data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"role": "user",
"content": "Calculate $500,000,000,000 - 3 \\times 111,111,111,111$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "166,666,666,667"
} | {
"split": "train",
"index": 38849,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Five dice with faces numbered 1 through 6 are arranged in a configuration where 14 of the visible faces are showing. The visible numbers are 1, 2, 3, 4, 5, 6, 2, 3, 4, 5, 6, 4, 5, 6. What is the total number of dots NOT visible in this view? Let's think step by step and put onl... | math | {
"style": "rule",
"ground_truth": "49"
} | {
"split": "train",
"index": 38850,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a sequence $\\{a_{n}\\}$ where $a_{1}=1$ and $a_{n+1}=\\left\\{\\begin{array}{l}{{a}_{n}+1, n \\text{ is odd}}\\\\{{a}_{n}+2, n \\text{ is even}}\\end{array}\\right.$\n\n$(1)$ Let $b_{n}=a_{2n}$, write down $b_{1}$ and $b_{2}$, and find the general formula for the sequenc... | math | {
"style": "rule",
"ground_truth": "300"
} | {
"split": "train",
"index": 38851,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Calculate the probability of selecting the letter \"$s$\" in the word \"statistics\". Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3}{10}"
} | {
"split": "train",
"index": 38852,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a segment \\( AB \\) of fixed length 3 with endpoints moving on the parabola \\( y^2 = x \\), find the shortest distance from the midpoint \\( M \\) of segment \\( AB \\) to the y-axis. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{5}{4}"
} | {
"split": "train",
"index": 38853,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Simplify\n\\[\\frac{3 + 5i}{3 - 5i} + \\frac{3 - 5i}{3 + 5i}.\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{16}{17}"
} | {
"split": "train",
"index": 38854,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "You want to arrange the numbers $1,2,3, \\ldots, 25$ in a sequence with the following property: if $n$ is divisible by $m$, then the $n$th number is divisible by the $m$ th number. How many such sequences are there? Let's think step by step and put only the final answer within ... | math | {
"style": "rule",
"ground_truth": "24"
} | {
"split": "train",
"index": 38855,
"solution": "Let the rearranged numbers be $a_{1}, \\ldots, a_{25}$. The number of pairs $(n, m)$ with $n \\mid m$ must equal the number of pairs with $a_{n} \\mid a_{m}$, but since each pair of the former type is also of the latter type, the converse must be true as well. Thus... |
deepscaler | [
{
"role": "user",
"content": "Cindy wishes to arrange her coins into $X$ piles, each consisting of the same number of coins, $Y$. Each pile will have more than one coin and no pile will have all the coins. If there are 13 possible values for $Y$ given all of the restrictions, what is the smallest number of ... | math | {
"style": "rule",
"ground_truth": "144"
} | {
"split": "train",
"index": 38856,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Three machines $\\text{P, Q, and R,}$ working together, can do a job in $x$ hours. When working alone, $\\text{P}$ needs an additional $6$ hours to do the job; $\\text{Q}$, one additional hour; and $\\text{R}$, $x$ additional hours. The value of $x$ is: Let's think step by step... | math | {
"style": "rule",
"ground_truth": "\\frac{2}{3}"
} | {
"split": "train",
"index": 38857,
"solution": "1. **Identify individual working times**: \n - Machine P takes $x+6$ hours to complete the job alone.\n - Machine Q takes $x+1$ hours to complete the job alone.\n - Machine R takes $2x$ hours to complete the job alone.\n\n2. **Set up the equation for combined... |
deepscaler | [
{
"role": "user",
"content": "If $C_n^2A_2^2=42$, then $\\frac{n!}{3!(n-3)!}=\\_\\_\\_\\_\\_\\_\\_\\_.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "35"
} | {
"split": "train",
"index": 38858,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given in the polar coordinate system, circle $C$: $p=2\\cos (\\theta+ \\frac {\\pi}{2})$ and line $l$: $\\rho\\sin (\\theta+ \\frac {\\pi}{4})= \\sqrt {2}$, point $M$ is a moving point on circle $C$. Find the maximum distance from point $M$ to line $l$. Let's think step by step... | math | {
"style": "rule",
"ground_truth": "\\frac {3 \\sqrt {2}}{2}+1"
} | {
"split": "train",
"index": 38859,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given two lines $l_1: ax+2y+6=0$, and $l_2: x+(a-1)y+a^2-1=0$.\n(1) If $l_1 \\perp l_2$, find the value of $a$;\n(2) If $l_1 \\parallel l_2$, find the value of $a$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"split": "train",
"index": 38860,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $\\left\\{\\left(s_{1}, s_{2}, \\cdots, s_{6}\\right) \\mid s_{i} \\in\\{0,1\\}, i \\in \\mathbf{N}_{+}, i \\leqslant 6\\right\\}$. For $\\forall x, y \\in S$, $x=\\left(x_{1}, x_{2}, \\cdots, x_{6}\\right)$ and $y=\\left(y_{1}, y_{2}, \\cdots, y_{6}\\right)$, define:\n\n1.... | math | {
