data_source large_stringclasses 1
value | prompt listlengths 1 1 | reward_model dict | extra_info dict |
|---|---|---|---|
math | [
{
"content": "What is the value of the expression \\( 4 + \\frac{3}{10} + \\frac{9}{1000} \\)? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "4.309",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 345
} |
math | [
{
"content": "How many positive factors does 30 have? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "8",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 204.5
} |
math | [
{
"content": "Given $\\delta(x) = 3x + 8$ and $\\phi(x) = 8x + 7$, what is $x$ if $\\delta(\\phi(x)) = 7$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "-\\dfrac{11}{12}",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 293.75
} |
math | [
{
"content": "In Pascal's Triangle, each number is the sum of the number just above it and to the left and the number just above it and to the right. So the middle number in Row 2 is $2$ because $1+1=2.$ What is the sum of the numbers in Row 8 of Pascal's Triangle?\n\n\\begin{tabular}{rccccccccccc}\nRow 0:& & &... | {
"ground_truth": "256",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 303.25
} |
math | [
{
"content": "Find the shortest distance from a point on the curve $y=x^{2}-\\ln x$ to the line $x-y-2=0$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\sqrt{2}",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 1122.25
} |
math | [
{
"content": "Let $d$ and $e$ denote the solutions of $2x^{2}+3x-5=0$. What is the value of $(d-1)(e-1)$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "0",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 639.75
} |
math | [
{
"content": "Shuffle the 12 cards of the four suits of A, K, Q in a deck of playing cards. \n(1) If a person draws 2 cards at random, what is the probability that both cards are Aces? \n(2) If the person has already drawn 2 Kings without replacement, what is the probability that another person draws 2 Aces? ... | {
"ground_truth": "\\frac{2}{15}",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 435
} |
math | [
{
"content": "A classroom has 9 desks arranged in a row. Two students, Alex and Jessie, choose their desks at random. What is the probability that they do not sit next to each other? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{7}{9}",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 1327.25
} |
math | [
{
"content": "If $x+\\sqrt{81}=25$, what is the value of $x$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "16",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 107
} |
math | [
{
"content": "What is the smallest positive value of $m$ so that the equation $10x^2 - mx + 360 = 0$ has integral solutions with one root being a multiple of the other? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "120",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 1238.25
} |
math | [
{
"content": "Bella begins to walk from her house toward her friend Ella's house. At the same time, Ella begins to ride her bicycle toward Bella's house. They each maintain a constant speed, and Ella rides $5$ times as fast as Bella walks. The distance between their houses is $2$ miles, which is $10,560$ feet, ... | {
"ground_truth": "704",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 641
} |
math | [
{
"content": "In triangle ABC, $\\sin A = \\frac{4}{5}$, $\\cos B = \\frac{5}{13}$, and $c=56$. Find $\\sin C$ and the circumference of the circumscribed circle of triangle ABC. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "65\\pi",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 1327
} |
math | [
{
"content": "A sphere with volume $V$ is inside a closed right triangular prism $ABC-A_{1}B_{1}C_{1}$, where $AB \\perp BC$, $AB=6$, $BC=8$, and $AA_{1}=3$. Find the maximum value of $V$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{9\\pi}{2}",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 743.5
} |
math | [
{
"content": "The altitudes of a triangle are $12$, $15$, and $20$. What is the area of this triangle? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "150",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 1379.5
} |
math | [
{
"content": "Given that $α$ is an angle in the second quadrant and $\\sin α= \\frac {3}{5}$, find $\\sin 2α$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "- \\frac{24}{25}",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 242
} |
math | [
{
"content": "Ten standard 6-sided dice are rolled. What is the probability that exactly one of the dice shows a 1? Express your answer as a decimal rounded to the nearest thousandth. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "0.323",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 621.25
} |
math | [
{
"content": "Simplify $(r^2 + 3r - 2) - (r^2 + 7r - 5)$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "-4r+3",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 141.75
