data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"role": "user",
"content": "What percent of the positive integers less than or equal to $150$ have no remainders when divided by $6$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "16.\\overline{6}\\%"
} | {
"split": "train",
"index": 17249,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Suppose \\(198 \\cdot 963 \\equiv m \\pmod{50}\\), where \\(0 \\leq m < 50\\).\n\nWhat is the value of \\(m\\)? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "24"
} | {
"split": "train",
"index": 17250,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Point \\( M \\) divides the side \\( BC \\) of parallelogram \\( ABCD \\) in the ratio \\( BM : MC = 3 \\). Line \\( AM \\) intersects the diagonal \\( BD \\) at point \\( K \\). Find the area of the quadrilateral \\( CMKD \\) if the area of parallelogram \\( ABCD \\) is 1. Let... | math | {
"style": "rule",
"ground_truth": "19/56"
} | {
"split": "train",
"index": 17251,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Suppose $a<0$ and $a<b<c$. Which of the following must be true?\n\n$ab < bc$\n$ac<bc$\n$ab< ac$\n$a+b<b+c$\n$c/a <1$\n\nEnter your answer as a list of those options that are always true. For instance, if you think only the first and third are true, enter A, C. Let's think step ... | math | {
"style": "rule",
"ground_truth": "D, E"
} | {
"split": "train",
"index": 17252,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the sum of every third odd number between $100$ and $300$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "6800"
} | {
"split": "train",
"index": 17253,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the value of the expression $x^2+ 5x-6$, when $x =-1$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-10"
} | {
"split": "train",
"index": 17254,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $a = \\pi/2008$. Find the smallest positive integer $n$ such that \\[2[\\cos(a)\\sin(a) + \\cos(4a)\\sin(2a) + \\cos(9a)\\sin(3a) + \\cdots + \\cos(n^2a)\\sin(na)]\\] is an integer. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "251"
} | {
"split": "train",
"index": 17255,
"solution": "By the product-to-sum identities, we have that $2\\cos a \\sin b = \\sin (a+b) - \\sin (a-b)$. Therefore, this reduces to a telescoping series: \\begin{align*} \\sum_{k=1}^{n} 2\\cos(k^2a)\\sin(ka) &= \\sum_{k=1}^{n} [\\sin(k(k+1)a) - \\sin((k-1)ka)]\\\\ &= -\\sin(... |
deepscaler | [
{
"role": "user",
"content": "In $\\triangle ABC$, $A$ satisfies $\\sqrt{3}\\sin A+\\cos A=1$, $AB=2$, $BC=2 \\sqrt{3}$, then the area of $\\triangle ABC$ is ________. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{3}"
} | {
"split": "train",
"index": 17256,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given \\( x \\in (0,1) \\) and \\( \\frac{1}{x} \\notin \\mathbf{Z} \\), define\n\\[ \na_{n}=\\frac{n x}{(1-x)(1-2 x) \\cdots(1-n x)} \\quad \\text{for} \\quad n=1,2, \\cdots \n\\]\n\nA number \\( x \\) is called a \"good number\" if and only if it makes the sequence \\(\\{a_{n... | math | {
"style": "rule",
"ground_truth": "61/210"
} | {
"split": "train",
"index": 17257,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Calculate $\\frac{1}{2} \\cdot \\frac{3}{5} \\cdot \\frac{7}{11}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{21}{110}"
} | {
"split": "train",
"index": 17258,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Determine the remainder when $$\\sum_{i=0}^{2015}\\left\\lfloor\\frac{2^{i}}{25}\\right\\rfloor$$ is divided by 100, where $\\lfloor x\\rfloor$ denotes the largest integer not greater than $x$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "14"
} | {
"split": "train",
"index": 17259,
"solution": "Let $r_{i}$ denote the remainder when $2^{i}$ is divided by 25. Note that because $2^{\\phi(25)} \\equiv 2^{20} \\equiv 1(\\bmod 25)$, $r$ is periodic with length 20. In addition, we find that 20 is the order of $2 \\bmod 25$. Since $2^{i}$ is never a multiple of 5... |
deepscaler | [
{
"role": "user",
"content": "In Perfectville, the streets are all $30$ feet wide and the blocks they enclose are all squares of side length $500$ feet. Jane runs around the block on the $500$-foot side of the street, while John runs on the opposite side of the street. How many more feet than Jane does John... | math | {
"style": "rule",
"ground_truth": "240"
} | {
"split": "train",
"index": 17260,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A rubber tire has an outer diameter of 25 inches. Calculate the approximate percentage increase in the number of rotations in one mile when the radius of the tire decreases by \\(\\frac{1}{4}\\) inch. Let's think step by step and put only the final answer within \\boxed{}."
