the network thus formed. How many parallel lines are in the first set of lines?", "answer_preview": "10", "source": "orca_math" }, { "sample_id": 17843, "sample_count": 4, "error_ema": 0.20249629020690918, "priority_score": 0.9956753253936768, "sampling_probability": 2.8372072847560048e-05, "seen": 1, "prompt_preview": "Given that the line $x+y-m=0$ is perpendicular to the line $x+(3-2m)y=0$, find the value of the real number $m$.", "answer_preview": "1", "source": "cn_k12" }, { "sample_id": 17567, "sample_count": 4, "error_ema": 0.20094257593154907, "priority_score": 0.9948984384536743, "sampling_probability": 2.8350284992484376e-05, "seen": 1, "prompt_preview": "Given that in the expansion of $(1+x)^n$, the binomial coefficients of the third and the eighth terms are equal, the sum of the binomial coefficients of the odd terms is \\_\\_\\_\\_\\_\\_.", "answer_preview": "2048", "source": "cn_k12" }, { "sample_id": 25514, "sample_count": 5, "error_ema": 0.20055696368217468, "priority_score": 0.9279171228408813, "sampling_probability": 2.653329647728242e-05, "seen": 1, "prompt_preview": "The distance between points A and B is 1200 meters. Da Cheng sets off from point A, and 6 minutes later, Xiao Gong sets off from point B. After another 12 minutes, they meet. Da Cheng walks 20 meters more per minute than Xiao Gong. How many", "answer_preview": "32", "source": "olympiads" }, { "sample_id": 8422, "sample_count": 5, "error_ema": 0.2002069056034088, "priority_score": 0.9277226328849792, "sampling_probability": 2.6528196030994877e-05, "seen": 1, "prompt_preview": "Worker A takes some hours to do a job. Worker B takes 6 hours to do the same job. Working together but independently, it takes both A and B 3.428571428571429 hours to do the same job. How long does it take for Worker A to do the job alone?", "answer_preview": "8.4", "source": "orca_math" }, { "sample_id": 12312, "sample_count": 5, "error_ema": 0.1976688802242279, "priority_score": 0.9263126254081726, "sampling_probability": 2.6491232347325422e-05, "seen": 1, "prompt_preview": "Given that point P and three non-collinear points A, B, and C are coplanar, and for any point O in space, it holds that $$\\overrightarrow {OP} = 2\\overrightarrow {OA} + \\overrightarrow {OB} + \\lambda \\overrightarrow {OC}$$, then $\\lambda = ", "answer_preview": "2", "source": "cn_k12" }, { "sample_id": 25079, "sample_count": 4, "error_ema": 0.19749373197555542, "priority_score": 0.9931740760803223, "sampling_probability": 2.830198354786262e-05, "seen": 1, "prompt_preview": "The cost of a slice of cake is three-fourths of the cost of a cup of milk tea. If the milk tea costs $2.40, how much do 2 slices of cake and 1 cup of milk tea cost?", "answer_preview": "6", "source": "openmath" }, { "sample_id": 22724, "sample_count": 5, "error_ema": 0.19445118308067322, "priority_score": 0.9245250225067139, "sampling_probability": 2.6444442482898012e-05, "seen": 1, "prompt_preview": "A wire is cut into two pieces so that one piece is 2/3 of the other. The shorter piece is 27.999999999999993 cm long. How long was the wire before it was cut?", "answer_preview": "46.67", "source": "orca_math" }, { "sample_id": 6807, "sample_count": 5, "error_ema": 0.19375310838222504, "priority_score": 0.9241371750831604, "sampling_probability": 2.643430525495205e-05, "seen": 1, "prompt_preview": "Truck X is some miles ahead of Truck Y, which is traveling the same direction along the same route as Truck X. If Truck X is traveling at an average speed of 47 miles per hour and Truck Y is traveling at an average speed of 53 miles per hou", "answer_preview": "23", "source": "orca_math" }, { "sample_id": 2709, "sample_count": 4, "error_ema": 0.19344374537467957, "priority_score": 0.9911490678787231, "sampling_probability": 2.824536568368785e-05, "seen": 1, "prompt_preview": "If some machines can finish a job in 36 days, then 5 more machines would be needed to finish the job in one-fourth less time. How many machines were initially working on the job?", "answer_preview": "20", "source": "orca_math" }, { "sample_id": 5605, "sample_count": 4, "error_ema": 0.19344374537467957, "priority_score": 0.9911490678787231, "sampling_probability": 2.824536568368785e-05, "seen": 1, "prompt_preview": "A rectangular tiled patio is composed of 48 square tiles. The rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles. After the change in layout, the patio will still have 48 tiles, and ", "answer_preview": "6", "source": "orca_math" }, { "sample_id": 16746, "sample_count": 4, "error_ema": 0.19344374537467957, "priority_score": 0.9911490678787231, "sampling_probability": 2.824536568368785e-05, "seen": 1, "prompt_preview": "The drama club meets in the school auditorium every 3 days, and the choir meets there every 5 days. If the groups are both meeting in the auditorium today, then how many days from now will they next have to share the auditorium?", "answer_preview": "30", "source": "orca_math" }, { "sample_id": 18647, "sample_count": 4, "error_ema": 0.19344374537467957, "priority_score": 0.9911490678787231, "sampling_probability": 2.824536568368785e-05, "seen": 1, "prompt_preview": "The sum of ages of 5 children is 50 years, and the age of the youngest child is 4 years. What is the interval between the birth of each child in years?", "answer_preview": "3.4", "source": "orca_math" }, { "sample_id": 21439, "sample_count": 4, "error_ema": 0.19344374537467957, "priority_score": 0.9911490678787231, "sampling_probability": 2.824536568368785e-05, "seen": 1, "prompt_preview": "Convert the decimal number 365 to an octal number.", "answer_preview": "555_8", "source": "cn_k12" }, { "sample_id": 27266, "sample_count": 4, "error_ema": 0.19344374537467957, "priority_score": 0.9911490678787231, "sampling_probability": 2.824536568368785e-05, "seen": 1, "prompt_preview": "Given \\( P = X^3 - 3X^2 - 1 \\), calculate the sum of the cubes of the roots (real or complex) of \\( P \\).", "answer_preview": "24", "source": "olympiads" }, { "sample_id": 6840, "sample_count": 4, "error_ema": 0.19300499558448792, "priority_score": 0.9909296631813049, "sampling_probability": 2.8239237508387305e-05, "seen": 1, "prompt_preview": "Eliza has 4 siblings. The total height of all 5 siblings combined is 330 inches. Two of her siblings are both 66 inches tall. Another sibling has a certain height. If Eliza is 2 inches shorter than the last sibling and she is 68 inches tall", "answer_preview": "70", "source": "orca_math" }, { "sample_id": 28119, "sample_count": 4, "error_ema": 0.19246718287467957, "priority_score": 0.9906607866287231, "sampling_probability": 2.823173053911887e-05, "seen": 1, "prompt_preview": "120 granite slabs weighing 7 tons each and 80 slabs weighing 9 tons each have been stockpiled at the quarry. A railroad platform can hold up to 40 tons. What is the minimum number of platforms required to transport all the slabs?", "answer_preview": "40", "source": "olympiads" }, { "sample_id": 28553, "sample_count": 4, "error_ema": 0.19201990962028503, "priority_score": 0.9904371500015259, "sampling_probability": 2.8225487767485902e-05, "seen": 1, "prompt_preview": "Robin's class is going on a field trip to the zoo. If each van can hold 8 people and there are 22 students and 2 adults going, how many vans will they need?", "answer_preview": "4", "source": "orca_math" }, { "sample_id": 19269, "sample_count": 4, "error_ema": 0.19186171889305115, "priority_score": 0.9903580546379089, "sampling_probability": 2.8223279514349997e-05, "seen": 1, "prompt_preview": "The length of the bridge is 200 m, which a 100 m long train crosses in 60 sec. What is the speed of the train?", "answer_preview": "18", "source": "orca_math" }, { "sample_id": 19546, "sample_count": 4, "error_ema": 0.19186171889305115, "priority_score": 0.9903580546379089, "sampling_probability": 2.8223279514349997e-05, "seen": 1, "prompt_preview": "A school has 26 senior teachers, 104 intermediate teachers, and a certain number of other teachers. To understand the salary situation of the teachers in the school, a stratified sampling of 56 people is conducted from all the teachers in t", "answer_preview": "52", "source": "cn_k12" }, { "sample_id": 18076, "sample_count": 6, "error_ema": 0.191616952419281, "priority_score": 0.8708992004394531, "sampling_probability": 2.507864155631978e-05, "seen": 1, "prompt_preview": "what is the smallest number which when diminished by 12 , is divisible 8 , 12 , 22 and 24 ?", "answer_preview": "252", "source": "orca_math" }, { "sample_id": 14258, "sample_count": 4, "error_ema": 0.19122889637947083, "priority_score": 0.9900416135787964, "sampling_probability": 