} |
math | [
{
"content": "This year is 2017, and the sum of the digits of the year is 10. Find the sum of all the years in this century whose digits sum to 10. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "18396",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 1482.75
} |
math | [
{
"content": "For some integers $m$ and $n$, the expression $(x+m)(x+n)$ is equal to a quadratic expression in $x$ with a constant term of -12. Which of the following cannot be a value of $m$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "5",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 1146.75
} |
math | [
{
"content": "In how many ways can 10 people be seated in a row of chairs if four of the people, Alice, Bob, Cindy, and Dave, refuse to sit in four consecutive seats? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "3507840",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 596.25
} |
math | [
{
"content": "To implement the \"double reduction\" policy and promote intangible cultural heritage, a certain school plans to organize extracurricular interest classes for students to visit the following projects: $A$ (Xiu Shui pottery art), $B$ (Xiu Shui tea-picking opera), $C$ (Jiujiang mountain song), $D$ (... | {
"ground_truth": "\\frac{1}{4}",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 568.25
} |
math | [
{
"content": "The circumference of a circle is 100. The diameter of this circle is equal to: Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "$\\frac{100}{\\pi}$",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 224
} |
math | [
{
"content": "Determine the smallest integer $k$ such that $k>1$ and $k$ has a remainder of $3$ when divided by any of $11,$ $4,$ and $3.$ Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "135",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 2392.5
} |
math | [
{
"content": "Given that the slant height of a certain cone is $4$ and the height is $2\\sqrt{3}$, calculate the total surface area of the cone. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "12\\pi",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 292
} |
math | [
{
"content": "If $x^2+y^2=1$, what is the largest possible value of $|x|+|y|$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\sqrt{2}",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 1075
} |
math | [
{
"content": "Determine how many divisors of \\(9!\\) are multiples of 3. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "128",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 864.5
} |
math | [
{
"content": "Let $\\triangle PQR$ be a right triangle with $Q$ as the right angle. A circle with diameter $QR$ intersects side $PR$ at point $S$. If the area of $\\triangle PQR$ is $200$ and $PR = 40$, find the length of $QS$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "10",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 1218.25
} |
math | [
{
"content": "A person rides a bicycle from place A to place B. If they increase their speed by 6 km/h, they can arrive 5 minutes earlier; if they decrease their speed by 5 km/h, they will be 6 minutes late. What is the distance between place A and place B in kilometers? Please output the final answer within \\... | {
"ground_truth": "15",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 1608.75
} |
math | [
{
"content": "The inverse of $f(x) = \\frac{3x - 2}{x + 4}$ may be written in the form $f^{-1}(x)=\\frac{ax+b}{cx+d}$, where $a$, $b$, $c$, and $d$ are real numbers. Find $a/c$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "-4",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 538.75
} |
math | [
{
"content": "Suppose that $x, y, z$ are real numbers such that $x=y+z+2$, $y=z+x+1$, and $z=x+y+4$. Compute $x+y+z$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "-7",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 882.25
} |
math | [
{
"content": "Consider an alphabet of 2 letters. A word is any finite combination of letters. We will call a word unpronounceable if it contains more than two identical letters in a row. How many unpronounceable words of 7 letters exist? Points for the problem: 8. Please output the final answer within \\boxed{}... | {
"ground_truth": "86",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 1219.5
} |
math | [
{
"content": "What is the number of units in the distance between $(2,5)$ and $(-6,-1)$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "10",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 212
} |
math | [
{
"content": "Simplify the expression:\n\\[\n\\frac{1}{\\dfrac{3}{\\sqrt{5}+2} - \\dfrac{4}{\\sqrt{7}+2}}.\n\\] Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{3(9\\sqrt{5} + 4\\sqrt{7} + 10)}{(9\\sqrt{5} - 4\\sqrt{7} - 10)(9\\sqrt{5} + 4\\sqrt{7} + 10)}",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 914