"style": "rule",
"ground_truth": "32"
} | {
"split": "train",
"index": 38861,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Each of five, standard, six-sided dice is rolled once. What is the probability that there is at least one pair but not a three-of-a-kind (that is, there are two dice showing the same value, but no three dice show the same value)? Let's think step by step and put only the final ... | math | {
"style": "rule",
"ground_truth": "\\frac{25}{36}"
} | {
"split": "train",
"index": 38862,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If the lengths of two sides of a right triangle are 5 and 12 units, what is the least possible length, in units, of the third side? Express your answer in simplest radical form. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{119}"
} | {
"split": "train",
"index": 38863,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "$A, B, C, D$ attended a meeting, and each of them received the same positive integer. Each person made three statements about this integer, with at least one statement being true and at least one being false. Their statements are as follows:\n\n$A:\\left(A_{1}\\right)$ The numb... | math | {
"style": "rule",
"ground_truth": "89"
} | {
"split": "train",
"index": 38864,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $\\{a_n\\}$ is a geometric sequence and $S_n$ is the sum of the first $n$ terms, with $S_3=2$ and $S_6=6$, find the value of $a_{13}+a_{14}+a_{15}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "32"
} | {
"split": "train",
"index": 38865,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the remainder when $6x^3-15x^2+21x-23$ is divided by $3x-6$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "7"
} | {
"split": "train",
"index": 38866,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Cut a cube into two cuboids. If the ratio of their surface areas is 1:2, what is the ratio of their volumes? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1:5"
} | {
"split": "train",
"index": 38867,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Buses leave Moscow for Voronezh every hour, at 00 minutes. Buses leave Voronezh for Moscow every hour, at 30 minutes. The trip between cities takes 8 hours. How many buses from Voronezh will a bus leaving Moscow meet on its way? Let's think step by step and put only the final a... | math | {
"style": "rule",
"ground_truth": "16"
} | {
"split": "train",
"index": 38868,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A function \\(f(x)\\) is defined for all real numbers \\(x\\). For all non-zero values \\(x\\), we have\n\\[3f\\left(x\\right) + f\\left(\\frac{1}{x}\\right) = 15x + 8.\\]\nLet \\(S\\) denote the sum of all of the values of \\(x\\) for which \\(f(x) = 2004\\). Compute the integ... | math | {
"style": "rule",
"ground_truth": "356"
} | {
"split": "train",
"index": 38869,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that the broad money supply $\\left(M2\\right)$ balance was 2912000 billion yuan, express this number in scientific notation. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2.912 \\times 10^{6}"
} | {
"split": "train",
"index": 38870,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the result of adding 0.45 to 52.7 and then subtracting 0.25? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "52.9"
} | {
"split": "train",
"index": 38871,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "On a map, a 12-centimeter length represents 72 kilometers. How many kilometers does a 17-centimeter length represent? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "102"
} | {
"split": "train",
"index": 38872,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\[f(x) = \\left\\{\n\\begin{array}{cl}\nx^2+1 &\\text{ if }x>5, \\\\\n2x-3 &\\text{ if } -5 \\le x \\le 5, \\\\\n3 &\\text{ if } x <-5.\n\\end{array}\n\\right.\\]Find $f(-7)+f(0)+f(7)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "50"
} | {
"split": "train",
"index": 38873,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the smallest positive integer $n$ for which $11n - 3$ and $8n + 2$ share a common factor greater than $1$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "19"
} | {
"split": "train",
"index": 38874,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that the angles A, B, C of triangle ABC correspond to the sides a, b, c respectively, and vectors $\\overrightarrow {m}$ = (a, $- \\sqrt {3}b$) and $\\overrightarrow {n}$ = (cosA, sinB), and $\\overrightarrow {m}$ is parallel to $\\overrightarrow {n}$.\n(1) Find angle A.\... | math | {
"style": "rule",
"ground_truth": "\\frac{5\\sqrt{3}}{2}"
} | {
"split": "train",
"index": 38875,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $S$ be the set of integers between $1$ and $2^{40}$ whose binary expansions have exactly two $1$'s. If a number is chosen at random from $S,$ the probability that it is divisible by $9$ is $p/q,$ where $p$ and $q$ are relatively prime positive integers. Find $p+q.$\n Let's ... | math | {