}... | math | {
"style": "rule",
"ground_truth": "2\\%"
} | {
"split": "train",
"index": 17261,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is $\\frac{3}{4}$ divided by $\\frac{7}{8}$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{6}{7}"
} | {
"split": "train",
"index": 17262,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $a_n = -n^2 + 10n + 11$, then find the value of $n$ for which the sum of the sequence $\\{a_n\\}$ from the first term to the nth term is maximized. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "11"
} | {
"split": "train",
"index": 17263,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A triangle has vertices $(0,0)$, $(1,1)$, and $(6m,0)$. The line $y = mx$ divides the triangle into two triangles of equal area. What is the sum of all possible values of $m$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "- \\frac {1}{6}"
} | {
"split": "train",
"index": 17264,
"solution": "1. **Identify the vertices and the line dividing the triangle**: \n Let's label the vertices of the triangle as $A = (0,0)$, $B = (1,1)$, and $C = (6m,0)$. The line $y = mx$ is supposed to divide the triangle into two triangles of equal area.\n\n2. **Determine th... |
deepscaler | [
{
"role": "user",
"content": "Find the area of quadrilateral \\(ABCD\\) if \\(AB = BC = 3\\sqrt{3}\\), \\(AD = DC = \\sqrt{13}\\), and vertex \\(D\\) lies on a circle of radius 2 inscribed in the angle \\(ABC\\), where \\(\\angle ABC = 60^\\circ\\). Let's think step by step and put only the final answer wit... | math | {
"style": "rule",
"ground_truth": "3\\sqrt{3}"
} | {
"split": "train",
"index": 17265,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the number of integers $n$ that satisfy\n\\[10 < n^2 < 99.\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 17266,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A school has $100$ students and $5$ teachers. In the first period, each student is taking one class, and each teacher is teaching one class. The enrollments in the classes are $50, 20, 20, 5,$ and $5$. Let $t$ be the average value obtained if a teacher is picked at random and t... | math | {
"style": "rule",
"ground_truth": "-13.5"
} | {
"split": "train",
"index": 17267,
"solution": "To find $t$ and $s$, we use the expected value formula, which is given by:\n\\[\n\\text{Expected Value} = \\sum (\\text{Outcome} \\cdot \\text{Probability})\n\\]\n\n1. **Calculating $t$:** \n $t$ is the average number of students per class if a teacher is picked... |
deepscaler | [
{
"role": "user",
"content": "The lines with equations $ax-2y=c$ and $2x+by=-c$ are perpendicular and intersect at $(1, -5)$. What is $c$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "13"
} | {
"split": "train",
"index": 17268,
"solution": "1. **Convert to slope-intercept form**: \n The given equations are $ax-2y=c$ and $2x+by=-c$. We can rearrange these to solve for $y$:\n \\[\n y = \\frac{a}{2}x - \\frac{c}{2}\n \\]\n \\[\n y = -\\frac{2}{b}x - \\frac{c}{b}\n \\]\n The slopes of the ... |
deepscaler | [
{
"role": "user",
"content": "One cube has each of its faces covered by one face of an identical cube, making a solid as shown. The volume of the solid is \\(875 \\ \\text{cm}^3\\). What, in \\(\\text{cm}^2\\), is the surface area of the solid?\n\nA) 750\n\nB) 800\n\nC) 875\n\nD) 900\n\nE) 1050 Let's think ... | math | {
"style": "rule",
"ground_truth": "750"
} | {
"split": "train",
"index": 17269,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $P(x) = x^2 - 3x - 9$. A real number $x$ is chosen at random from the interval $5 \\le x \\le 15$. The probability that $\\lfloor\\sqrt{P(x)}\\rfloor = \\sqrt{P(\\lfloor x \\rfloor)}$ is equal to $\\frac{\\sqrt{a} + \\sqrt{b} + \\sqrt{c} - d}{e}$ , where $a$, $b$, $c$, $d$,... | math | {
"style": "rule",
"ground_truth": "850"
} | {
"split": "train",
"index": 17270,
"solution": "Note that all the \"bounds\" have to be less than the number+1, otherwise it wouldn't fit the answer format. Therefore, the answer is $\\frac{3*3+\\sqrt{9+4(4+9)}-10+\\sqrt{9+4(16+9)}-12+\\sqrt{9+4(144+9)}}{20} \\implies \\boxed{850}$\n ~Lcz"
} |
deepscaler | [
{
"role": "user",
"content": "Lil Wayne, the rain god, determines the weather. If Lil Wayne makes it rain on any given day, the probability that he makes it rain the next day is $75 \\%$. If Lil Wayne doesn't make it rain on one day, the probability that he makes it rain the next day is $25 \\%$. He decides... | math | {
"style": "rule",
"ground_truth": "9"
} | {
"split": "train",
"index": 17271,
"solution": "Let $p_{n}$ denote the probability that Lil Wayne makes it rain $n$ days from today. We have $p_{0}=0$ and $$ p_{n+1}=\\frac{3}{4} p_{n}+\\frac{1}{4}\\left(1-p_{n}\\right)=\\frac{1}{4}+\\frac{1}{2} p_{n} $$ This can be written as $$ p_{n+1}-\\frac{1}{2}=\\frac{1}{2... |
