data_source large_stringclasses 1
value | prompt listlengths 1 1 | reward_model dict | extra_info dict |
|---|---|---|---|
math | [
{
"content": "The first three stages of a pattern are shown below, in which each line segment represents a toothpick. If the pattern continues such that at each successive stage, three toothpicks are added to the previous arrangement, how many toothpicks are necessary to create the arrangement for the 250th sta... | {
"ground_truth": "751",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 686
} |
math | [
{
"content": "The minute hand on a clock points at the 12. After rotating $120^{\\circ}$ clockwise, which number will it point at? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "4",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 415.75
} |
math | [
{
"content": "If $x - 2x + 3x = 100$, what is the value of $x$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "50",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 158.75
} |
math | [
{
"content": "What is the eighth term in the arithmetic sequence $\\frac 23, 1, \\frac 43, \\dots$? Express your answer in simplest form. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "3",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 264.25
} |
math | [
{
"content": "Find the maximum value of the real constant $C$ such that $x^{2}+y^{2}+1\\geq C(x+y)$ , and $ x^{2}+y^{2}+xy+1\\geq C(x+y)$ for all reals $x,y$ . Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\sqrt{2}",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 1123.75
} |
math | [
{
"content": "What is the integer value of $y$ in the arithmetic sequence $2^2, y, 2^4$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "10",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 237
} |
math | [
{
"content": "A math conference is hosting a series of lectures by seven distinct lecturers. Dr. Smith's lecture depends on Dr. Jones’s lecture, and additionally, Dr. Brown's lecture depends on Dr. Green’s lecture. How many valid orders can these seven lecturers be scheduled, given these dependencies? Please ou... | {
"ground_truth": "1260",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 1033.5
} |
math | [
{
"content": "Suppose that $a^2$ varies inversely with $b^3$. If $a=7$ when $b=3$, find the value of $a^2$ when $b=6$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "6.125",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 627.25
} |
math | [
{
"content": "I have 5 marbles numbered 1 through 5 in a bag. Suppose I take out two different marbles at random. What is the expected value of the sum of the numbers on the marbles? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "6",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 1061.75
} |
math | [
{
"content": "Fifty cards, numbered 1-50, are placed in a box. One card is randomly selected. What is the probability that the number on the card is prime and is a multiple of 7? Express your answer as a common fraction. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{1}{50}",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 481.25
} |
math | [
{
"content": "Given the letters in the word $SUCCESS$, determine the number of distinguishable rearrangements where all the vowels are at the end. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "20",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 557
} |
math | [
{
"content": "Evaluate the infinite sum $\\sum_{n=0}^{\\infty}\\binom{2 n}{n} \\frac{1}{5^{n}}$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\sqrt{5}",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 347.75
} |
math | [
{
"content": "Given the vectors $\\overrightarrow{a}=(\\cos 40^{\\circ},\\sin 40^{\\circ})$, $\\overrightarrow{b}=(\\sin 20^{\\circ},\\cos 20^{\\circ})$, and $\\overrightarrow{u}= \\sqrt {3} \\overrightarrow{a}+λ \\overrightarrow{b}$ (where $λ∈R$), find the minimum value of $|\\overrightarrow{u}|$. Please outpu... | {
"ground_truth": "\\frac {\\sqrt {3}}{2}",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 841.5
} |
math | [
{
"content": "There is a positive integer $n$ such that $(n+1)! + (n+2)! = n! \\cdot 440$. What is the sum of the digits of $n$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "10",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 622.25
} |
math | [
{
"content": "How many integers satisfy the inequality $(x+3)^{2}\\leq1$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "3",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 464
} |
math | [
{
"content": "In a chess tournament, each pair of players plays exactly one game. The winner of each game receives 2 points, the loser receives 0 points, and in case of a draw, both players receive 1 point each. Four scorers have recorded the total score of the tournament, but due to negligence, the scores reco... | {