2.8214450139785185e-05, "seen": 1, "prompt_preview": "a river 2 m deep and 45 m wide is flowing at the rate of 3 kmph the amount of water that runs into the sea per minute is ?", "answer_preview": "9000", "source": "orca_math" }, { "sample_id": 5708, "sample_count": 4, "error_ema": 0.1896468698978424, "priority_score": 0.9892506003379822, "sampling_probability": 2.8192387617309578e-05, "seen": 1, "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", "source": "orca_math" }, { "sample_id": 10272, "sample_count": 6, "error_ema": 0.18936914205551147, "priority_score": 0.8695504665374756, "sampling_probability": 2.5045212169061415e-05, "seen": 1, "prompt_preview": "If 5% more is gained by selling an article for Rs. 360 than by selling it for Rs. 340, what is the cost of the article?", "answer_preview": "400", "source": "orca_math" }, { "sample_id": 15224, "sample_count": 6, "error_ema": 0.18896076083183289, "priority_score": 0.869305431842804, "sampling_probability": 2.5039142201421782e-05, "seen": 1, "prompt_preview": "Two circles intersect at points A(1, 3) and B(m, -1). The centers of both circles lie on the line $x - y + c = 0$. Find the value of $m + c$.", "answer_preview": "-1", "source": "cn_k12" }, { "sample_id": 1093, "sample_count": 4, "error_ema": 0.18886488676071167, "priority_score": 0.9888596534729004, "sampling_probability": 2.8181491870782338e-05, "seen": 1, "prompt_preview": "The mean of 100 values was 235. It was detected on rechecking that three values, 190, 215, and 150, were wrongly copied as 170, 195, and 130 for the computation of the mean. Find the correct mean after correcting these values.", "answer_preview": "235.60", "source": "orca_math" }, { "sample_id": 25173, "sample_count": 4, "error_ema": 0.1884603500366211, "priority_score": 0.9886573553085327, "sampling_probability": 2.8175853003631346e-05, "seen": 1, "prompt_preview": "In a mathematics competition, 1000 students are numbered as follows: 0001, 0002, 0003, ..., 1000. It is planned to draw a sample of 50 students by dividing them into 50 parts using systematic sampling. If the first part includes the numbers", "answer_preview": "0195", "source": "cn_k12" }, { "sample_id": 9448, "sample_count": 4, "error_ema": 0.187443345785141, "priority_score": 0.9881488680839539, "sampling_probability": 2.8161690352135338e-05, "seen": 1, "prompt_preview": "a train travelling at 48 kmph completely crosses another train having half its length and travelling in opposite direction at 42 kmph , in 12 seconds . it also passes a railway platform in 45 seconds . the length of the platform is", "answer_preview": "600", "source": "orca_math" }, { "sample_id": 2724, "sample_count": 4, "error_ema": 0.18607330322265625, "priority_score": 0.9874638319015503, "sampling_probability": 2.814261824823916e-05, "seen": 1, "prompt_preview": "A son is 4 times younger than his dad. The difference in their ages is 27. How old is the dad if the son is 9 years old?", "answer_preview": "63", "source": "orca_math" }, { "sample_id": 13294, "sample_count": 5, "error_ema": 0.1851896047592163, "priority_score": 0.9193796515464783, "sampling_probability": 2.6310231987736188e-05, "seen": 1, "prompt_preview": "Given that the internal angles of a regular triangle and a dodecagon are 60\u00b0 and 150\u00b0 respectively, according to the conditions for plane tiling, the sum of the internal angles at a vertex must be 360\u00b0. Determine the number of possible ways", "answer_preview": "1", "source": "big_math" }, { "sample_id": 578, "sample_count": 4, "error_ema": 0.18347692489624023, "priority_score": 0.9861656427383423, "sampling_probability": 2.8106511308578774e-05, "seen": 1, "prompt_preview": "A statue is being carved by a sculptor. The original piece of marble weighed some amount. In the first week 30 percent is cut away. In the second week 30 percent of the remainder is cut away. In the third week the statue is completed when 1", "answer_preview": "299.94", "source": "orca_math" }, { "sample_id": 17382, "sample_count": 5, "error_ema": 0.1831236183643341, "priority_score": 0.9182319045066833, "sampling_probability": 2.628038782859221e-05, "seen": 1, "prompt_preview": "Nelly is very pleased with the painting she bought at the auction. She tells her daughter that she outbid her rival Joe by