deepscaler | [
{
"role": "user",
"content": "How many distinct trees with exactly 7 vertices are there? Here, a tree in graph theory refers to a connected graph without cycles, which can be simply understood as connecting \\(n\\) vertices with \\(n-1\\) edges. Let's think step by step and put only the final answer within ... | math | {
"style": "rule",
"ground_truth": "11"
} | {
"split": "train",
"index": 17272,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $A B C D$ be a quadrilateral inscribed in a circle with diameter $\\overline{A D}$. If $A B=5, A C=6$, and $B D=7$, find $C D$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{38}"
} | {
"split": "train",
"index": 17273,
"solution": "We have $A D^{2}=A B^{2}+B D^{2}=A C^{2}+C D^{2}$, so $C D=\\sqrt{A B^{2}+B D^{2}-A C^{2}}=\\sqrt{38}$."
} |
deepscaler | [
{
"role": "user",
"content": "The arithmetic mean of four numbers is 15. Two of the numbers are 10 and 18 and the other two are equal. What is the product of the two equal numbers? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "256"
} | {
"split": "train",
"index": 17274,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the hyperbola $C: \\frac{x^2}{a^2} - \\frac{y^2}{b^2} = 1$ ($a > 0, b > 0$), perpendiculars are drawn from the right focus $F(2\\sqrt{2}, 0)$ to the two asymptotes, with the feet of the perpendiculars being $A$ and $B$, respectively. Let point $O$ be the origin. If the ar... | math | {
"style": "rule",
"ground_truth": "\\sqrt{2}"
} | {
"split": "train",
"index": 17275,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $\\tan (\\alpha+ \\frac{\\pi}{3})=2 \\sqrt {3}$, find the value of $\\tan (\\alpha- \\frac{2\\pi}{3})$ and $2\\sin^{2}\\alpha-\\cos^{2}\\alpha$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{43}{52}"
} | {
"split": "train",
"index": 17276,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If there exists a real number $x$ such that the inequality $\\left(e^{x}-a\\right)^{2}+x^{2}-2ax+a^{2}\\leqslant \\dfrac{1}{2}$ holds with respect to $x$, determine the range of real number $a$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\left\\{\\dfrac{1}{2}\\right\\}"
} | {
"split": "train",
"index": 17277,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In $\\triangle ABC$, it is given that $\\cos A= \\frac{5}{13}$, $\\tan \\frac{B}{2}+\\cot \\frac{B}{2}= \\frac{10}{3}$, and $c=21$.\n1. Find the value of $\\cos (A-B)$;\n2. Find the area of $\\triangle ABC$. Let's think step by step and put only the final answer within \\boxed{... | math | {
"style": "rule",
"ground_truth": "126"
} | {
"split": "train",
"index": 17278,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the expression $\\frac{1 \\cdot 2 \\cdot 3 \\cdot 4 \\cdot 5 \\cdot 6 \\cdot 7 \\cdot 8 \\cdot 9}{1+2+3+4+5+6+7+8+9+10}$, evaluate the expression. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "6608"
} | {
"split": "train",
"index": 17279,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Suppose that $a$ is inversely proportional to $b$. Let $a_1,a_2$ be two nonzero values of $a$ such that $\\frac{a_1}{a_2}=\\frac{2}{3}$. Let the corresponding $b$ values be $b_1,b_2$. If $b_1,b_2$ are nonzero, find the value of $\\frac{b_1}{b_2}$. Let's think step by step an... | math | {
"style": "rule",
"ground_truth": "\\frac{3}{2}"
} | {
"split": "train",
"index": 17280,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "An ant moves on the following lattice, beginning at the dot labeled $A$. Each minute he moves to one of the dots neighboring the dot he was at, choosing from among its neighbors at random. What is the probability that after 5 minutes he is at the dot labeled $B$? [asy]\ndraw((-... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{4}"
} | {
"split": "train",
"index": 17281,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A fair coin is flipped $7$ times. What is the probability that at least $5$ consecutive flips come up heads? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{16}"
} | {
"split": "train",
"index": 17282,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given \\(\\theta = \\arctan \\frac{5}{12}\\), find the principal value of the argument of the complex number \\(z = \\frac{\\cos 2\\theta + i \\sin 2\\theta}{239 + i}\\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\pi}{4}"
} | {
"split": "train",
"index": 17283,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that M is a point on the parabola $y^2 = 2px$ ($p > 0$), F is the focus of the parabola $C$, and $|MF| = p$. K is the intersection point of the directrix of the parabola $C$ and the x-axis. Calculate the measure of angle $\\angle MKF$. Let's think step by step and put onl... | math | {
"style": "rule",
"ground_truth": "45"
} | {
"split": "train",