"ground_truth": "45",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 1090
} |
math | [
{
"content": "How many pairs $(m,n)$ of integers satisfy the equation $m+n=mn$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "2",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 430
} |
math | [
{
"content": "The product of two whole numbers is 24. Calculate the smallest possible sum of these two numbers. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "10",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 323
} |
math | [
{
"content": "What is the least positive integer with exactly $12$ positive factors? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "60",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 1007.25
} |
math | [
{
"content": "A cylinder has a radius of 5 cm and a height of 12 cm. What is the longest segment, in centimeters, that would fit inside the cylinder? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "2\\sqrt{61}",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 1355.25
} |
math | [
{
"content": "The area of a circle is doubled when its radius $r$ is increased by $n$. Then $r$ equals: Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "n(\\sqrt{2} + 1)",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 1054
} |
math | [
{
"content": "If $\\tan \\alpha= \\sqrt {2}$, then $2\\sin ^{2}\\alpha-\\sin \\alpha\\cos \\alpha+\\cos ^{2}\\alpha=$ \\_\\_\\_\\_\\_\\_ . Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac {5- \\sqrt {2}}{3}",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 950.75
} |
math | [
{
"content": "What is the sum of all four-digit integers from 1000 to 5000, where each number increases by 4 from the previous one? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "3003000",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 563.75
} |
math | [
{
"content": "Find the sum of all positive integral values of $n$ for which $\\frac{n+6}{n}$ is an integer. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "12",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 236.5
} |
math | [
{
"content": "Given a $6 \\times 6$ square of $36$ square blocks, find the number of different combinations of $4$ blocks that can be selected so that no two are in the same row or column. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "5400",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 1095.25
} |
math | [
{
"content": "\nA polynomial $P(x)$ with integer coefficients possesses the properties\n\n$$\nP(1)=2019, \\quad P(2019)=1, \\quad P(k)=k,\n$$\n\nwhere $k$ is an integer. Find this integer $k$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "1010",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 1502.5
} |
math | [
{
"content": "The value of $\\log_{10}{17}$ is between the consecutive integers $a$ and $b$. Find $a+b$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "3",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 578.25
} |
math | [
{
"content": "How many cubic centimeters are in the volume of a cone having a diameter of 12 cm and a slant height of 10 cm? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "96 \\pi",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 443.25
} |
math | [
{
"content": "Find all positive integer solutions $(m, n)$ to the following equation: $$ m^{2}=1!+2!+\\cdots+n! $$ Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "(1,1), (3,3)",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 1078.75
} |
math | [
{
"content": "A series of lockers, numbered 1 through 100, are all initially closed. Student 1 goes through and opens every locker. Student 3 goes through and \"flips\" every 3rd locker (\"fipping\") a locker means changing its state: if the locker is open he closes it, and if the locker is closed he opens it. ... | {
"ground_truth": "10",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 542.5
} |
math | [
{
"content": "Six congruent copies of the parabola $y = x^2$ are arranged in the plane so that each vertex is tangent to a circle, and each parabola is tangent to its two neighbors. Find the radius of the circle.\n\n[asy]\nunitsize(1 cm);\n\nreal func (real x) {\n return (x^2 + 3/4);\n}\n\npath parab = graph(... | {
"ground_truth": "\\frac{3}{4}",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 987.25
} |
math | [
{
"content": "$1,000,000,000,000-777,777,777,777=$ Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "$222,222,222,223$",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 74
} |
math | [
{
"content": "While walking on a plane surface, a traveler first headed 18 miles north, then 11 miles west, then 6 miles south and finally 6 miles east. How many miles from the starting point was the traveler after these four legs of the journey? Please output the final answer within \\boxed{}.",