paying $2000 more than a certain multiple of his bid. Joe\u2019s bid was $160,000, and Nelly got the painting for $482,000", "answer_preview": "2", "source": "orca_math" }, { "sample_id": 22380, "sample_count": 4, "error_ema": 0.18294373154640198, "priority_score": 0.985899031162262, "sampling_probability": 2.809910620271694e-05, "seen": 1, "prompt_preview": "Given $$\\frac {a+bi}{2-i} = 3+i, \\quad (a, b \\in \\mathbb{R}, i \\text{ is the imaginary unit}),$$ find the value of $a+b$.", "answer_preview": "20", "source": "cn_k12" }, { "sample_id": 28129, "sample_count": 4, "error_ema": 0.18260934948921204, "priority_score": 0.985731840133667, "sampling_probability": 2.809445868479088e-05, "seen": 1, "prompt_preview": "Find the sum of all roots of the equation $\\log_{2}(x+8)=\\frac{|x|}{2}$.", "answer_preview": "8", "source": "cn_k12" }, { "sample_id": 25044, "sample_count": 4, "error_ema": 0.18257156014442444, "priority_score": 0.9857129454612732, "sampling_probability": 2.8093932996853255e-05, "seen": 1, "prompt_preview": "if the sum of two numbers is 18 and the sum of their squares is 220 , then the product of the numbers is", "answer_preview": "56", "source": "orca_math" }, { "sample_id": 3066, "sample_count": 5, "error_ema": 0.18164122104644775, "priority_score": 0.9174083471298218, "sampling_probability": 2.6258992875227705e-05, "seen": 1, "prompt_preview": "Jimmy and Irene go shopping for clothes on a Tuesday, where senior citizens get a 10% discount on their purchases. Jimmy picks out some shorts from the $15 rack. Irene grabs 5 shirts from the $17 rack. They give $117 to the cashier. How man", "answer_preview": "2", "source": "orca_math" }, { "sample_id": 26537, "sample_count": 4, "error_ema": 0.18130800127983093, "priority_score": 0.9850811958312988, "sampling_probability": 2.807639066304546e-05, "seen": 1, "prompt_preview": "Victor wanted to give each of his six friends an equal amount of candy. At the store he bought three hundred seventy-nine pieces total to give to them. How many more pieces should he have bought so he didn't have any extra?", "answer_preview": "378", "source": "orca_math" }, { "sample_id": 19816, "sample_count": 5, "error_ema": 0.18095384538173676, "priority_score": 0.9170264601707458, "sampling_probability": 2.624907938297838e-05, "seen": 1, "prompt_preview": "The sum of 1 ^ 1 + 2 ^ 2 + 3 ^ 3 + . . . + 7 ^ 7 is divided by 7. What is the remainder?", "answer_preview": "1", "source": "orca_math" }, { "sample_id": 19895, "sample_count": 4, "error_ema": 0.17920546233654022, "priority_score": 0.9840298891067505, "sampling_probability": 2.804721771099139e-05, "seen": 1, "prompt_preview": "The tangent line to the graph of the function $y=x^2$ ($x>0$) at the point $(a_k, a_k^2)$ intersects the x-axis at the x-coordinate $a_{k+1}$, where $k$ is a positive integer. Given $a_1=16$, find the sum $a_1+a_3+a_5$.", "answer_preview": "133", "source": "cn_k12" }, { "sample_id": 1886, "sample_count": 5, "error_ema": 0.17776528000831604, "priority_score": 0.915255069732666, "sampling_probability": 2.6203138986602426e-05, "seen": 1, "prompt_preview": "Sheela deposits some amount in her bank savings account. If this is 28% of her monthly income, and her monthly income is Rs. 16071.42857142857, how much does she deposit in her bank savings account?", "answer_preview": "4500.00", "source": "orca_math" }, { "sample_id": 14090, "sample_count": 5, "error_ema": 0.17618979513645172, "priority_score": 0.9143797755241394, "sampling_probability": 2.6180468921666034e-05, "seen": 1, "prompt_preview": "In a chess tournament, there are 120 games played. Each participant plays a certain number of games with each of the remaining participants. If there are 16 participants, how many games does each participant play with the remaining particip", "answer_preview": "120", "source": "orca_math" }, { "sample_id": 28715, "sample_count": 4, "error_ema": 0.1760077178478241, "priority_score": 0.9824310541152954, "sampling_probability": 2.8002907129121013e-05, "seen": 1, "prompt_preview": "Three numbers are in the ratio of 3 : 4 : 5 and their LCM is 2400. What is the HCF of these three numbers?", "answer_preview": "20", "source": "orca_math" }, { "sample_id": 24890, "sample_count": 4, "error_ema": 0.1739734262228012, "priority_score": 0.9814139008522034, "sampling_probability": 