"style": "rule",
"ground_truth": "913"
} | {
"split": "train",
"index": 38876,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In $\\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are denoted as $a$, $b$, and $c$, respectively. Given vectors $\\overrightarrow{m}=(\\sin B+\\sin C, \\sin A-\\sin B)$ and $\\overrightarrow{n}=(\\sin B-\\sin C, \\sin(B+C))$, and $\\overrightarrow{m} \\perp \\... | math | {
"style": "rule",
"ground_truth": "\\frac{4\\sqrt{3}-3}{10}"
} | {
"split": "train",
"index": 38877,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $\\frac{x}{y}=\\frac{3}{4}$, then the incorrect expression in the following is: Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{4}"
} | {
"split": "train",
"index": 38878,
"solution": "We are given that \\(\\frac{x}{y} = \\frac{3}{4}\\). We need to evaluate each expression and determine which one is incorrect.\n\n1. **Option A:**\n \\[\n \\frac{x+y}{y} = \\frac{x}{y} + \\frac{y}{y} = \\frac{3}{4} + 1 = \\frac{3}{4} + \\frac{4}{4} = \\frac{7}{... |
deepscaler | [
{
"role": "user",
"content": "Given that $\\sin(x+\\pi) + \\cos(x-\\pi) = \\frac{1}{2}, x \\in (0, \\pi)$.\n(1) Find the value of $\\sin x \\cos x$;\n(2) Find the value of $\\sin x - \\cos x$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{7}}{2}"
} | {
"split": "train",
"index": 38879,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Margie's car can go $32$ miles on a gallon of gas, and gas currently costs $4$ per gallon. How many miles can Margie drive on $20$ worth of gas? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "160"
} | {
"split": "train",
"index": 38880,
"solution": "1. **Calculate the number of gallons Margie can buy with $\\textdollar 20$:**\n Given that the cost of one gallon of gas is $\\textdollar 4$, the number of gallons Margie can buy with $\\textdollar 20$ is calculated by dividing the total amount of money by the co... |
deepscaler | [
{
"role": "user",
"content": "Two positive rational numbers $x$ and $y$, when written in lowest terms, have the property that the sum of their numerators is 9 and the sum of their denominators is 10 . What is the largest possible value of $x+y$ ? Let's think step by step and put only the final answer within... | math | {
"style": "rule",
"ground_truth": "73 / 9"
} | {
"split": "train",
"index": 38881,
"solution": "For fixed denominators $a<b$ (with sum 10), we maximize the sum of the fractions by giving the smaller denominator as large a numerator as possible: $8 / a+1 / b$. Then, if $a \\geq 2$, this quantity is at most $8 / 2+1 / 1=5$, which is clearly smaller than the sum... |
deepscaler | [
{
"role": "user",
"content": "Given point $F(0,1)$, moving point $M$ lies on the line $l:y=-1$. The line passing through point $M$ and perpendicular to the $x$-axis intersects the perpendicular bisector of segment $MF$ at point $P$. Let the locus of point $P$ be curve $C$. \n$(1)$ Find the equation of curv... | math | {
"style": "rule",
"ground_truth": "36"
} | {
"split": "train",
"index": 38882,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the planar vectors $\\overrightarrow {e_{1}}$ and $\\overrightarrow {e_{2}}$ that satisfy $|\\overrightarrow {e_{1}}| = |3\\overrightarrow {e_{1}} + \\overrightarrow {e_{2}}| = 2$, determine the maximum value of the projection of $\\overrightarrow {e_{1}}$ onto $\\overrig... | math | {
"style": "rule",
"ground_truth": "-\\frac{4\\sqrt{2}}{3}"
} | {
"split": "train",
"index": 38883,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For the smallest value of $n$, the following condition is met: if $n$ crosses are placed in some cells of a $6 \\times 6$ table in any order (no more than one cross per cell), three cells will definitely be found forming a strip of length 3 (vertical or horizontal) in each of w... | math | {
"style": "rule",
"ground_truth": "25"
} | {
"split": "train",
"index": 38884,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the polynomial $f(x) = x^5 + 4x^4 + x^2 + 20x + 16$, evaluate $f(-2)$ using the Qin Jiushao algorithm to find the value of $v_2$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-4"
} | {
"split": "train",
"index": 38885,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "I have a bag containing red and green marbles. Initially, the ratio of red to green marbles is 3:2. If I remove 18 red marbles and add 15 green marbles, the new ratio becomes 2:5. How many red marbles were there in the bag initially? Let's think step by step and put only the fi... | math | {
"style": "rule",
"ground_truth": "33"
} | {
"split": "train",
"index": 38886,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\( a \\), \\( b \\), and \\( c \\) be the roots of the polynomial equation \\( x^3 - 2x^2 + x - 1 = 0 \\). Calculate \\( \\frac{1}{a-2} + \\frac{1}{b-2} + \\frac{1}{c-2} \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-5"