"role": "u... | {
"ground_truth": "13",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 241
} |
math | [
{
"content": "Ana and Bonita were born on the same date in different years, $n$ years apart. Last year Ana was $5$ times as old as Bonita. This year Ana's age is the square of Bonita's age. What is $n?$ Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "12",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 568.5
} |
math | [
{
"content": "What is the sum of all the integers between -12.1 and 3.3? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "-72",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 478.5
} |
math | [
{
"content": "What is that largest positive integer $n$ for which $n^3+100$ is divisible by $n+10$?\n ~ pi_is_3.14\n ~ momeme Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "890",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 1322.5
} |
math | [
{
"content": "If $3 \times n=6 \times 2$, what is the value of $n$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "4",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 109.75
} |
math | [
{
"content": "What is the first nonzero digit to the right of the decimal point of the fraction $\\frac{1}{129}$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "7",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 265
} |
math | [
{
"content": "The value of $\\sqrt{3^{3}+3^{3}+3^{3}}$ is what? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "9",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 130
} |
math | [
{
"content": "If $(x + y)^2 = 25$ and $xy = 6$, what is the value of $x^2 + y^2$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "13",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 166
} |
math | [
{
"content": "If an integer is divisible by $4$ and the sum of its last two digits is $13$, then what is the product of its last two digits? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "42",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 486.5
} |
math | [
{
"content": "In $\\triangle PQR$, point $T$ is on side $QR$ such that $QT=6$ and $TR=10$. What is the ratio of the area of $\\triangle PQT$ to the area of $\\triangle PTR$? [asy]\nsize(6cm);\npair q = (0, 0); pair t = (6, 0); pair r = (16, 0);\npair p = (4, 8);\ndraw(p--q--r--cycle--t);\nlabel(\"$P$\", p, N);\... | {
"ground_truth": "3:5",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 443.75
} |
math | [
{
"content": "What is the area enclosed by the graph of $|x| + |3y| = 9$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "54",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 1390.25
} |
math | [
{
"content": "The yearly changes in the population census of a town for four consecutive years are, respectively, 25% increase, 25% increase, 25% decrease, 25% decrease. The net change over the four years, to the nearest percent, is: Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "-12",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 843
} |
math | [
{
"content": "Alice and Carol each have a rectangular sheet of paper. Alice has a sheet of paper measuring 10 inches by 12 inches and rolls it into a tube by taping the two 10-inch sides together. Carol rolls her sheet, which measures 8 inches by 15 inches, by taping the two 15-inch sides together. Calculate $\... | {
"ground_truth": "150",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 766
} |
math | [
{
"content": "Expand $-(3-c)(c+2(3-c))$. What is the sum of the coefficients of the expanded form? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "-10",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 337.75
} |
math | [
{
"content": "Given $(2x-1)^{5}=a\\_{0}+a\\_{1}x+a\\_{2}x^{2}+…+a\\_{5}x^{5}$, find the values of:\n\n(1) $a\\_{0}+a\\_{1}+a\\_{2}+a\\_{3}+a\\_{4}$,\n\n(2) $|a\\_{0}|+|a\\_{1}|+|a\\_{2}|+|a\\_{3}|+|a\\_{4}|+|a\\_{5}|$,\n\n(3) $a\\_{1}+a\\_{3}+a\\_{5}$,\n\n(4) $(a\\_{0}+a\\_{2}+a\\_{4})^{2}-(a\\_{1}+a\\_{3}+a\\_... | {
"ground_truth": "-243",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 1036.75
} |
math | [
{
"content": "Calculate using your preferred method!\n\n100 - 54 - 46 \n234 - (134 + 45) \n125 × 7 × 8 \n15 × (61 - 45) \n318 ÷ 6 + 165. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "218",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 433.75
} |
math | [
{
"content": "For each real number \\( x \\), \\( f(x) \\) is defined to be the minimum of the values of \\( 2x + 3 \\), \\( 3x - 2 \\), and \\( 25 - x \\). What is the maximum value of \\( f(x) \\)? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{53}{3}",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 1474.25
} |
math | [
{
