data_source large_stringclasses 1
value | prompt listlengths 1 1 | reward_model dict | extra_info dict |
|---|---|---|---|
math | [
{
"content": "Let $a,$ $b,$ $c,$ $d,$ $e,$ $f$ be positive real numbers such that $a + b + c + d + e + f = 7.$ Find the minimum value of\n\\[\\frac{1}{a} + \\frac{4}{b} + \\frac{9}{c} + \\frac{16}{d} + \\frac{25}{e} + \\frac{36}{f}.\\] Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "63",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "How many perfect squares are between 50 and 250? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "8",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "Compute $\\tan \\left (\\operatorname{arccot} \\frac{4}{7} \\right).$ Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{7}{4}",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "The volume of a sphere is $72\\pi$ cubic inches. A cylinder has the same height as the diameter of the sphere. The radius of the cylinder is equal to the radius of the sphere. Calculate the total surface area of the sphere plus the total surface area (including the top and bottom) of the cylinder.... | {
"ground_truth": "90\\pi \\sqrt[3]{4}",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "The mean (average) of 6, 9 and 18 is equal to the mean (average) of 12 and $y$. What is the value of $y$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "10",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "The cost price of a certain product is 1360 yuan. When it is sold at 80% of the marked price, the profit margin is 15%. What should be the marked price of the product in yuan? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "1955",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "Evaluate $\\cfrac{\\left\\lceil\\cfrac{17}{7}-\\left\\lceil\\cfrac{27}{17}\\right\\rceil\\right\\rceil}{\\left\\lceil\\cfrac{27}{7}+\\left\\lceil\\cfrac{7\\cdot17}{27}\\right\\rceil\\right\\rceil}$ Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{1}{9}",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "Two chords \\( PQ \\) and \\( PR \\) are drawn in a circle with diameter \\( PS \\). The point \\( T \\) lies on \\( PR \\) and \\( QT \\) is perpendicular to \\( PR \\). The angle \\(\\angle QPR = 60^\\circ\\), \\( PQ = 24 \\text{ cm} \\), and \\( RT = 3 \\text{ cm} \\). What is the length of the... | {
"ground_truth": "2\\sqrt{3}",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "For how many integers $n$ between 1 and 100 is the greatest common divisor of 15 and $n$ equal to 3? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "27",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "Given that the sum of the first n terms of the sequence {a_n} is S_n, with a_1 = 2 and S_{n+1} = 2S_n - 1 for all positive integers n, find the value of a_{10}. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "256",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "Abe, Bobby, Charles, Devin and Edwin are the participants in a race. How many different 1st-2nd-3rd place outcomes are possible if there are no ties? Two different outcomes to include are Bobby-Devin-Edwin and Devin-Bobby-Edwin. Please output the final answer within \\boxed{}.",
"role": "user"... | {
"ground_truth": "60",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "One dimension of a cube is increased by $1$, another is decreased by $1$, and the third is left unchanged. The volume of the new rectangular solid is $5$ less than that of the cube. What was the volume of the cube? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "125",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "The positive divisors of the integer 630 (including 1 and 630) total how many? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "24",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "Starting from $2$, the sum of consecutive even numbers is shown in the table below:\n\n| Number of terms $n$ | $S$ |\n|----------------------|-----------|\n| $1$ | $2=1\\times 2$ |\n| $2$ | $2+4=6=2\\times 3$ |\n| $3$ | $2+4+6=12=3\\times 4$... | {
"ground_truth": "8792",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "Subtract $111.11$ from $333.33.$ Express the result as a decimal to the nearest hundredth. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "222.22",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "Find $\\left \\lceil \\frac{12}{7} \\cdot \\frac{-29}{3}\\right\\rceil - \\left\\lfloor \\frac{12}{7} \\cdot \\left \\lfloor \\frac{-29}{3}\\right \\rfloor \\right \\rfloor$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "2",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "George is about to get a certain amount of change less than one dollar from the cash register. If he gets the most quarters possible and the rest in pennies, he would need to receive 3 pennies to meet the amount. If he gets the most dimes possible and the rest in pennies, he would need to receive ... | {
"ground_truth": "106",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "What is the smallest positive integer with exactly 12 positive integer divisors? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "60",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "Compute $26\\times33+67\\times26$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "2600",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "Two congruent cones with radius 12 cm and height 12 cm are enclosed within a cylinder. The base of each cone is a base of the cylinder, and the height of the cylinder is 24 cm. What is the number of cubic centimeters in the volume of the cylinder not occupied by the cones? Express your answer in t... | {