} | {
"split": "train",
"index": 38887,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $\\begin{vmatrix} a & b \\\\ c & d \\end{vmatrix} = a \\cdot d - b \\cdot c$, what is the value of $\\begin{vmatrix} 3 & 4 \\\\ 1 & 2 \\end{vmatrix}$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2"
} | {
"split": "train",
"index": 38888,
"solution": "Given the determinant formula for a $2 \\times 2$ matrix $\\begin{pmatrix} a & b \\\\ c & d \\end{pmatrix}$, the determinant is calculated as:\n\\[ \\text{det} = ad - bc \\]\n\nFor the specific matrix $\\begin{pmatrix} 3 & 4 \\\\ 1 & 2 \\end{pmatrix}$, we identify ... |
deepscaler | [
{
"role": "user",
"content": "If \\( b \\) and \\( n \\) are positive integers with \\( b, n \\leq 18 \\), what is the greatest number of positive factors \\( b^n \\) can have? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "703"
} | {
"split": "train",
"index": 38889,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A right pyramid has a square base with side length 10 cm. Its peak is 12 cm above the center of its base. What is the total surface area of the pyramid, in square centimeters? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "360"
} | {
"split": "train",
"index": 38890,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"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 (... | math | {
"style": "rule",
"ground_truth": "\\text{D}"
} | {
"split": "train",
"index": 38891,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What's the coefficient of the $x^2y^4$ term in the expansion of $(x+y)^6$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "15"
} | {
"split": "train",
"index": 38892,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The number $10!$ ($10$ is written in base $10$), when written in the base $12$ system, ends with exactly $k$ zeros. The value of $k$ is Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4"
} | {
"split": "train",
"index": 38893,
"solution": "1. **Understanding the problem**: We need to find how many zeros are at the end of $10!$ when it is expressed in base $12$. This means we need to determine the highest power of $12$ that divides $10!$.\n\n2. **Factorizing $12$**: Since $12 = 2^2 \\cdot 3$, we need ... |
deepscaler | [
{
"role": "user",
"content": "For a positive number $x$, define $f(x)=\\frac{x}{x+1}$. For example, $f(1)=\\frac{1}{1+1}=\\frac{1}{2}$, $f(2)=\\frac{2}{2+1}=\\frac{2}{3}$, $f(\\frac{1}{2})=\\frac{\\frac{1}{2}}{\\frac{1}{2}+1}=\\frac{1}{3}$. \n$(1)$ Find the value of: $f(3)+f(\\frac{1}{3})=$______; $f(4)+f(... | math | {
"style": "rule",
"ground_truth": "2022.5"
} | {
"split": "train",
"index": 38894,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Any five points are taken inside or on a square with side length $1$. Let a be the smallest possible number with the property that it is always possible to select one pair of points from these five such that the distance between them is equal to or less than $a$. Then $a$ is:\n... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{2}}{2}"
} | {
"split": "train",
"index": 38895,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A solid right prism $PQRSTU$ has a height of 20, as shown. Its bases are equilateral triangles with side length 15. Points $M$, $N$, and $O$ are the midpoints of edges $PQ$, $QR$, and $RS$, respectively. Determine the perimeter of triangle $MNO$. Let's think step by step and pu... | math | {
"style": "rule",
"ground_truth": "32.5"
} | {
"split": "train",
"index": 38896,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There are positive integers that have these properties:\n\n$\\bullet$ I. The sum of the squares of their digits is $50,$ and\n\n$\\bullet$ II. Each digit is larger than the one on its left.\n\nWhat is the product of the digits of the largest integer with both properties? Let's ... | math | {
"style": "rule",
"ground_truth": "36"
} | {
"split": "train",
"index": 38897,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In city \"N\", there are 10 horizontal and 12 vertical streets. A pair of horizontal and a pair of vertical streets form the rectangular boundary of the city, while the rest divide it into blocks shaped like squares with a side length of 100 meters. Each block has an address co... | math | {
"style": "rule",
"ground_truth": "14"
} | {
"split": "train",
"index": 38898,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A particular $12$-hour digital clock displays the hour and minute of a day. Unfortunately, whenever it is supposed to display a $1$, it mistakenly displays a $9$. For example, when it is 1:16 PM the clock incorrectly shows 9:96 PM. What fraction of the day will the clock show t... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"split": "train",
"index": 38899,
"solution": "\nTo determine the fraction of the day during which the clock displays the correct time, we need to consider both the hours and the minutes separately.\n\n#### Step 1: Analyzing the Hours\nThe clock displays the hours from 1 to 12. The clock will display the incorr... |