"index": 17284,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that \\( P \\) is the vertex of a right circular cone with an isosceles right triangle as its axial cross-section, \\( PA \\) is a generatrix of the cone, and \\( B \\) is a point on the base of the cone. Find the maximum value of \\(\\frac{PA + AB}{PB}\\). Let's think st... | math | {
"style": "rule",
"ground_truth": "\\sqrt{4 + 2\\sqrt{2}}"
} | {
"split": "train",
"index": 17285,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that Joy has 40 thin rods, one each of every integer length from 1 cm through 40 cm, with rods of lengths 4 cm, 9 cm, and 18 cm already placed on a table, determine how many of the remaining rods can be chosen as the fourth rod to form a quadrilateral with positive area. ... | math | {
"style": "rule",
"ground_truth": "22"
} | {
"split": "train",
"index": 17286,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Convert $2014_{10}$ to base 9. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2677_9"
} | {
"split": "train",
"index": 17287,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Alice and Bob are stuck in quarantine, so they decide to play a game. Bob will write down a polynomial $f(x)$ with the following properties:\n\n(a) for any integer $n$ , $f(n)$ is an integer;\n(b) the degree of $f(x)$ is less than $187$ .\n\nAlice knows that $f(x)$ sa... | math | {
"style": "rule",
"ground_truth": "187"
} | {
"split": "train",
"index": 17288,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the letters in the word $SUCCESS$, determine the number of distinguishable rearrangements where all the vowels are at the end. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "20"
} | {
"split": "train",
"index": 17289,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the rectangular coordinate system $(xOy)$, the parametric equation of line $l$ is $\\begin{cases}x=1+t\\cdot\\cos \\alpha \\\\ y=2+t\\cdot\\sin \\alpha \\end{cases} (t \\text{ is a parameter})$, and in the polar coordinate system (with the same length unit as the rectangular... | math | {
"style": "rule",
"ground_truth": "2\\sqrt{7}"
} | {
"split": "train",
"index": 17290,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that the complex number $z$ satisfies the equation $\\frac{1-z}{1+z}={i}^{2018}+{i}^{2019}$ (where $i$ is the imaginary unit), find the value of $|2+z|$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{5\\sqrt{2}}{2}"
} | {
"split": "train",
"index": 17291,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A rectangular table of size \\( x \\) cm by 80 cm is covered with identical sheets of paper of size 5 cm by 8 cm. The first sheet is placed in the bottom-left corner, and each subsequent sheet is placed one centimeter higher and one centimeter to the right of the previous one. ... | math | {
"style": "rule",
"ground_truth": "77"
} | {
"split": "train",
"index": 17292,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The numeral $65$ in base $c$ represents the same number as $56$ in base $d$. Assuming that both $c$ and $d$ are positive integers, find the least possible value of $c+d$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "13"
} | {
"split": "train",
"index": 17293,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the parabola C: y² = 3x with focus F, and a line l with slope $\\frac{3}{2}$ intersecting C at points A and B, and the x-axis at point P.\n(1) If |AF| + |BF| = 4, find the equation of line l;\n(2) If $\\overrightarrow{AP}$ = 3$\\overrightarrow{PB}$, find |AB|. Let's think... | math | {
"style": "rule",
"ground_truth": "\\frac{4\\sqrt{13}}{3}"
} | {
"split": "train",
"index": 17294,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $x+\\frac{1}{y}=1$ and $y+\\frac{1}{z}=1$, what is the value of the product $xyz$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"split": "train",
"index": 17295,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Compute the maximum number of sides of a polygon that is the cross-section of a regular hexagonal prism. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "8"
} | {
"split": "train",
"index": 17296,
"solution": "Note that since there are 8 faces to a regular hexagonal prism and a cross-section may only intersect a face once, the upper bound for our answer is 8. Indeed, we can construct a cross-section of the prism with 8 sides. Let $ABCDEF$ and $A'B'C'D'E'F'$ be the two ba... |
deepscaler | [
{
"role": "user",
"content": "In triangle $ABC$, the sides opposite to angles $A$, $B$, and $C$ are denoted by $a$, $b$, and $c$ respectively. Given that angle $A = \\frac{\\pi}{4}$, $\\sin A + \\sin (B - C) = 2\\sqrt{2}\\sin 2C$, and the area of triangle $ABC$ is $1$. Find the length of side $BC$. Let's th... | math | {
"style": "rule",
"ground_truth": "\\sqrt{5}"
} | {
"split": "train",