"ground_truth": "2304\\pi",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "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 segment $C D$, respectively, such that points $P, M$, and $... | {
"ground_truth": "36",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "The noon temperatures for ten consecutive days were $78^{\\circ}$, $80^{\\circ}$, $82^{\\circ}$, $85^{\\circ}$, $88^{\\circ}$, $90^{\\circ}$, $92^{\\circ}$, $95^{\\circ}$, $97^{\\circ}$, and $95^{\\circ}$ Fahrenheit. The increase in temperature over the weekend days (days 6 to 10) is attributed to... | {
"ground_truth": "88.2",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "Grady distributed $x$ pieces of candy evenly among nine Halloween bags such that every bag received the greatest possible number of whole pieces of candy, but some candy was left over. What is the greatest possible number of pieces that could have been left over? Please output the final answer wit... | {
"ground_truth": "8",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "What is the area, in square units, of triangle $ABC$? [asy]\nunitsize(0.15inch);\npath X = (-6.5, 0)--(5.5, 0);\npath Y = (0, -3.5)--(0, 7.5);\ndraw(X); draw(Y);\n\nfor(int n=-6; n <= 5; ++n)\nif( n != 0 )\ndraw( (n,0.25)--(n,-0.25) );\nfor(int n=-3; n <= 7; ++n)\nif( n != 0 )\ndraw( (0.25,n)--(-0... | {
"ground_truth": "19",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "The sum of the first $n$ terms of an arithmetic sequence $\\{a_n\\}$ is $S_n$. Given that $S_{10}=0$ and $S_{15}=25$, find the minimum value of $nS_n$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "-49",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "Suppose that a polynomial of the form $p(x)=x^{2010} \\pm x^{2009} \\pm \\cdots \\pm x \\pm 1$ has no real roots. What is the maximum possible number of coefficients of -1 in $p$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "1005",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "Given an arithmetic sequence $\\{a\\_n\\}$ with a common difference $d > 0$, and $a\\_2$, $a\\_5-1$, $a\\_{10}$ form a geometric sequence. If $a\\_1=5$, and $S\\_n$ represents the sum of the first $n$ terms of the sequence, find the minimum value of $\\frac{2S\\_n+n+32}{a\\_n+1}$. Please output th... | {
"ground_truth": "\\frac{20}{3}",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "What is $88 \\div 4 \\div 2$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "11",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "If $\\tan x+\\tan y=25$ and $\\cot x + \\cot y=30$, what is $\\tan(x+y)$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "150",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "A box contains a collection of triangular and square tiles. There are $25$ tiles in the box, containing $84$ edges total. How many square tiles are there in the box? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "9",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "A sequence of ten $0$s and/or $1$s is randomly generated. If the probability that the sequence does not contain two consecutive $1$s can be written in the form $\\dfrac{m}{n}$, where $m,n$ are relatively prime positive integers, find $m+n$.\n Please output the final answer within \\boxed{}.",
... | {
"ground_truth": "73",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "Find one third of 7.2, expressed as a simplified fraction or a mixed number. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "2 \\frac{2}{5}",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "If $x$ is a real number and $x^2 = 16$, what is the sum of all possible values of $x$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "0",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "Find a nonzero $p$ such that $px^2-12x+4=0$ has only one solution. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "9",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "The set \\( M = \\left\\{(x, y) \\mid \\log_{4} x + \\log_{4} y \\leq 1, x, y \\in \\mathbf{N}^{*}\\right\\} \\) has how many subsets? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "256",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "In trapezoid \\(ABCD\\) with bases \\(AD\\) and \\(BC\\), the diagonals intersect at point \\(E\\). The areas of \\(\\triangle ADE\\) and \\(\\triangle BCE\\) are given as 12 and 3, respectively. Find the area of the trapezoid. Please output the final answer within \\boxed{}.",
"role": "user"
... | {