} |
math | [
{
"content": "In $\\triangle ABC$, if $\\angle B=30^{\\circ}$, $AB=2 \\sqrt {3}$, $AC=2$, find the area of $\\triangle ABC$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "2 \\sqrt {3}",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 1528.5
} |
math | [
{
"content": "To take quizzes, each of 30 students in a class is paired with another student. If the pairing is done randomly, what is the probability that Margo is paired with her best friend, Irma? Express your answer as a common fraction. Please output the final answer within \\boxed{}.",
"role": "user"
... | {
"ground_truth": "\\frac{1}{29}",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 714.5
} |
math | [
{
"content": "A shop advertises everything is \"half price in today's sale.\" In addition, a coupon gives a 20% discount on sale prices. Using the coupon, the price today represents what percentage off the original price? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "60",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 484.25
} |
math | [
{
"content": "In the following diagram, $AB=50$. Find $AX$.\n\n[asy]\nimport markers;\n\nreal t=.67;\npair A=(0,0);\npair B=(3,-2);\npair C=(1.5,1.5);\npair X=t*A+(1-t)*B;\n\ndraw(C--A--B--C--X);\n\nlabel(\"$A$\",A,SW);\nlabel(\"$B$\",B,E);\nlabel(\"$C$\",C,N);\nlabel(\"$X$\",X,SW);\n\nmarkangle(n=1,radius=15,... | {
"ground_truth": "\\frac{50}3",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 525.5
} |
math | [
{
"content": "Points $A(3,5)$ and $B(7,10)$ are the endpoints of a diameter of a circle graphed in a coordinate plane. How many square units are in the area of the circle? Express your answer in terms of $\\pi$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{41\\pi}{4}",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 361.5
} |
math | [
{
"content": "What is the value of $x^5 - 5x$ when $x = 4$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "1004",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 145.75
} |
math | [
{
"content": "Find $\\frac{12}{15} + \\frac{7}{9} + 1\\frac{1}{6}$ and simplify the result to its lowest terms. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{247}{90}",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 522.25
} |
math | [
{
"content": "Zach has twelve identical-looking chocolate eggs. Exactly three of the eggs contain a special prize inside. Zach randomly gives three of the twelve eggs to each of Vince, Wendy, Xin, and Yolanda. What is the probability that only one child will receive an egg that contains a special prize (that is... | {
"ground_truth": "1/55",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 1350
} |
math | [
{
"content": "What is the 10th term of an arithmetic sequence of 20 terms with the first term being 7 and the last term being 67? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{673}{19}",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 1677.5
} |
math | [
{
"content": "One out of every five Americans suffers from allergies. In a random sample of 250 Americans, how many would you expect to suffer from allergies? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "50",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 140.5
} |
math | [
{
"content": "Let $x$, $y$, and $z$ be positive integers such that $x + y + z = 12$. What is the smallest possible value of $(x+y+z)\\left(\\frac{1}{x+y}+\\frac{1}{x+z}+\\frac{1}{y+z}\\right)$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{9}{2}",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 1233.75
} |
math | [
{
"content": "If $x-y>x$ and $x+y<y$, then Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "$x<0,y<0$",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 222.5
} |
math | [
{
"content": "Five fair ten-sided dice are rolled. Calculate the probability that at least four of the five dice show the same value. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{23}{5000}",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 784.75
} |
math | [
{
"content": "If $x+\\frac{1}{y}=1$ and $y+\\frac{1}{z}=1$, what is the value of the product $xyz$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "-1",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 1094.25
} |
math | [
{
"content": "The sum of the positive divisors of a positive integer of the form $2^i3^j$ is equal to $600$. What is $i + j$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "6",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 1178.75
} |
math | [
{
"content": "Jori has 3 gallons of distilled water. She uses 5/4 gallons in the first science experiment and 1/3 gallon in a second experiment. How much distilled water does she have left after both experiments? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{17}{12}",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 366.75
} |