"index": 17297,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The integer $n$ is the smallest positive multiple of $15$ such that every digit of $n$ is either $8$ or $0$. Compute $\\frac{n}{15}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "592"
} | {
"split": "train",
"index": 17298,
"solution": "Any multiple of 15 is a multiple of 5 and a multiple of 3.\n Any multiple of 5 ends in 0 or 5; since $n$ only contains the digits 0 and 8, the units digit of $n$ must be 0.\n The sum of the digits of any multiple of 3 must be divisible by 3. If $n$ has $a$ digits e... |
deepscaler | [
{
"role": "user",
"content": "Let $S$ be a set of $6$ integers taken from $\\{1,2,\\dots,12\\}$ with the property that if $a$ and $b$ are elements of $S$ with $a<b$, then $b$ is not a multiple of $a$. What is the least possible value of an element in $S$? Let's think step by step and put only the final answ... | math | {
"style": "rule",
"ground_truth": "4"
} | {
"split": "train",
"index": 17299,
"solution": "To solve this problem, we need to ensure that no element in the set $S$ is a multiple of any other element in $S$. We start by partitioning the set $\\{1, 2, \\dots, 12\\}$ into subsets where each element in a subset is a multiple of the smallest element in that su... |
deepscaler | [
{
"role": "user",
"content": "An inverted cone with base radius $12 \\mathrm{cm}$ and height $18 \\mathrm{cm}$ is full of water. The water is poured into a tall cylinder whose horizontal base has radius of $24 \\mathrm{cm}$. What is the height in centimeters of the water in the cylinder? Let's think step by... | math | {
"style": "rule",
"ground_truth": "1.5"
} | {
"split": "train",
"index": 17300,
"solution": "1. **Calculate the volume of the water in the cone**: \n The formula for the volume $V$ of a cone is given by:\n \\[\n V = \\frac{1}{3} \\pi r^2 h\n \\]\n where $r$ is the radius of the base and $h$ is the height of the cone. For the given cone, $r = 12 ... |
deepscaler | [
{
"role": "user",
"content": "Line $a$ is parallel to line $y=2x+4$ and passes through the point $(2,5)$. What is the y-intercept of line $a$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1"
} | {
"split": "train",
"index": 17301,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Mientka Publishing Company prices its bestseller Where's Walter? as follows:\n$C(n) = \\begin{cases} 12n, & \\text{if } 1 \\le n \\le 24 \\\\ 11n, & \\text{if } 25 \\le n \\le 48 \\\\ 10n, & \\text{if } 49 \\le n \\end{cases}$\nwhere $n$ is the number of books ordered, and $C(n... | math | {
"style": "rule",
"ground_truth": "6"
} | {
"split": "train",
"index": 17302,
"solution": "We are given a piecewise function for the cost of books, $C(n)$, depending on the number of books, $n$, ordered. We need to determine for how many values of $n$ it is cheaper to buy more than $n$ books than to buy exactly $n$ books.\n\nThe function is defined as:\n... |
deepscaler | [
{
"role": "user",
"content": "Evaluate the expression \\(\\dfrac{\\sqrt[4]{7}}{\\sqrt[6]{7}}\\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "7^{\\frac{1}{12}}"
} | {
"split": "train",
"index": 17303,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A block of iron solidifies from molten iron, and its volume reduces by $\\frac{1}{34}$. Then, if this block of iron melts back into molten iron (with no loss in volume), by how much does its volume increase? Let's think step by step and put only the final answer within \\boxed{... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{33}"
} | {
"split": "train",
"index": 17304,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "By expanding the expression \\((1+\\sqrt{11})^{214}\\) using the binomial theorem, we obtain terms of the form \\(C_{214}^{k}(\\sqrt{11})^{k}\\). Find the value of \\( k \\) for which this term has the greatest value. Let's think step by step and put only the final answer withi... | math | {
"style": "rule",
"ground_truth": "165"
} | {
"split": "train",
"index": 17305,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The four zeros of the polynomial $x^4 + jx^2 + kx + 256$ are distinct real numbers in arithmetic progression. Compute the value of $j$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-40"
} | {
"split": "train",
"index": 17306,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $\\mathbf{u}$ and $\\mathbf{v}$ be unit vectors, and let $\\mathbf{w}$ be a vector such that $\\mathbf{u} \\times \\mathbf{v} + \\mathbf{u} = \\mathbf{w}$ and $\\mathbf{w} \\times \\mathbf{u} = \\mathbf{v}.$ Compute $\\mathbf{u} \\cdot (\\mathbf{v} \\times \\mathbf{w}).$ L... | math | {
"style": "rule",
"ground_truth": "1"
} | {
"split": "train",