"ground_truth": "27",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "The diagram shows a semicircle with diameter $20$ and the circle with greatest diameter that fits inside the semicircle. The area of the shaded region is $N\\pi$ , where $N$ is a positive integer. Find $N$ . Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "25",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "Find the remainder when $2^{2^{2^2}}$ is divided by 500. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "36",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "The number of distinct points common to the curves $x^2+4y^2=1$ and $4x^2+y^2=4$ is: Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "2",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "For how many bases between two and nine inclusive does the representation of $576_{10}$ have a final digit of 1? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "1",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "The difference between two numbers is 9, and the sum of the squares of each number is 153. What is the value of the product of the two numbers? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "36",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "If point $P$ is any point on the curve $y=x^{2}-\\ln x$, then the minimum distance from point $P$ to the line $y=x-2$ is ____. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\sqrt{2}",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "A line is expressed in the form\n\\[\\begin{pmatrix} 1 \\\\ 3 \\end{pmatrix} \\cdot \\left( \\begin{pmatrix} x \\\\ y \\end{pmatrix} - \\begin{pmatrix} -2 \\\\ 8 \\end{pmatrix} \\right) = 0.\\]The equation of the line can be expressed in the form $y = mx + b.$ Enter the ordered pair $(m,b).$ Plea... | {
"ground_truth": "\\left( -\\frac{1}{3}, \\frac{22}{3} \\right)",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "In the Cartesian coordinate plane $(xOy)$, two acute angles $\\alpha$ and $\\beta$ are formed with the non-negative semi-axis of $Ox$ as the initial side. Their terminal sides intersect the unit circle at points $A$ and $B$ respectively. The vertical coordinates of $A$ and $B$ are $\\frac{\\sqrt{5... | {
"ground_truth": "\\frac{3\\sqrt{10}}{10}",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "Sandwiches at Joe's Fast Food cost $3 each and sodas cost $2 each. How many dollars will it cost to purchase 5 sandwiches and 8 sodas? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "31",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "The product of two consecutive negative integers is 2550. What is the sum of the two integers? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "-101",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "Add $26_7 + 245_7.$ Express your answer in base 7. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "304_7",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "What is the greatest integer value of $x$ for which $5-4x>17$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "-4",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "In $\\triangle ABC$, $a$, $b$, $c$ are the sides opposite to angles $A$, $B$, $C$ respectively, and it is given that $a\\sin C= \\sqrt {3}c\\cos A$. \n$(1)$ Find the measure of angle $A$; \n$(2)$ If $a= \\sqrt {13}$ and $c=3$, find the area of $\\triangle ABC$. Please output the final answer wit... | {
"ground_truth": "3 \\sqrt {3}",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "The median of the set $\\{n, n + 5, n + 6, n + 9, n + 15\\}$ is 9. What is the mean? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "10",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "What is the following value when expressed as a common fraction: $$\\frac{1}{3^{1}}+\\frac{1}{3^{2}}+\\frac{1}{3^{3}}+\\frac{1}{3^{4}}+\\frac{1}{3^{5}}+\\frac{1}{3^{6}}?$$ Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{364}{729}",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "Write the expression $\\frac{4+3c}{7}+2$ as a single fraction. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{18+3c}{7}",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "Evaluate $\\log_3 27\\sqrt3$. Express your answer as an improper fraction. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac72",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "Simplify $(3-2i)-(5-2i)$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "-2",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "The sum of three numbers is $20$. The first is four times the sum of the other two. The second is seven times the third. What is the product of all three? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "28",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "Find an ordered pair $(u,v)$ that solves the system: \\begin{align*} 5u &= -7 - 2v,\\\\ 3u &= 4v - 25 \\end{align*} Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "(-3,4)",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "Calculate the expression $\\left(100 - \\left(5000 - 500\\right)\\right) \\times \\left(5000 - \\left(500 - 100\\right)\\right)$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "-20240000",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "Determine the coefficient of the term containing $x^3$ in the expansion of ${(1+2x)}^{5}$. (The result should be represented as a number.) Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "80",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "If the graph of the line $y = ax + b$ passes through the points $(4,5)$ and $(8,17)$, what is $a - b$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "10",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "Compute $\\cos \\left( \\arcsin \\frac{2}{3} \\right).$ Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{\\sqrt{5}}{3}",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "The fraction \\(\\frac{1}{221}\\) is represented as a repeating decimal. Find the length of the repeating sequence. (For example, the length of the repeating sequence for the fraction \\(\\frac{25687}{99900} = 0.25712712712 \\ldots = 0.25(712)\\) is 3.) Please output the final answer within \\boxe... | {