math | [
{
"content": "Paint is to be mixed so that the ratio of red paint to white paint is 3 to 2. If Ben wants to make 30 cans of the mixture and all cans hold the same volume of paint, how many cans of red paint will he need? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "18",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 457
} |
math | [
{
"content": "A right circular cylinder with radius 3 is inscribed in a hemisphere with radius 7 so that its bases are parallel to the base of the hemisphere. What is the height of this cylinder? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\sqrt{40}",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 377.25
} |
math | [
{
"content": "A cylinder has a radius of 2 inches and a height of 3 inches. What is the radius of a sphere that has the same volume as this cylinder? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\sqrt[3]{9}",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 379.25
} |
math | [
{
"content": "The center of the circle with equation $x^2+y^2=4x+12y-39$ is the point $(h,k)$. What is $h+k$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "8",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 357.75
} |
math | [
{
"content": "What is the intersection of the lines given by $2y=-x+3$ and $-y=5x+1$? Enter the answer as an ordered pair. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\left(-\\frac{5}{9}, \\frac{16}{9}\\right)",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 475
} |
math | [
{
"content": "Given Tom paid $180, Dorothy paid $200, Sammy paid $240, and Alice paid $280, and they agreed to split the costs evenly, calculate the amount that Tom gave to Sammy minus the amount that Dorothy gave to Alice. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "20",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 1606.5
} |
math | [
{
"content": "Compute $\\dbinom{5}{1}$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "5",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 223
} |
math | [
{
"content": "What is the total volume in cubic feet of three boxes if each box is a cube with edge length 4 feet? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "192",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 95
} |
math | [
{
"content": "The diagram shows the ellipse whose equation is \\(x^{2}+y^{2}-xy+x-4y=12\\). The curve cuts the \\(y\\)-axis at points \\(A\\) and \\(C\\) and cuts the \\(x\\)-axis at points \\(B\\) and \\(D\\). What is the area of the inscribed quadrilateral \\(ABCD\\)? Please output the final answer within \\b... | {
"ground_truth": "28",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 1032.5
} |
math | [
{
"content": "Keiko tosses one penny and Ephraim tosses two pennies. What is the probability that Ephraim gets the same number of heads that Keiko gets? Express your answer as a common fraction. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{3}{8}",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 905.25
} |
math | [
{
"content": "Let $f(x) = x^2-3x$. For what values of $x$ is $f(f(x)) = f(x)$? Enter all the solutions, separated by commas. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "0, 3, -1, 4",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 659.5
} |
math | [
{
"content": "A group of $10$ students from Class 9(1) of a certain school are doing \"pull-up\" training. The number of times they have done it is recorded in the table below. Find the median of the number of times these $10$ students have done.\n\n| Times | $4$ | $5$ | $6$ | $7$ | $8$ |\n|-------|-----|-----|... | {
"ground_truth": "5.5",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 350.25
} |
math | [
{
"content": "Consider a regular octagon. How many triangles can be formed whose vertices are the vertices of the octagon? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "56",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 206
} |
math | [
{
"content": "Find the sum of $453_6$, $436_6$, and $42_6$ in base 6. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "1415_6",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 705.5
} |
math | [
{
"content": "Let $\\mathbf{R}$ be the matrix for rotating about the origin counter-clockwise by an angle of $58^\\circ.$ Find $\\det \\mathbf{R}.$ Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "1",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 470
} |
math | [
{
"content": "Four years ago you invested some money at $10\\%$ interest. You now have $\\$439.23$ in the account. If the interest was compounded yearly, how much did you invest 4 years ago? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "300",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 332.25
} |
math | [
{
"content": "What is the length of the segment of the number line whose endpoints satisfy $|x-\\sqrt[5]{16}|=3$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "6",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 326.5