deepscaler | [
{
"role": "user",
"content": "In an infinite increasing sequence of natural numbers, each number is divisible by at least one of the numbers 1005 and 1006, but none is divisible by 97. Additionally, any two consecutive numbers differ by no more than $k$. What is the smallest possible $k$ for this scenario? ... | math | {
"style": "rule",
"ground_truth": "2011"
} | {
"split": "train",
"index": 38900,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Isosceles trapezoid $ABCD$ has side lengths $AB = 6$ and $CD = 12$ , while $AD = BC$ . It is given that $O$ , the circumcenter of $ABCD$ , lies in the interior of the trapezoid. The extensions of lines $AD$ and $BC$ intersect at $T$ . Given that $OT = 18$ , the ar... | math | {
"style": "rule",
"ground_truth": "84"
} | {
"split": "train",
"index": 38901,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the sum of the first n terms of two arithmetic sequences, ${a_n}$ and ${b_n}$, are $S_n$ and $T_n$ respectively, and the ratio $\\frac{S_n}{T_n} = \\frac{2n+1}{3n+2}$, calculate the value of $\\frac{a_3 + a_{11} + a_{19}}{b_7 + b_{15}}$. Let's think step by step and put o... | math | {
"style": "rule",
"ground_truth": "\\frac{129}{130}"
} | {
"split": "train",
"index": 38902,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $x_1,$ $x_2,$ $x_3,$ $x_4$ be the roots of the polynomial $f(x) = x^4 - x^3 + x^2 + 1$. Define $g(x) = x^2 - 3$. Find the product:\n\\[ g(x_1) g(x_2) g(x_3) g(x_4). \\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "142"
} | {
"split": "train",
"index": 38903,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the radius of the circle inscribed in triangle $PQR$ if $PQ = 26$, $PR=10$, and $QR=18$. Express your answer in simplest radical form. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{17}"
} | {
"split": "train",
"index": 38904,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given $x > 0$, $y > 0$, and $2x+8y-xy=0$, find the minimum value of $x+y$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "18"
} | {
"split": "train",
"index": 38905,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the hyperbola $\\dfrac {x^{2}}{9}- \\dfrac {y^{2}}{27}=1$ with its left and right foci denoted as $F_{1}$ and $F_{2}$ respectively, and $F_{2}$ being the focus of the parabola $y^{2}=2px$, find the area of $\\triangle PF_{1}F_{2}$. Let's think step by step and put only th... | math | {
"style": "rule",
"ground_truth": "36 \\sqrt {6}"
} | {
"split": "train",
"index": 38906,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "When Scott completes the square on the quadratic $x^2 + 8x - 1 = 0$, he obtains an equation of the form $(x + a)^2 = b$. What is $b$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "17"
} | {
"split": "train",
"index": 38907,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "We write on the board the equation\n\n$$\n(x-1)(x-2) \\cdots(x-2016)=(x-1)(x-2) \\cdots(x-2016),\n$$\n\nwhere there are 2016 linear factors on each side. What is the smallest positive value of $k$ such that we can omit exactly $k$ of these 4032 linear factors in such a way that... | math | {
"style": "rule",
"ground_truth": "2016"
} | {
"split": "train",
"index": 38908,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "At a family outing to a theme park, the Thomas family, comprising three generations, plans to purchase tickets. The two youngest members, categorized as children, get a 40% discount. The two oldest members, recognized as seniors, enjoy a 30% discount. The middle generation no l... | math | {
"style": "rule",
"ground_truth": "49.27"
} | {
"split": "train",
"index": 38909,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let the function $f(x)=\\ln x-\\frac{1}{2} ax^{2}-bx$.\n\n$(1)$ When $a=b=\\frac{1}{2}$, find the maximum value of the function $f(x)$;\n\n$(2)$ Let $F(x)=f(x)+\\frac{1}{2} x^{2}+bx+\\frac{a}{x} (0 < x\\leqslant 3)$. If the slope $k$ of the tangent line at any point $P(x_{0},y_... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"split": "train",
"index": 38910,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the planar vectors $\\overrightarrow {a}$ and $\\overrightarrow {b}$, where $\\overrightarrow {a}$ = (2cosα, 2sinα) and $\\overrightarrow {b}$ = (cosβ, sinβ), if the minimum value of $|\\overrightarrow {a} - λ\\overrightarrow {b}|$ for any positive real number λ is $\\sqr... | math | {
"style": "rule",
"ground_truth": "\\sqrt{3}"
} | {
"split": "train",
"index": 38911,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the polynomial $f(x) = 4x^5 + 2x^4 + 3.5x^3 - 2.6x^2 + 1.7x - 0.8$, find the value of $V_1$ when calculating $f(5)$ using the Horner's Method. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "22"
} | {
"split": "train",