"index": 17307,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A certain calculator has only two keys [+1] and [x2]. When you press one of the keys, the calculator automatically displays the result. For instance, if the calculator originally displayed \"9\" and you pressed [+1], it would display \"10.\" If you then pressed [x2], it would d... | math | {
"style": "rule",
"ground_truth": "9"
} | {
"split": "train",
"index": 17308,
"solution": "To solve this problem, we will work backwards from 200 to 1, determining the optimal sequence of operations that corresponds to the fewest number of keystrokes on the calculator. The operations we use in reverse (working from 200 to 1) will be dividing by 2 (corres... |
deepscaler | [
{
"role": "user",
"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? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "256"
} | {
"split": "train",
"index": 17309,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given positive integers \\(a, b,\\) and \\(c\\) that satisfy \\(2017 \\geq 10a \\geq 100b \\geq 1000c\\), determine how many such ordered triples \\((a, b, c)\\) exist. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "574"
} | {
"split": "train",
"index": 17310,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Bob has a seven-digit phone number and a five-digit postal code. The sum of the digits in his phone number and the sum of the digits in his postal code are the same. Bob's phone number is 346-2789. What is the largest possible value for Bob's postal code, given that no two digi... | math | {
"style": "rule",
"ground_truth": "98765"
} | {
"split": "train",
"index": 17311,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find all positive integer solutions $(m, n)$ to the following equation: $$ m^{2}=1!+2!+\\cdots+n! $$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "(1,1), (3,3)"
} | {
"split": "train",
"index": 17312,
"solution": "A square must end in the digit $0,1,4,5,6$, or 9 . If $n \\geq 4$, then $1!+2!+\\cdots+n$ ! ends in the digit 3 , so cannot be a square. A simple check for the remaining cases reveals that the only solutions are $(1,1)$ and $(3,3)$."
} |
deepscaler | [
{
"role": "user",
"content": "Let $a,b,c,d,e,f,g$ and $h$ be distinct elements in the set \\[\n\\{-7,-5,-3,-2,2,4,6,13\\}.\n\\]What is the minimum possible value of \\[\n(a+b+c+d)^{2} + (e+f+g+h)^{2}?\n\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "34"
} | {
"split": "train",
"index": 17313,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the line $l: x+2y+1=0$, and the set $A=\\{n|n<6, n\\in \\mathbb{N}^*\\}$, if we randomly select 3 different elements from set $A$ to be $a$, $b$, and $r$ in the circle equation $(x-a)^2+(y-b)^2=r^2$, then the probability that the line connecting the center $(a, b)$ of the... | math | {
"style": "rule",
"ground_truth": "\\frac {1}{10}"
} | {
"split": "train",
"index": 17314,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the diagram below, $ABCD$ is a rectangle with side lengths $AB=3$ and $BC=11$, and $AECF$ is a rectangle with side lengths $AF=7$ and $FC=9,$ as shown. The area of the shaded region common to the interiors of both rectangles is $\\frac mn$, where $m$ and $n$ are relatively p... | math | {
"style": "rule",
"ground_truth": "109"
} | {
"split": "train",
"index": 17315,
"solution": "Let the intersection of $AE$ and $BC$ be $G$, and let $BG=x$, so $CG=11-x$.\n By the Pythagorean theorem, ${AG}^2={AB}^2+{BG}^2$, so $AG=\\sqrt{x^2+9}$, and thus $EG=9-\\sqrt{x^2+9}$.\n By the Pythagorean theorem again, ${CG}^2={EG}^2+{CE}^2$: \\[11-x=\\sqrt{7^2+(9... |
deepscaler | [
{
"role": "user",
"content": "Let \\( a \\) and \\( b \\) be integers such that \\( ab = 72 \\). Find the minimum value of \\( a + b \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-17"
} | {
"split": "train",
"index": 17316,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Ten points are marked on a circle. How many distinct convex polygons of three or more sides can be drawn using some (or all) of the ten points as vertices?\n Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "968"
} | {
"split": "train",
"index": 17317,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Calculate the value of $\\left(\\left((4-1)^{-1} - 1\\right)^{-1} - 1\\right)^{-1} - 1$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{-7}{5}"
} | {
"split": "train",
"index": 17318,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many four-digit numbers, without repeating digits, that can be formed using the digits 0, 1, 2, 3, 4, 5, are divisible by 25? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "21"
} | {
"split": "train",
"index": 17319,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given \\( A \\subseteq \\{1, 2, \\ldots, 25\\} \\) such that \\(\\forall a, b \\in A\\), \\(a \\neq b\\), then \\(ab\\) is not a perfect square. Find the maximum value of \\( |A| \\) and determine how many such sets \\( A \\) exist where \\( |A| \\) achieves this maximum value.... | math | {