} |
math | [
{
"content": "Compute $\\arcsin \\left( -\\frac{\\sqrt{3}}{2} \\right).$ Express your answer in radians. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "-\\frac{\\pi}{3}",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 418.75
} |
math | [
{
"content": "How many positive integers less than 500 are congruent to 7 (mod 13)? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "38",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 311.25
} |
math | [
{
"content": "In the arithmetic sequence $\\{a_n\\}$, $S_{10} = 10$, $S_{20} = 30$, then $S_{30} = \\ ?$ Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "60",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 630.5
} |
math | [
{
"content": "A square with side length 8 is cut in half, creating two congruent rectangles. What are the dimensions of one of these rectangles? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "4 \\times 8",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 124.5
} |
math | [
{
"content": "For what base is the representation of $285_{10}$ a four digit number whose final digit is odd? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "6",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 1008.75
} |
math | [
{
"content": "What is the base ten equivalent of the base three number $102012_3$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "302",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 249
} |
math | [
{
"content": "In the following diagram, \\(\\angle ACB = 90^\\circ\\), \\(DE \\perp BC\\), \\(BE = AC\\), \\(BD = \\frac{1}{2} \\mathrm{~cm}\\), and \\(DE + BC = 1 \\mathrm{~cm}\\). Suppose \\(\\angle ABC = x^\\circ\\). Find the value of \\(x\\). Please output the final answer within \\boxed{}.",
"role": "u... | {
"ground_truth": "30",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 1638.75
} |
math | [
{
"content": "If $x - y = 12$ and $x + y = 6$, what is the value of $y$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "-3",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 222.25
} |
math | [
{
"content": "Given that $\\binom{24}{5}=42504$, and $\\binom{24}{6}=134596$, find $\\binom{26}{6}$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "230230",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 1210.5
} |
math | [
{
"content": "When the polynomial $x^3-2$ is divided by the polynomial $x^2-2$, the remainder is Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "2x-2",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 700.75
} |
math | [
{
"content": "If the quadratic $x^2+4mx+m$ has exactly one real root, find the positive value of $m$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac14",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 335.25
} |
math | [
{
"content": "Two connected rooms have different sizes and temperatures. One room has a length of $5 \\,\\mathrm{m}$, a width of $3 \\,\\mathrm{m}$, a height of $4 \\,\\mathrm{m}$, and a temperature of $22 \\,^{\\circ}\\mathrm{C}$; the other room has a length of $6 \\,\\mathrm{m}$, a width of $5 \\,\\mathrm{m}$... | {
"ground_truth": "16",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 799
} |
math | [
{
"content": "If 2 cards from a standard deck are selected randomly, what is the probability that either two kings or at least 1 ace occurs? (There are 4 Aces, 4 kings and 52 total cards in a standard deck.) Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": " \\frac{2}{13}",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 924
} |
math | [
{
"content": "If \\( x = 1 + \\frac{1}{\\sqrt{2}} + \\frac{1}{\\sqrt{3}} + \\cdots + \\frac{1}{\\sqrt{10^{6}}} \\), then the value of \\([x]\\) is Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "1998",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 1020.75
} |
math | [
{
"content": "If $2^{x}=16$, what is the value of $2^{x+3}$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "128",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 172
} |
math | [
{
"content": "Write $\\frac{5}{8}$ as a decimal. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "0.625",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 68.5
} |
math | [
{
"content": "Given $\\tan \\alpha = 3$, evaluate the expression $2\\sin ^{2}\\alpha + 4\\sin \\alpha \\cos \\alpha - 9\\cos ^{2}\\alpha$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\dfrac{21}{10}",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 762.75
} |
math | [
{
"content": "The numbers $4x, 2x-3, 4x-3$ are three consecutive terms in an arithmetic sequence. What is the value of $x$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "-\\frac{3}{4}",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 437.5
} |
math | [
{