"ground_truth": "48",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "The sum of the $x$-coordinates of the vertices of a triangle in the Cartesian plane equals $10$. Find the sum of the $x$-coordinates of the midpoints of the sides of the triangle. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "10",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "Given the ellipse $\\frac{x^2}{3} + y^2 = 1$ and the line $l: y = kx + m$ intersecting the ellipse at two distinct points $A$ and $B$.\n\n(1) If $m = 1$ and $\\overrightarrow{OA} \\cdot \\overrightarrow{OB} = 0$ ($O$ is the origin), find the value of $k$.\n\n(2) If the distance from the origin $O$... | {
"ground_truth": "\\frac{\\sqrt{3}}{2}",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "Given the function $f(x)=ax^{4}+bx^{2}-x+1$, where $a,b\\in\\mathbb{R}$, if $f(2)=9$, find $f(-2)$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "13",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "Two reals \\( x \\) and \\( y \\) are such that \\( x-y=4 \\) and \\( x^{3}-y^{3}=28 \\). Compute \\( x y \\). Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "-3",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "If $x \\neq 0$, $\\frac{x}{2} = y^2$ and $\\frac{x}{4} = 4y$, then $x$ equals Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "128",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "Given the function $f(x) = \\frac {1}{2}x^{2} + x - 2\\ln{x}$ ($x > 0$): \n(1) Find the intervals of monotonicity for $f(x)$. \n(2) Find the extreme values of the function $f(x)$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac {3}{2}",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "Find the minimum value of\n\\[2 \\sqrt{x} + \\frac{1}{x}\\]for $x > 0.$ Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "3",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "At a certain grocery store, cookies may be bought in boxes of $10$ or $21.$ What is the minimum positive number of cookies that must be bought so that the cookies may be split evenly among $13$ people?\n\n*Author: Ray Li* Please output the final answer within \\boxed{}.",
"role": "user"
... | {
"ground_truth": "52",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "A three-quarter sector of a circle of radius $4$ inches together with its interior can be rolled up to form the lateral surface area of a right circular cone by taping together along the two radii shown. What is the volume of the cone in cubic inches? Please output the final answer within \\boxed{... | {
"ground_truth": "$3 \\pi \\sqrt{7}$",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "I have a picture with dimensions $x$ and $y$ (in inches), such that $x$ and $y$ are both integers greater than one. I would like to place this picture in an elongated frame of dimensions $(2x + 3)$ and $(y+2)$. If I measured the area of the frame to be $34$ square inches, what is the area of the ... | {
"ground_truth": "8",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "Find the largest value of $t$ such that \\[\\frac{13t^2 - 34t + 12}{3t - 2 } + 5t = 6t - 1.\\] Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{5}{2}",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "Monica is trying to solve the following equation by completing the square: $$x^2-8x+8 = 0.$$She successfully rewrites the above equation in the following form: $$(x + b)^2 = c,$$where $b$ and $c$ are integers. What is the value of $b + c$? Please output the final answer within \\boxed{}.",
"ro... | {
"ground_truth": "4",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "$JKLM$ is a square and $PQRS$ is a rectangle. If $JK$ is parallel to $PQ$, $JK = 8$ and $PS = 2$, then the total area of the shaded regions is: Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "48",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "\nAlong a straight alley at equal intervals, there are 400 lampposts, numbered sequentially from 1 to 400. At the same time, Alla and Boris started walking towards each other from opposite ends of the alley with different constant speeds (Alla started from the first lamppost and Boris from the fou... | {
"ground_truth": "163",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "Determine the complex number $z$ satisfying the equation $2z-3i\\bar{z}=-7+3i$. Note that $\\bar{z}$ denotes the conjugate of $z$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "1+3i",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "In how many ways can 8 people be seated in a row of chairs if two of the people, Alice and Bob, must not sit next to each other, and Charlie has to sit at one end of the row? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "7200",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "Find the greatest value of $t$ such that \\[\\frac{t^2 - t -56}{t-8} = \\frac{3}{t+5}.\\] Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "-4",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "Solve for $x$:\n\n$$x^2 + 4x + 3 = -(x + 3)(x + 5).