2.7974754630122334e-05, "seen": 1, "prompt_preview": "A 600 meter long train crosses a signal post in a certain amount of time. It takes 6 minutes to cross a 5.4 kilometer long bridge at the same speed. How long does it take for the train to cross the signal post?", "answer_preview": "40", "source": "orca_math" }, { "sample_id": 7049, "sample_count": 4, "error_ema": 0.1738061010837555, "priority_score": 0.9813302159309387, "sampling_probability": 2.797243905661162e-05, "seen": 1, "prompt_preview": "Tamia is making dinner. She is using 5 bell peppers to make her meal. She likes to have a variety of sizes so some will melt and some will be thick enough to eat whole. First she cuts each bell pepper into 20 large slices. Then she takes ha", "answer_preview": "2", "source": "orca_math" }, { "sample_id": 5896, "sample_count": 5, "error_ema": 0.17324109375476837, "priority_score": 0.9127416014671326, "sampling_probability": 2.6138090106542222e-05, "seen": 1, "prompt_preview": "James prints out 2 books. They are each 600 pages long. He prints out double-sided and a certain number of pages per side. He uses 150 sheets of paper. How many pages does he print per side?", "answer_preview": "8", "source": "orca_math" }, { "sample_id": 21051, "sample_count": 4, "error_ema": 0.17318978905677795, "priority_score": 0.98102205991745, "sampling_probability": 2.7963917091256008e-05, "seen": 1, "prompt_preview": "The average American consumes 1483 pounds of candy in a lifetime. Assuming that 1 year $=$ 52 weeks and the average life-span is 75 years, how many pounds of candy per week does the average American consume? Express your answer as a decimal", "answer_preview": ".38", "source": "math" }, { "sample_id": 15807, "sample_count": 5, "error_ema": 0.17271743714809418, "priority_score": 0.9124506711959839, "sampling_probability": 2.6130570404347964e-05, "seen": 1, "prompt_preview": "How many pieces of 137 2/3 cm length can be cut from a rod of 58.75 meters long?", "answer_preview": "58.75", "source": "orca_math" }, { "sample_id": 27057, "sample_count": 4, "error_ema": 0.17194527387619019, "priority_score": 0.9803998470306396, "sampling_probability": 2.7946716727456078e-05, "seen": 1, "prompt_preview": "A cube of sides 9 is first painted red and then cut into smaller cubes of some side length. There are 12 smaller cubes with paint on exactly 2 sides. What is the side length of the smaller cubes?", "answer_preview": "4.5", "source": "orca_math" }, { "sample_id": 19992, "sample_count": 4, "error_ema": 0.17125311493873596, "priority_score": 0.980053722858429, "sampling_probability": 2.7937152481172234e-05, "seen": 1, "prompt_preview": "Martin owns a farm with some hens. These hens lay 80 eggs in 10 days. Martin decided to buy 15 more hens. All hens will lay 300 eggs in 15 days. How many hens did Martin initially have?", "answer_preview": "25", "source": "orca_math" }, { "sample_id": 16720, "sample_count": 3, "error_ema": 0.17124617099761963, "priority_score": 1.0733911991119385, "sampling_probability": 3.063849362661131e-05, "seen": 1, "prompt_preview": "A sequence $\\\\{a_n\\\\}$ is defined by the formula $a_n=(-1)^{n+1}(2n-1)$. Compute the sum of the first $100$ terms.", "answer_preview": "100", "source": "cn_k12" }, { "sample_id": 9126, "sample_count": 5, "error_ema": 0.1707894653081894, "priority_score": 0.9113795757293701, "sampling_probability": 2.6102909032488242e-05, "seen": 1, "prompt_preview": "tough and tricky questions : remainders . 1 ^ 1 + 2 ^ 2 + 3 ^ 3 + . . . + 7 ^ 7 is divided by 7 . what is the remainder ?", "answer_preview": "1", "source": "orca_math" }, { "sample_id": 9648, "sample_count": 4, "error_ema": 0.17066249251365662, "priority_score": 0.9797584414482117, "sampling_probability": 2.7928992494707927e-05, "seen": 1, "prompt_preview": "In the sequence $\\{a_n\\}$, $a_{n-1}=2a_n$. If $a_5=4$, then the product $a_4a_5a_6=$ _______.", "answer_preview": "128", "source": "cn_k12" }, { "sample_id": 20114, "sample_count": 4, "error_ema": 0.17066249251365662, "priority_score": 0.9797584414482117, "sampling_probability": 2.7928992494707927e-05, "seen": 1, "prompt_preview": "The problem involves the application of the laws of exponents and logarithms, and is of medium difficulty. Solve the following expression: $\\left({27}^{\\frac{2}{3}}-{2}^{{{\\log }\\_{2}}3}\\bullet {{\\log }\\_{2}}\\dfrac{1}{8}+{\\log }_{10} 4+{\\lo", "answer_preview": "20.000", "source": "cn_k12" }, { "sample_id": 20691, "sample_count": 4, "error_ema": 0.17066249251365662, "priority_score": 0.9797584414482117, "sampling_probability": 2.7928992494707927e-05, "seen": 1, "prompt_preview": "The speed of a boat in still water is some km/hr, and the rate of current is 6 km/hr. The distance travelled downstream in 44 minutes is 35.2 km. What is the speed of the boat in still water?", "answer_preview": "42.0", "source": "orca_math" }, { "sample_id": 13501, "sample_count": 4, "error_ema": 0.1697835922241211, "priority_score": 0.9793189764022827, "sampling_probability": 2.7916859835386276e-05, "seen": 1, "prompt_preview": "On the first day of school, Mrs. McGillicuddy had 25 students registered for the morning session of kindergarten, but 3 students were absent; and she had some students registered for the afternoon session, but 4 students were absent. Mrs. M", "answer_preview": "17", "source": "orca_math" }, { "sample_id": 18706, "sample_count": 4, "error_ema": 0.1683843731880188, "priority_score": 0.9786193370819092, "sampling_probability": 2.789755308185704e-05, "seen": 1, "prompt_preview": "Given a sequence $\\{a_n\\}$ satisfying $\\log_{2}a_{n+1}=1+\\log_{2}a_{n}$ $(n\\in\\mathbb{N}^*)$, and $a_{1}+a_{2}+a_{3}+\\ldots+a_{10}=1$, then $\\log_{2}(a_{101}+a_{102}+\\ldots+a_{110})=$ ______.", "answer_preview": "10", "source": "cn_k12" }, { "sample_id": 11479, "sample_count": 4, "error_ema": 0.16822615265846252, "priority_score": 0.9785402417182922, "sampling_probability": 2.7895370294572785e-05, "seen": 1, "prompt_preview": "Given that the terminal side of angle a passes through point P(1,-2), calculate the value of 2*sin(a)/cos(a). Express your answer as a single number.", "answer_preview": "4", "source": "big_math" }, { "sample_id": 18928, "sample_count": 4, "error_ema": 0.1675652414560318, "priority_score": 0.9782097935676575, "sampling_probability": 2.788625715766102e-05, "seen": 1, "prompt_preview": "Jake's neighbors hire him to mow their lawn and plant some flowers. Mowing the lawn takes 1 hour and pays $15. If Jake wants to make $20/hour working for the neighbors, and planting the flowers takes a certain amount of time, Jake should ch", "answer_preview": "2.25", "source": "orca_math" }, { "sample_id": 854, "sample_count": 4, "error_ema": 0.1675174981355667, "priority_score": 0.9781859517097473, "sampling_probability": 2.7885596864507534e-05, "seen": 1, "prompt_preview": "Given that \\\\(k\\\\) is a constant, if the minimum value of the function \\\\(y=x^2+\\frac{k}{x} (x > 0, k > 0)\\\\) is \\\\(3\\\\), then the value of \\\\(k\\\\) at this time is.", "answer_preview": "1", "source": "cn_k12" }, { "sample_id": 8165, "sample_count": 4, "error_ema": 0.16710293292999268, "priority_score": 0.9779786467552185, "sampling_probability": 2.7879881599801593e-05, "seen": 1, "prompt_preview": "How many pieces of 85 cm length can be cut from a rod of 34 meters long?", "answer_preview": "34", "source": "orca_math" }, { "sample_id": 7024, "sample_count": 3, "error_ema": 0.16710275411605835, "priority_score": 1.07161545753479, "sampling_probability": 3.058474248973653e-05, "seen": 1, "prompt_preview": "Define a new operation \"\u203b\" with the rule: $a\u203bb=ab-a-b$. For instance, $1\u203b2=1\u00d72-1-2=-1$. If the two roots of the equation $x^2+x-1=0$ are $x_1$ and $x_2$, then $x_1\u203bx_2 =$ __________.", "answer_preview": "1", "source": "cn_k12" }, { "sample_id": 27363, "sample_count": 6, "error_ema": 0.1662636697292328, "priority_score": 0.8556872010231018, "sampling_probability": 2.4704206225578673e-05, "seen": 1, "prompt_preview": "a leak in the bottom of a tank can empty the full tank in 6 hours . an inlet pipe fills water at the rate of 4 litres a minute . when the tank is full , the inlet is opened and due to the leak the tank is empty in 8 hours . the capacity of ", "answer_preview": "823", "source": "orca_math" }, { "sample_id": 5481, "sample_count": 5, "error_ema": 0.16610954701900482, "priority_score": 0.9087796211242676, "sampling_probability": 2.603588654892519e-05, "seen": 1, "prompt_preview": "Use the Horner's method to calculate the polynomial $f(x) = x^5 + 4x^4 + 3x^3 + 2x^2 + 1$ when $x=5$. The