"style": "rule",
"ground_truth": "16"
} | {
"split": "train",
"index": 17320,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Calculate the definite integral:\n\n$$\n\\int_{0}^{\\pi} 2^{4} \\cdot \\sin^{2}\\left(\\frac{x}{2}\\right) \\cos^{6}\\left(\\frac{x}{2}\\right) \\, dx\n$$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{5 \\pi}{8}"
} | {
"split": "train",
"index": 17321,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Select 4 out of 7 different books to distribute to 4 students, one book per student, with the restriction that books A and B cannot be given to student C, and calculate the number of different distribution methods. Let's think step by step and put only the final answer within \... | math | {
"style": "rule",
"ground_truth": "600"
} | {
"split": "train",
"index": 17322,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Rectangle $ABCD$ has area $4032$. An ellipse with area $4032\\pi$ passes through points $A$ and $C$ and has foci at points $B$ and $D$. Determine the perimeter of the rectangle. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "8\\sqrt{2016}"
} | {
"split": "train",
"index": 17323,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Equilateral $\\triangle ABC$ is inscribed in a circle of radius $2$. Extend $\\overline{AB}$ through $B$ to point $D$ so that $AD=13,$ and extend $\\overline{AC}$ through $C$ to point $E$ so that $AE = 11.$ Through $D,$ draw a line $l_1$ parallel to $\\overline{AE},$ and throug... | math | {
"style": "rule",
"ground_truth": "865"
} | {
"split": "train",
"index": 17324,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Seven teams play a soccer tournament in which each team plays every other team exactly once. No ties occur, each team has a $50\\%$ chance of winning each game it plays, and the outcomes of the games are independent. In each game, the winner is awarded a point and the loser get... | math | {
"style": "rule",
"ground_truth": "831"
} | {
"split": "train",
"index": 17325,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Suppose in a right triangle where angle \\( Q \\) is at the origin and \\( \\cos Q = 0.5 \\). If the length of \\( PQ \\) is \\( 10 \\), what is \\( QR \\)? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "20"
} | {
"split": "train",
"index": 17326,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Two adjacent faces of a tetrahedron, which are equilateral triangles with a side length of 1, form a dihedral angle of 45 degrees. The tetrahedron is rotated around the common edge of these faces. Find the maximum area of the projection of the rotating tetrahedron onto the plan... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{3}}{4}"
} | {
"split": "train",
"index": 17327,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Compute the perimeter of the triangle that has area $3-\\sqrt{3}$ and angles $45^\\circ$ , $60^\\circ$ , and $75^\\circ$ . Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3\\sqrt{2} + 2\\sqrt{3} - \\sqrt{6}"
} | {
"split": "train",
"index": 17328,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the diagram, $ABCD$ and $EFGD$ are squares each of area 16. If $H$ is the midpoint of both $BC$ and $EF$, find the total area of polygon $ABHFGD$.\n\n[asy]\nunitsize(3 cm);\n\npair A, B, C, D, E, F, G, H;\n\nF = (0,0);\nG = (1,0);\nD = (1,1);\nE = (0,1);\nH = (E + F)/2;\nA ... | math | {
"style": "rule",
"ground_truth": "24"
} | {
"split": "train",
"index": 17329,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Alberto, Bernardo, and Carlos are collectively listening to three different songs. Each is simultaneously listening to exactly two songs, and each song is being listened to by exactly two people. In how many ways can this occur? Let's think step by step and put only the final a... | math | {
"style": "rule",
"ground_truth": "6"
} | {
"split": "train",
"index": 17330,
"solution": "We have $\\binom{3}{2}=3$ choices for the songs that Alberto is listening to. Then, Bernardo and Carlos must both be listening to the third song. Thus, there are 2 choices for the song that Bernardo shares with Alberto. From here, we see that the songs that everyon... |
deepscaler | [
{
"role": "user",
"content": "Add $5.467$ and $3.92$ as a decimal. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "9.387"
} | {
"split": "train",
"index": 17331,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Determine how many non-similar regular 500-pointed stars exist, given that a regular $n$-pointed star adheres to the rules set in the original problem description. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "100"
} | {
"split": "train",