$$ Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "-3",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "Solve for t: $3 \\cdot 3^t + \\sqrt{9 \\cdot 9^t} = 18$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "1",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "Solve for $x$: $2^{x-3}=4^{x+1}$ Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "-5",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "How many miles can a car travel in 20 minutes if it travels $ \\, \\frac{3}{4} \\, $ as fast as a train going 80 miles per hour? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "20\\text{ miles}",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "Determine which of the following numbers is smallest in value: $54 \\sqrt{3}, 144,108 \\sqrt{6}-108 \\sqrt{2}$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "$54 \\sqrt{3}$",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "A gardener plants three maple trees, four oaks, and five birch trees in a row. He plants them in random order, each arrangement being equally likely. Let $\\frac m n$ in lowest terms be the probability that no two birch trees are next to one another. Find $m+n$. Please output the final answer with... | {
"ground_truth": "106",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "If \\( x = 2 \\) and \\( y = x^2 - 5 \\) and \\( z = y^2 - 5 \\), what is the value of \\( z \\)? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "-4",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "Evaluate the infinite geometric series: $$\\frac{4}{3} - \\frac{5}{12} + \\frac{25}{144} - \\frac{125}{1728} + \\dots$$ Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{64}{63}",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "Square A has a perimeter of $24$ cm. Square B has an area equal to one-fourth the area of square A. What is the perimeter of square B?\n\n[asy]\ndraw((0,0)--(7,0));\ndraw((7,0)--(7,7));\ndraw((7,7)--(0,7));\ndraw((0,7)--(0,0));\ndraw((11,2)--(11,5));\ndraw((11,5)--(14,5));\ndraw((14,5)--(14,2));... | {
"ground_truth": "12",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "A store increased the original price of a shirt by a certain percent and then lowered the new price by the same amount. Given that the resulting price was $84\\%$ of the original price, by what percent was the price increased and decreased? Please output the final answer within \\boxed{}.",
"r... | {
"ground_truth": "40",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "Find the largest prime divisor of $36^2 + 49^2$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "3697",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "Let $a$ and $b$ be real numbers such that\n\\[\\frac{a}{b} + \\frac{a}{b^2} + \\frac{a}{b^3} + \\dots = 4.\\]Find\n\\[\\frac{a}{a + b} + \\frac{a}{(a + b)^2} + \\frac{a}{(a + b)^3} + \\dotsb.\\] Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{4}{5}",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "In triangle $ABC,$ $\\sin A = \\frac{3}{5}$ and $\\cos B = \\frac{5}{13}.$ Find $\\cos C.$ Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{16}{65}",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "Given that the terminal side of angle $\\alpha$ passes through point $P(\\sqrt{3}, m)$ ($m \\neq 0$), and $\\cos \\alpha = \\frac{m}{6}$, find the value of $\\sin \\alpha$ ___. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{\\sqrt{3}}{2}",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "Let $x$ and $y$ be real numbers such that $3x + 2y \\le 7$ and $2x + 4y \\le 8.$ Find the largest possible value of $x + y.$ Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{11}{4}",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "What is the least positive integer that can be added to 412 to yield a multiple of 3? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "2",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "Find the product of the roots of the equation $24x^2 + 60x - 750 = 0$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "-\\frac{125}{4}",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "If $x$ is a real number, find $(x+1)^2+2(x+1)(3-x)+(3-x)^2$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "16",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "What is the value of $\\left(\\frac{2}{3}\\right)\\left(\\frac{3}{4}\\right)\\left(\\frac{4}{5}\\right)\\left(\\frac{5}{6}\\right)$? Express your answer as a common fraction. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{1}{3}",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "A cube, all of whose surfaces are painted, is cut into $1000$ smaller cubes of the same size. Find the expected value $E(X)$, where $X$ denotes the number of painted faces of a small cube randomly selected. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{3}{5}",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "Joanie takes a $\\$6,\\!000$ loan to pay for her car. The annual interest rate on the loan is $12\\%$. She makes no payments for 4 years, but has to pay back all the money she owes at the end of 4 years. How much more money will she owe if the interest compounds quarterly than if the interest co... | {
"ground_truth": "\\$187.12",
"style": "rule"
} | {
"strict_n_correct": 4
} |
math | [
{
"content": "Find the matrix $\\mathbf{M}$ such that\n\\[\\mathbf{M} \\begin{pmatrix} 1 & -4 \\\\ 3 & -2 \\end{pmatrix} = \\begin{pmatrix} -16 & -6 \\\\ 7 & 2 \\end{pmatrix}.\\] Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\begin{pmatrix} 5 & -7 \\\\ -2 & 3 \\end{pmatrix}",
"style": "rule"
} | {
"strict_n_correct": 4
} |
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