"content": "What is the base-10 integer 789 when expressed in base 7? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "2205_7",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 271
} |
math | [
{
"content": "Find the intersection of the lines $9x-4y=30$ and $7x+y=11.$ Express your answer as an ordered pair $(x,y).$ Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "(2,-3)",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 312.75
} |
math | [
{
"content": "Given that all edges of a tetrahedron have a length of $\\sqrt{2}$, and the four vertices are on the same sphere, calculate the surface area of this sphere. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "3 \\pi",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 362.5
} |
math | [
{
"content": "Given the equations $y = 2x^2$ and $y = 4x + c$, determine the value(s) of $c$ for which these two equations have precisely two identical solutions. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "-2",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 551
} |
math | [
{
"content": "Given the function $f(x) = x^3 - 3x^2 - 9x + 2$,\n(I) Determine the intervals of monotonicity for the function $f(x)$;\n(II) Find the minimum value of function $f(x)$ on the interval [-2, 2]. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "-20",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 778.75
} |
math | [
{
"content": "Two reals $a$ and $b$ are such that $a+b=7$ and $a^3+b^3=91$. Compute $ab$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "12",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 355.5
} |
math | [
{
"content": "A company plans to promote the same car in two locations, A and B. It is known that the relationship between the sales profit (unit: ten thousand yuan) and the sales volume (unit: cars) in the two locations is $y_1=5.06t-0.15t^2$ and $y_2=2t$, respectively, where $t$ is the sales volume ($t\\in\\m... | {
"ground_truth": "45.6",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 983
} |
math | [
{
"content": "A $\\textit{palindrome}$ is a positive integer which reads the same forward and backward, like $12321$ or $4884$.\n\nHow many $4$-digit palindromes are there? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "90",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 442.5
} |
math | [
{
"content": "What is the value of $9^3 + 3(9^2) + 3(9) + 1$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "1000",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 401.25
} |
math | [
{
"content": "On January 15 in the stormy town of Stormville, there is a $50\\%$ chance of rain. Every day, the probability of it raining has a $50\\%$ chance of being $\\frac{2017}{2016}$ times that of the previous day (or $100\\%$ if this new quantity is over $100\\%$ ) and a $50\\%$ chance of bein... | {
"ground_truth": "243/2048",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 1132.25
} |
math | [
{
"content": "Two jars each contain the same number of marbles, and every marble is either blue or green. In Jar $1$ the ratio of blue to green marbles is $9:1$, and the ratio of blue to green marbles in Jar $2$ is $8:1$. There are $95$ green marbles in all. How many more blue marbles are in Jar $1$ than in Jar... | {
"ground_truth": "5",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 891.5
} |
math | [
{
"content": "Determine the coefficient of $x^{8}$ in the expansion of \\\\((x^{3}+ \\frac{1}{2 \\sqrt {x}})^{5}\\\\). Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{5}{2}",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 724
} |
math | [
{
"content": "Sam is hired for a 20-day period. On days that he works, he earns $\\$$60. For each day that he does not work, $\\$$30 is subtracted from his earnings. At the end of the 20-day period, he received $\\$$660. How many days did he not work? Please output the final answer within \\boxed{}.",
"role... | {
"ground_truth": "6",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 437
} |
math | [
{
"content": "How many integer values of $x$ satisfy $|x|<3\\pi$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "19",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 301.5
} |
math | [
{
"content": "There are 100 chips numbered from 1 to 100 placed in the vertices of a regular 100-gon in such a way that they follow a clockwise order. In each move, it is allowed to swap two chips located at neighboring vertices if their numbers differ by at most $k$. What is the smallest value of $k$ for which... | {
"ground_truth": "50",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 809.5
} |
math | [
{
"content": "Let $r$, $s$, and $t$ be the three roots of the equation $$\n8x^3 + 1001x + 2008 = 0.\n$$Find $(r + s)^3 + (s + t)^3 + (t + r)^3.$ Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "753",
"style": "rule"
} | {
"n_correct": 4,
"mean_len": 722
} |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.