"content": "The number of roots satisfying the equation $\\sqrt{5 - x} = x\\sqrt{5 - x}$ is: Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "2",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 422.5
} |
math | [
{
"content": "The value of \\(0.9 + 0.99\\) is: Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "1.89",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 30
} |
math | [
{
"content": "How many positive four-digit integers are divisible by both 7 and 6? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "215",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 630
} |
math | [
{
"content": "Find the greatest root of $f(x) = 15x^4-13x^2+2$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{\\sqrt{6}}{3}",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 725.5
} |
math | [
{
"content": "How many three-digit numbers satisfy the property that the middle digit is the average of the first and the last digits? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "45",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 1151
} |
math | [
{
"content": "Find all pairs $(n, p)$ of positive integers such that $p$ is prime and\n\\[ 1 + 2 + \\cdots + n = 3 \\cdot (1^2 + 2^2 + \\cdot + p^2). \\] Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "(5, 2)",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 1388.75
} |
math | [
{
"content": "What is $\\left(\\frac{6}{7}\\right)^2 \\cdot \\left(\\frac{1}{2}\\right)^2$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{9}{49}",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 198.5
} |
math | [
{
"content": "Expand the product ${(2x+3)(x+5)}$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "2x^2 + 13x + 15",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 151
} |
math | [
{
"content": "An acute triangle $ABC$ is inscribed in a circle of radius 1 with centre $O;$ all the angles of $ABC$ are greater than $45^\\circ.$ \n$B_{1}$ is the foot of perpendicular from $B$ to $CO,$ $B_{2}$ is the foot of perpendicular from $B_{1}$ to $AC.$ \nSimilarly, $C_{1}$ is the foot of perpendicular ... | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 871.5
} |
math | [
{
"content": "There are several sets of three different numbers whose sum is $15$ which can be chosen from $\\{ 1,2,3,4,5,6,7,8,9 \\}$. How many of these sets contain a $5$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "4",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 782.75
} |
math | [
{
"content": "A person rolls two dice simultaneously and gets the scores $a$ and $b$. The eccentricity $e$ of the ellipse $\\frac{y^2}{a^2} + \\frac{x^2}{b^2} = 1$ satisfies $e \\geq \\frac{\\sqrt{3}}{2}$. Calculate the probability that this event occurs. Please output the final answer within \\boxed{}.",
"... | {
"ground_truth": "\\frac{1}{4}",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 969.75
} |
math | [
{
"content": "The lines $x=\\frac{1}{4}y+a$ and $y=\\frac{1}{4}x+b$ intersect at the point $(1,2)$. What is $a+b$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{9}{4}",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 346.5
} |
math | [
{
"content": "Let $x,$ $y,$ and $z$ be real numbers such that\n\\[x^3 + y^3 + z^3 - 3xyz = 1.\\]Find the minimum value of $x^2 + y^2 + z^2.$ Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "1",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 1523.5
} |
math | [
{
"content": "Compute $\\sqrt{(31)(30)(29)(28)+1}$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "869",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 1103
} |
math | [
{
"content": "What is the largest value of $x$ such that the expression \\[\\dfrac{x+1}{8x^2-65x+8}\\] is not defined? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "8",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 326.5
} |
math | [
{
"content": "King Middle School has $1200$ students. Each student takes $5$ classes a day. Each teacher teaches $4$ classes. Each class has $30$ students and $1$ teacher. How many teachers are there at King Middle School? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "50",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 792.75
} |
math | [
{
"content": "How many numbers can you get by multiplying two or more distinct members of the set $\\{1,2,3,5,11\\}$ together? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "15",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 1393.5
} |
math | [
{
"content": "If the sum of the first $3n$ positive integers is $150$ more than the sum of the first $n$ positive integers, then the sum of the first $4n$ positive integers is Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "300",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 561.5
} |
math | [
{