sum of the number of multiplication operations and addition operations is \\_\\_\\_\\_\\_\\_.", "answer_preview": "8", "source": "cn_k12" }, { "sample_id": 25681, "sample_count": 4, "error_ema": 0.16512538492679596, "priority_score": 0.9769898653030396, "sampling_probability": 2.785263495752588e-05, "seen": 1, "prompt_preview": "If a = 105 and a ^ 3 = some number * 25 * 35 * 63, what is the value of that number?", "answer_preview": "7", "source": "orca_math" }, { "sample_id": 6801, "sample_count": 5, "error_ema": 0.16447728872299194, "priority_score": 0.9078727960586548, "sampling_probability": 2.6012547095888294e-05, "seen": 1, "prompt_preview": "Find the value of 72516 x 9999. What is the product of these two numbers?", "answer_preview": "724987484", "source": "orca_math" }, { "sample_id": 18890, "sample_count": 4, "error_ema": 0.1643378734588623, "priority_score": 0.9765961170196533, "sampling_probability": 2.7841793780680746e-05, "seen": 1, "prompt_preview": "A farm cultivated a type of rice in the same paddy field for 8 consecutive years. The annual average yields (in kg) for these years are as follows: 450, 430, 460, 440, 450, 440, 470, 460. Calculate the variance of the dataset. Express your ", "answer_preview": "171", "source": "big_math" }, { "sample_id": 6299, "sample_count": 4, "error_ema": 0.16382217407226562, "priority_score": 0.976338267326355, "sampling_probability": 2.783469608402811e-05, "seen": 1, "prompt_preview": "While reading in bed with his wife Susan, Charlie heard a noise at the door. It was Sarah entering the bedroom with 4 friends. If there were also 8 people in the living room, how many people are in the house?", "answer_preview": "14", "source": "orca_math" }, { "sample_id": 4722, "sample_count": 4, "error_ema": 0.16240429878234863, "priority_score": 0.9756293296813965, "sampling_probability": 2.781518742267508e-05, "seen": 1, "prompt_preview": "If a is the smallest positive integer such that 5880 multiplied by a is the square of an integer, what is the value of a?", "answer_preview": "15", "source": "orca_math" }, { "sample_id": 19243, "sample_count": 6, "error_ema": 0.16222189366817474, "priority_score": 0.8532621264457703, "sampling_probability": 2.464503631927073e-05, "seen": 1, "prompt_preview": "By the time Anne is two times as old as Emile, Emile will be six times as old as Maude. If Anne will be 96 years old, how old will Maude be at that time?", "answer_preview": "96", "source": "orca_math" }, { "sample_id": 25709, "sample_count": 3, "error_ema": 0.16219687461853027, "priority_score": 1.069512963294983, "sampling_probability": 3.052121610380709e-05, "seen": 1, "prompt_preview": "Find the number of positive integer solutions for the equation 3x + 5y = 501. Express your answer as a single integer.", "answer_preview": "34", "source": "big_math" }, { "sample_id": 1707, "sample_count": 3, "error_ema": 0.1616782397031784, "priority_score": 1.0692906379699707, "sampling_probability": 3.0514507670886815e-05, "seen": 1, "prompt_preview": "What are the last two digits of \\(1 \\times 2 \\times 3 \\times 4 \\times \\cdots \\times 2004 \\times 2005 \\times 2006\\)?", "answer_preview": "00", "source": "olympiads" }, { "sample_id": 22369, "sample_count": 4, "error_ema": 0.16138514876365662, "priority_score": 0.9751197695732117, "sampling_probability": 2.7801175747299567e-05, "seen": 1, "prompt_preview": "From a vertex of a pentagon, how many diagonals can be drawn?", "answer_preview": "3", "source": "cn_k12" }, { "sample_id": 8411, "sample_count": 4, "error_ema": 0.16076405346393585, "priority_score": 0.9748092293739319, "sampling_probability": 2.7792637411039323e-05, "seen": 1, "prompt_preview": "Given an arithmetic sequence $\\{a_n\\}$, the sum of the first $m$ terms is 30, and the sum of the first $2m$ terms is 100. Find the sum of the first $3m$ terms.", "answer_preview": "170", "source": "cn_k12" }, { "sample_id": 29271, "sample_count": 4, "error_ema": 0.16041092574596405, "priority_score": 0.9746326208114624, "sampling_probability": 2.7787784347310662e-05, "seen": 1, "prompt_preview": "Given the function $f(x) = mx^3 + nx + 1$ (where $mn \\neq 0$), and $f(-1) = 5$, then $f(1) = \\_\\_\\_\\_\\_\\_$.", "answer_preview": "7", "source": "cn_k12" }, { "sample_id": 4609, "sample_count": 4, "error_ema": 