"index": 38912,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The gas tank in Catherine's car is $\\frac{1}{8}$ full. When 30 litres of gas are added, the tank becomes $\\frac{3}{4}$ full. If the gas costs Catherine $\\$ 1.38$ per litre, how much will it cost her to fill the remaining quarter of the tank? Let's think step by step and put ... | math | {
"style": "rule",
"ground_truth": "\\$16.56"
} | {
"split": "train",
"index": 38913,
"solution": "When Catherine adds 30 litres of gasoline, the tank goes from $\\frac{1}{8}$ full to $\\frac{3}{4}$ full. Since $\\frac{3}{4}-\\frac{1}{8}=\\frac{6}{8}-\\frac{1}{8}=\\frac{5}{8}$, then $\\frac{5}{8}$ of the capacity of the tank is 30 litres. Thus, $\\frac{1}{8}$ of... |
deepscaler | [
{
"role": "user",
"content": "Given a list of $3000$ positive integers with a unique mode occurring exactly $12$ times, calculate the least number of distinct values that can occur in the list. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "273"
} | {
"split": "train",
"index": 38914,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The largest whole number such that seven times the number is less than 100 is Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "14"
} | {
"split": "train",
"index": 38915,
"solution": "1. **Identify the inequality**: We need to find the largest whole number $x$ such that $7x < 100$.\n\n2. **Solve the inequality**:\n - Divide both sides of the inequality $7x < 100$ by 7:\n \\[\n x < \\frac{100}{7}\n \\]\n - Calculate the division:\... |
deepscaler | [
{
"role": "user",
"content": "Let $s$ be the limiting sum of the geometric series $4 - \\frac{8}{3} + \\frac{16}{9} - \\dots$, as the number of terms increases without bound. Then $s$ equals: Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2.4"
} | {
"split": "train",
"index": 38916,
"solution": "1. **Identify the first term and common ratio**: \n The given series is $4 - \\frac{8}{3} + \\frac{16}{9} - \\dots$. The first term $a$ is clearly $4$. To find the common ratio $r$, we observe the ratio between successive terms:\n \\[\n r = \\frac{-\\frac{8}{... |
deepscaler | [
{
"role": "user",
"content": "Right $\\triangle PQR$ has sides $PQ = 5$, $QR = 12$, and $PR = 13$. Rectangle $ABCD$ is inscribed in $\\triangle PQR$ such that $A$ and $B$ are on $\\overline{PR}$, $D$ on $\\overline{PQ}$, and $C$ on $\\overline{QR}$. If the height of the rectangle (parallel to side $\\overli... | math | {
"style": "rule",
"ground_truth": "7.5"
} | {
"split": "train",
"index": 38917,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In $\\triangle ABC$, $A=\\frac{\\pi}{4}, B=\\frac{\\pi}{3}, BC=2$.\n\n(I) Find the length of $AC$;\n\n(II) Find the length of $AB$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1+ \\sqrt{3}"
} | {
"split": "train",
"index": 38918,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $(x,y)$ satisfy the constraints $\\begin{cases} 8x - y - 4 \\leqslant 0 \\\\ x + y + 1 \\geqslant 0 \\\\ y - 4x \\leqslant 0 \\end{cases}$, and the maximum value of the objective function $z = ax + by (a > 0, b > 0)$ is $2$. Find the minimum value of $\\frac{1}{a} + \\frac{... | math | {
"style": "rule",
"ground_truth": "\\frac{9}{2}"
} | {
"split": "train",
"index": 38919,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A contest began at noon one day and ended $1000$ minutes later. At what time did the contest end? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4:40 a.m"
} | {
"split": "train",
"index": 38920,
"solution": "1. **Convert the contest duration to hours and minutes**: The contest lasted for 1000 minutes. To convert this into hours, we divide by 60 (since there are 60 minutes in an hour):\n \\[\n \\frac{1000}{60} = 16 \\text{ hours and } 40 \\text{ minutes}\n \\]\n ... |
deepscaler | [
{
"role": "user",
"content": "Five guys are eating hamburgers. Each one puts a top half and a bottom half of a hamburger bun on the grill. When the buns are toasted, each guy randomly takes two pieces of bread off of the grill. What is the probability that each guy gets a top half and a bottom half? Let's t... | math | {
"style": "rule",
"ground_truth": "8/63"
} | {
"split": "train",
"index": 38921,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many positive 3-digit numbers are multiples of 30, but not of 75? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "24"
} | {
"split": "train",
"index": 38922,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $ABC$ be a triangle with sides 3, 4, and 5, and $DEFG$ be a 6-by-7 rectangle. A segment is drawn to divide triangle $ABC$ into a triangle $U_1$ and a trapezoid $V_1$ and another segment is drawn to divide rectangle $DEFG$ into a triangle $U_2$ and a trapezoid $V_2$ such tha... | math | {
"style": "rule",
"ground_truth": "35"
} | {
"split": "train",
"index": 38923,
"solution": "We let $AB=3, AC=4, DE=6, DG=7$ for the purpose of labeling. Clearly, the dividing segment in $DEFG$ must go through one of its vertices, without loss of generality $D$. The other endpoint ($D'$) of the segment can either lie on $\\overline{EF}$ or $\\overline{FG}$... |