"content": "Football tickets are normally priced at $15 each. After buying 5 tickets, any additional tickets are sold at a discounted price of $12 each. If Jane has $150, what is the maximum number of tickets she can buy? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "11",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 506.25
} |
math | [
{
"content": "In a collection of red, blue, and green marbles, there are $25\\%$ more red marbles than blue marbles, and there are $60\\%$ more green marbles than red marbles. Suppose that there are $r$ red marbles. What is the total number of marbles in the collection? Please output the final answer within \\b... | {
"ground_truth": "3.4r",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 475
} |
math | [
{
"content": "Phil rolls 6 fair 6-sided dice. What is the probability that at least two dice show the same number? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\dfrac{319}{324}",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 391.5
} |
math | [
{
"content": "Let $S = 1 - 2 + 3 - 4 + \\cdots + 2009 - 2010$. What is the residue of $S$, modulo 2010? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "1005",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 521.25
} |
math | [
{
"content": "Find the quadratic polynomial $p(x)$ such that $p(-7) = 0,$ $p(4) = 0,$ and $p(5) = -36.$ Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "-3x^2 - 9x + 84",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 534.75
} |
math | [
{
"content": "Convert the binary number $1101100_{(2)}$ to a decimal number. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "108",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 266
} |
math | [
{
"content": "If $\\frac{1}{9}+\\frac{1}{18}=\\frac{1}{\\square}$, what is the number that replaces the $\\square$ to make the equation true? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "6",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 230
} |
math | [
{
"content": "Simplify $t^3\\cdot t^4$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "t^7",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 31
} |
math | [
{
"content": "One angle of a parallelogram is 120 degrees, and two consecutive sides have lengths of 8 inches and 15 inches. What is the area of the parallelogram? Express your answer in simplest radical form. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "60\\sqrt{3}",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 499.5
} |
math | [
{
"content": "Find the radius of the circle with the equation $x^2 - 8x + y^2 - 10y + 34 = 0$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\sqrt{7}",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 524.5
} |
math | [
{
"content": "Find the sum of the $x$-coordinates of the solutions to the system of equations $y=|x^2-8x+12|$ and $y=4-x$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "16",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 703.5
} |
math | [
{
"content": "The integer $x$ has 12 positive factors. The numbers 12 and 15 are factors of $x$. What is $x$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "60",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 1008.75
} |
math | [
{
"content": "What is the remainder when $333^{333}$ is divided by $11$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "5",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 410.5
} |
math | [
{
"content": "The graph of $y = f(x)$ is shown below.\n\n[asy]\nunitsize(0.5 cm);\n\nreal func(real x) {\n real y;\n if (x >= -3 && x <= 0) {y = -2 - x;}\n if (x >= 0 && x <= 2) {y = sqrt(4 - (x - 2)^2) - 2;}\n if (x >= 2 && x <= 3) {y = 2*(x - 2);}\n return(y);\n}\n\nint i, n;\n\nfor (i = -5; i <= 5; ++i)... | {
"ground_truth": "\\text{A}",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 662
} |
math | [
{
"content": "Find a necessary and sufficient condition on the natural number $ n$ for the equation\n\\[ x^n \\plus{} (2 \\plus{} x)^n \\plus{} (2 \\minus{} x)^n \\equal{} 0\n\\]\nto have a integral root. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "n=1",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 1441
} |
math | [
{
"content": "Marie has 75 raspberry lollipops, 132 mint lollipops, 9 blueberry lollipops, and 315 coconut lollipops. She decides to distribute these lollipops equally among her 13 friends, distributing as many as possible. How many lollipops does Marie end up keeping for herself? Please output the final answer... | {
"ground_truth": "11",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 445.25
} |
math | [
{
"content": "Let \\[f(n) = \\left\\{\n\\begin{array}{cl}\nn^2-2 & \\text{ if }n<0, \\\\\n2n-20 & \\text{ if }n \\geq 0.\n\\end{array}\n\\right.\\]What is the positive difference between the two values of $a$ that satisfy the equation $f(-2)+f(2)+f(a)=0$? Please output the final answer within \\boxed{}.",