0.1599796563386917, "priority_score": 0.9744170308113098, "sampling_probability": 2.778186353680212e-05, "seen": 1, "prompt_preview": "Sangita is required to fly a certain number of hours to earn an airplane pilot certificate. She has already completed 50 hours of day flying, 9 hours of night flying, and 121 hours flying cross-country. To meet her goal in exactly 6 months,", "answer_preview": "1140", "source": "orca_math" }, { "sample_id": 5536, "sample_count": 5, "error_ema": 0.15913650393486023, "priority_score": 0.9049057364463806, "sampling_probability": 2.5936333258869126e-05, "seen": 1, "prompt_preview": "Solve the equation for x: 19(x + y) + 17 = 19(-x + y) - 21. What is the solution for x?", "answer_preview": "-2", "source": "orca_math" }, { "sample_id": 1808, "sample_count": 3, "error_ema": 0.15865275263786316, "priority_score": 1.0679939985275269, "sampling_probability": 3.047540485567879e-05, "seen": 1, "prompt_preview": "Annie calculated she has three times more toys than Mike, and a certain difference less than Tom. Mike has 6 toys. Annie, Mike, and Tom have a total of 56 toys. What is the difference between the number of toys Annie has and the number of t", "answer_preview": "2", "source": "orca_math" }, { "sample_id": 4743, "sample_count": 4, "error_ema": 0.15679165720939636, "priority_score": 0.9728230237960815, "sampling_probability": 2.773810592771042e-05, "seen": 1, "prompt_preview": "A train 100 m long running at a certain speed takes 10.889128869690424 seconds to cross a bridge 142 m in length. What is the speed of the train in km/hr?", "answer_preview": "79.99", "source": "orca_math" }, { "sample_id": 20998, "sample_count": 3, "error_ema": 0.15678808093070984, "priority_score": 1.067194938659668, "sampling_probability": 3.0451334168901667e-05, "seen": 1, "prompt_preview": "For what value of the parameter \\( m \\) is the sum of the squares of the roots of the equation \\[ x^{2}-(m+1) x+m-1=0 \\] the smallest?", "answer_preview": "3", "source": "olympiads" }, { "sample_id": 1442, "sample_count": 5, "error_ema": 0.15640947222709656, "priority_score": 0.9033907055854797, "sampling_probability": 2.5897508749039844e-05, "seen": 1, "prompt_preview": "Given the function f(x) = ln((x^2 + 1)) / (x + 4), find the x-value such that the functions y = f(3-x) and y = f(3+x) are symmetric about a line x = a. Express your answer as a single numerical value.", "answer_preview": "0", "source": "big_math" }, { "sample_id": 26955, "sample_count": 3, "error_ema": 0.15574218332767487, "priority_score": 1.066746711730957, "sampling_probability": 3.0437840905506164e-05, "seen": 1, "prompt_preview": "A sum was put at simple interest at a certain rate for 10 years. Had it been put at a 5% higher rate, it would have fetched Rs. 200 more. What was the sum?", "answer_preview": "2000", "source": "orca_math" }, { "sample_id": 23123, "sample_count": 3, "error_ema": 0.15524402260780334, "priority_score": 1.0665332078933716, "sampling_probability": 3.0431414415943436e-05, "seen": 1, "prompt_preview": "There are 2 red balls, 3 yellow balls, and 4 white balls, with balls of the same color being indistinguishable. How many different ways can these 9 balls be arranged in a row? (Answer with a number)", "answer_preview": "2520", "source": "cn_k12" }, { "sample_id": 21218, "sample_count": 5, "error_ema": 0.15503081679344177, "priority_score": 0.902624785900116, "sampling_probability": 2.5877898224280216e-05, "seen": 1, "prompt_preview": "A number consists of 4 tens of millions, 6 hundreds of thousands, and 5 hundreds. Write this number.", "answer_preview": "46000050", "source": "cn_k12" }, { "sample_id": 1779, "sample_count": 5, "error_ema": 0.15463322401046753, "priority_score": 0.9024038910865784, "sampling_probability": 2.5872248443192802e-05, "seen": 1, "prompt_preview": "January 1, 2015 was a Thursday. What day of the week was June 1, 2015?", "answer_preview": "1", "source": "olympiads" }, { "sample_id": 16764, "sample_count": 3, "error_ema": 0.1545732319355011, "priority_score": 1.066245675086975, "sampling_probability": 3.0422763302340172e-05, "seen": 1, "prompt_preview": "Given that point A $(a, 4)$ is symmetric to point B across the y-axis, and the coordinates of point B are $(-2, b)$, find the value of $a+b$.", "answer_preview": "2", "source": "cn_k12" } ] }