deepscaler | [
{
"role": "user",
"content": "From a \\(6 \\times 6\\) square grid, gray triangles were cut out. What is the area of the remaining shape? The length of each side of the cells is 1 cm. Provide your answer in square centimeters. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "27"
} | {
"split": "train",
"index": 38924,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "$A B C D E$ is a cyclic convex pentagon, and $A C=B D=C E . A C$ and $B D$ intersect at $X$, and $B D$ and $C E$ intersect at $Y$. If $A X=6, X Y=4$, and $Y E=7$, then the area of pentagon $A B C D E$ can be written as $\\frac{a \\sqrt{b}}{c}$, where $a, b, c$ are integers, $c$... | math | {
"style": "rule",
"ground_truth": "2852"
} | {
"split": "train",
"index": 38925,
"solution": "Since $A C=B D, A B C D$ is an isosceles trapezoid. Similarly, $B C D E$ is also an isosceles trapezoid. Using this, we can now calculate that $C Y=D Y=D X-X Y=A X-X Y=2$, and similarly $B X=C X=3$. By applying Heron's formula we find that the area of triangle $C X... |
deepscaler | [
{
"role": "user",
"content": "Given positive numbers \\( a \\) and \\( b \\) that satisfy \\( 2 + \\log_{2} a = 3 + \\log_{3} b = \\log_{6}(a+b) \\), find the value of \\( \\frac{1}{a} + \\frac{1}{b} \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "108"
} | {
"split": "train",
"index": 38926,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "One line is described by\n\\[\\begin{pmatrix} 2 \\\\ 3 \\\\ 4 \\end{pmatrix} + t \\begin{pmatrix} 1 \\\\ 1 \\\\ -k \\end{pmatrix}.\\]Another line is described by\n\\[\\begin{pmatrix} 1 \\\\ 4 \\\\ 5 \\end{pmatrix} + u \\begin{pmatrix} k \\\\ 2 \\\\ 1 \\end{pmatrix}.\\]If the li... | math | {
"style": "rule",
"ground_truth": "0,-3"
} | {
"split": "train",
"index": 38927,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\( a \\) be a positive integer that is a multiple of 5 such that \\( a+1 \\) is a multiple of 7, \\( a+2 \\) is a multiple of 9, and \\( a+3 \\) is a multiple of 11. Determine the smallest possible value of \\( a \\). Let's think step by step and put only the final answer ... | math | {
"style": "rule",
"ground_truth": "1735"
} | {
"split": "train",
"index": 38928,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In any isosceles triangle $ABC$ with $AB=AC$, the altitude $AD$ bisects the base $BC$ so that $BD=DC$.\n\nDetermine the area of $\\triangle ABC$.\n\n[asy]\ndraw((0,0)--(14,0)--(7,24)--cycle,black+linewidth(1));\ndraw((7,24)--(7,0),black+linewidth(1)+dashed);\ndraw((7,0)--(7,1)-... | math | {
"style": "rule",
"ground_truth": "168"
} | {
"split": "train",
"index": 38929,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the probability that a randomly selected 8-digit number composed of 0s and 1s has the sum of the digits in even positions equal to the sum of the digits in odd positions. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "35/128"
} | {
"split": "train",
"index": 38930,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The polynomial \\( g(x) = x^4 + ax^3 + bx^2 + cx + d \\) has real coefficients, with the roots \\( 3i \\) and \\( 1+2i \\). Calculate the sum of the coefficients \\( a + b + c + d \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "39"
} | {
"split": "train",
"index": 38931,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If \\( AC = 1 \\ \\text{cm} \\) and \\( AD = 4 \\ \\text{cm} \\), what is the relationship between the areas of triangles \\( \\triangle ABC \\) and \\( \\triangle CBD \\)? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1/3"
} | {
"split": "train",
"index": 38932,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the line $l: ax+y+b=0$ intersects with the circle $O: x^{2}+y^{2}=4$ at points $A$ and $B$, and $M(\\sqrt{3},-1)$, and $\\overrightarrow{OA}+ \\overrightarrow{OB}= \\frac{2}{3} \\overrightarrow{OM}$, calculate the value of $\\sqrt{3}ab$. Let's think step by step and put o... | math | {
"style": "rule",
"ground_truth": "-4"
} | {
"split": "train",
"index": 38933,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Calculate the value of the expression $\\left(2 \\times \\frac{1}{3}\\right) \\times \\left(3 \\times \\frac{1}{2}\\right)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1"
} | {
"split": "train",
"index": 38934,
"solution": "Re-arranging the order of the numbers being multiplied, $\\left(2 \\times \\frac{1}{3}\\right) \\times \\left(3 \\times \\frac{1}{2}\\right) = 2 \\times \\frac{1}{2} \\times 3 \\times \\frac{1}{3} = \\left(2 \\times \\frac{1}{2}\\right) \\times \\left(3 \\times \\f... |
deepscaler | [
{
"role": "user",
"content": "In triangle \\( \\triangle ABC \\), \\( M \\) is the midpoint of side \\( BC \\), and \\( N \\) is the midpoint of line segment \\( BM \\). Given that \\( \\angle A = \\frac{\\pi}{3} \\) and the area of \\( \\triangle ABC \\) is \\( \\sqrt{3} \\), find the minimum value of \\( ... | math | {