"... | {
"ground_truth": "21",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 456.75
} |
math | [
{
"content": "What is the least positive integer value of $x$ such that $(2x)^2 + 2\\cdot 37\\cdot 2x + 37^2$ is a multiple of 47? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "5",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 374.25
} |
math | [
{
"content": "At HappyTails Training Center, cats can learn to do three tricks: jump, fetch, and spin. Of the cats at the center:\n- 40 cats can jump\n- 25 cats can fetch\n- 30 cats can spin\n- 15 cats can jump and fetch\n- 10 cats can fetch and spin\n- 12 cats can jump and spin\n- 5 cats can do all three\n- 7 ... | {
"ground_truth": "70",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 467.25
} |
math | [
{
"content": "In triangle \\( ABC \\), angle \\( B \\) is right. The midpoint \\( M \\) is marked on side \\( BC \\), and there is a point \\( K \\) on the hypotenuse such that \\( AB = AK \\) and \\(\\angle BKM = 45^{\\circ}\\). Additionally, there are points \\( N \\) and \\( L \\) on sides \\( AB \\) and \\(... | {
"ground_truth": "1:2",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 1170.5
} |
math | [
{
"content": "Simplify: $(\\sqrt{5})^4$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "25",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 42.25
} |
math | [
{
"content": "If the line that passes through the points $(2,7)$ and $(a, 3a)$ has a slope of 2, what is the value of $a$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "3",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 287.75
} |
math | [
{
"content": "What is the sum of the eight terms in the arithmetic sequence $-2, 3, \\dots, 33$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "124",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 489.25
} |
math | [
{
"content": "How many integers $n$ satisfy the inequality $-8\\pi\\le n\\le10\\pi$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "57",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 450.5
} |
math | [
{
"content": "In the diagram, $D$ and $E$ are the midpoints of $\\overline{AB}$ and $\\overline{BC}$ respectively. Find the sum of the slope and $y$-intercept of the line passing through the points $C$ and $D.$ [asy]\nsize(180); defaultpen(linewidth(.7pt)+fontsize(10pt));\npair A, B, C, D, E, F;\nA=(0,6);\nB=(0... | {
"ground_truth": "\\frac{21}{8}",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 586.25
} |
math | [
{
"content": "In right triangle $ABC$ with $\\angle B = 90^\\circ$, sides $AB=1$ and $BC=3$. The bisector of $\\angle BAC$ meets $\\overline{BC}$ at $D$. Calculate the length of segment $BD$.\nA) $\\frac{1}{2}$\nB) $\\frac{3}{4}$\nC) $1$\nD) $\\frac{5}{4}$\nE) $2$ Please output the final answer within \\boxed{}... | {
"ground_truth": "\\frac{3}{4}",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 1368.25
} |
math | [
{
"content": "What is the simplified value of the sum: $-1^{2004} + (-1)^{2005} + 1^{2006} -1^{2007}$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "-2",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 220.75
} |
math | [
{
"content": "The mean of the set of numbers $\\{106, 102, 95, 103, 100, y, x\\}$ is 104. What is the median of this set of seven numbers? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "103",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 1504
} |
math | [
{
"content": "Given that $\\frac{\\cos \\alpha}{1 + \\sin \\alpha} = \\sqrt{3}$, find the value of $\\frac{\\cos \\alpha}{\\sin \\alpha - 1}$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "-\\frac{\\sqrt{3}}{3}",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 1005.75
} |
math | [
{
"content": "Find all values of $x$ with $0 \\le x < \\pi$ that satisfy $\\sin x - \\cos x = 1$. Enter all the solutions, separated by commas. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{\\pi}{2}",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 813.5
} |
math | [
{
"content": "How many strictly positive integers less than or equal to 120 are not divisible by 3, 5, or 7? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "54",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 571.5
} |
math | [
{
"content": "Given that $-1 - 4\\sqrt{2}$ is a root of the equation \\[x^3 + ax^2 + bx + 31 = 0\\]and that $a$ and $b$ are rational numbers, compute $a.$ Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "1",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 923.25
} |
math | [
{
"content": "What is the remainder when $2001 \\cdot 2002 \\cdot 2003 \\cdot 2004 \\cdot 2005$ is divided by 19? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "11",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 971
} |
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