"style": "rule",
"ground_truth": "\\sqrt{3} + 1"
} | {
"split": "train",
"index": 38935,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Four primes $a$, $b$, $c$ and $d$ form an increasing arithmetic sequence with $a > 5$ and common difference 6. What is the ones digit of $a$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1"
} | {
"split": "train",
"index": 38936,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"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.) Let's think step by step... | math | {
"style": "rule",
"ground_truth": "48"
} | {
"split": "train",
"index": 38937,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the numbers 1, 2, 3, 4, 5, and 6, calculate the probability that three randomly selected numbers can be arranged in an arithmetic sequence in a certain order. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3}{10}"
} | {
"split": "train",
"index": 38938,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A number $x$ is $2$ more than the product of its reciprocal and its additive inverse. In which interval does the number lie? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "0 < x \\le 2"
} | {
"split": "train",
"index": 38939,
"solution": "Let's analyze the given problem step by step.\n\n1. **Understanding the terms:**\n - The **reciprocal** of a number $x$ is $\\frac{1}{x}$.\n - The **additive inverse** of a number $x$ is $-x$.\n\n2. **Setting up the equation:**\n The problem states that $x$ i... |
deepscaler | [
{
"role": "user",
"content": "A line passing through the vertex \\( A \\) of triangle \\( ABC \\) perpendicular to its median \\( BD \\) bisects this median.\n\nFind the ratio of the sides \\( AB \\) and \\( AC \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"split": "train",
"index": 38940,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given integers $x$ and $y$ satisfy the equation $2xy + x + y = 83$, find the values of $x + y$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-85"
} | {
"split": "train",
"index": 38941,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the Empire of Westeros, there were 1000 cities and 2017 roads (each road connects two cities). From each city, it was possible to travel to every other city. One day, an evil wizard cursed $N$ roads, making them impassable. As a result, 7 kingdoms emerged, such that within e... | math | {
"style": "rule",
"ground_truth": "2011"
} | {
"split": "train",
"index": 38942,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "John has 15 marbles of different colors, including one red, one green, one blue, and one yellow marble. In how many ways can he choose 5 marbles, if at least one of the chosen marbles is red, green, or blue, but not yellow? Let's think step by step and put only the final answer... | math | {
"style": "rule",
"ground_truth": "1540"
} | {
"split": "train",
"index": 38943,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $a<b<c$ be three integers such that $a,b,c$ is an arithmetic progression and $a,c,b$ is a geometric progression. What is the smallest possible value of $c$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2"
} | {
"split": "train",
"index": 38944,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the product of $\\frac{3}{2} \\times \\frac{4}{3} \\times \\frac{5}{4} \\times \\cdots \\times \\frac{2006}{2005}$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1003"
} | {
"split": "train",
"index": 38945,
"solution": "1. **Identify the Sequence**: The product given is a sequence of fractions where each fraction's numerator is one more than the previous fraction's denominator:\n \\[\n \\frac{3}{2} \\times \\frac{4}{3} \\times \\frac{5}{4} \\times \\cdots \\times \\frac{2006}{... |
deepscaler | [
{
"role": "user",
"content": "Let $P$ and $Q$ be points on the circle $(x-0)^2+(y-6)^2=2$ and the ellipse $\\frac{x^2}{10}+y^2=1$, respectively. What is the maximum distance between $P$ and $Q$?\nA) $5\\sqrt{2}$\nB) $\\sqrt{46}+\\sqrt{2}$\nC) $7+\\sqrt{2}$\nD) $6\\sqrt{2}$ Let's think step by step and put o... | math | {
"style": "rule",
"ground_truth": "6\\sqrt{2}"
} | {
"split": "train",
"index": 38946,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Two standard 6-sided dice are tossed. What is the probability that the sum of the numbers shown on the dice is a prime number? Express your answer as a common fraction. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{5}{12}"
} | {
"split": "train",
"index": 38947,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "An ice cream shop offers 6 kinds of ice cream. What is the greatest number of two scoop sundaes that can be made such that each sundae contains two types of ice cream and no two sundaes are the same combination? Let's think step by step and put only the final answer within \\bo... | math | {
"style": "rule",
"ground_truth": "15"
} | {
"split": "train",
"index": 38948,
"solution": ""
} |
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