"index": 17332,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $PQRST$ be a convex pentagon with $PQ \\parallel RT, QR \\parallel PS, QS \\parallel PT, \\angle PQR=100^\\circ, PQ=4, QR=7,$ and $PT = 21.$ Given that the ratio between the area of triangle $PQR$ and the area of triangle $RST$ is $m/n,$ where $m$ and $n$ are relatively pri... | math | {
"style": "rule",
"ground_truth": "232"
} | {
"split": "train",
"index": 17333,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For how many positive integers $n$ , $1\\leq n\\leq 2008$ , can the set \\[\\{1,2,3,\\ldots,4n\\}\\] be divided into $n$ disjoint $4$ -element subsets such that every one of the $n$ subsets contains the element which is the arithmetic mean of all the elements in that sub... | math | {
"style": "rule",
"ground_truth": "1004"
} | {
"split": "train",
"index": 17334,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "You have 5 identical buckets, each with a maximum capacity of some integer number of liters, and a 30-liter barrel containing an integer number of liters of water. All the water from the barrel was poured into the buckets, with the first bucket being half full, the second one-t... | math | {
"style": "rule",
"ground_truth": "29"
} | {
"split": "train",
"index": 17335,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "From the 200 natural numbers from 1 to 200, how many numbers must be selected to ensure that there are at least 2 numbers whose sum is a multiple of 5? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "82"
} | {
"split": "train",
"index": 17336,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $64$ is divided into three parts proportional to $2$, $4$, and $6$, the smallest part is: Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "10\\frac{2}{3}"
} | {
"split": "train",
"index": 17337,
"solution": "1. **Identify the Proportions**: The problem states that $64$ is divided into three parts proportional to $2$, $4$, and $6$. We can simplify these ratios by dividing each by the smallest number, which is $2$. This gives us the simplified ratio $1:2:3$.\n\n2. **Set ... |
deepscaler | [
{
"role": "user",
"content": "Students from three middle schools worked on a summer project.\n\nSeven students from Allen school worked for 3 days.\nFour students from Balboa school worked for 5 days.\nFive students from Carver school worked for 9 days.\nThe total amount paid for the students' work was 744.... | math | {
"style": "rule",
"ground_truth": "180.00"
} | {
"split": "train",
"index": 17338,
"solution": "1. **Calculate the total number of student-days worked**: \n Each student-day is a unit representing one student working for one day. We calculate the total student-days for each school and sum them up:\n - Allen school: $7$ students $\\times 3$ days $= 21$ stu... |
deepscaler | [
{
"role": "user",
"content": "The maximum and minimum values of the function y=2x^3-3x^2-12x+5 on the interval [0,3] need to be determined. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-15"
} | {
"split": "train",
"index": 17339,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Each principal of Lincoln High School serves exactly one $3$-year term. What is the maximum number of principals this school could have during an $8$-year period? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4"
} | {
"split": "train",
"index": 17340,
"solution": "To determine the maximum number of principals that can serve during an 8-year period at Lincoln High School, where each principal serves a 3-year term, we need to consider how the terms can overlap with the 8-year period.\n\n1. **Understanding the Term Length**: Ea... |
deepscaler | [
{
"role": "user",
"content": "A tetrahedron has all its faces triangles with sides $13,14,15$. What is its volume? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "42 \\sqrt{55}"
} | {
"split": "train",
"index": 17341,
"solution": "Let $A B C$ be a triangle with $A B=13, B C=14, C A=15$. Let $A D, B E$ be altitudes. Then $B D=5, C D=9$. (If you don't already know this, it can be deduced from the Pythagorean Theorem: $C D^{2}-B D^{2}=\\left(C D^{2}+A D^{2}\\right)-\\left(B D^{2}+A D^{2}\\right... |
deepscaler | [
{
"role": "user",
"content": "A jar is filled with red, orange and yellow jelly beans. The probability of randomly selecting a red jelly bean from this jar is $0.2$, and the probability of randomly selecting an orange jelly bean from this jar is $0.5$. What is the probability of randomly selecting a yello... | math | {
"style": "rule",
"ground_truth": "0.3"
} | {
"split": "train",
"index": 17342,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The number of distinct pairs of integers $(x, y)$ such that $0<x<y$ and $\\sqrt{1984}=\\sqrt{x}+\\sqrt{y}$ is Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3"
} | {
"split": "train",
"index": 17343,
"solution": "1. **Simplify the given equation**: We start by simplifying $\\sqrt{1984}$. We factorize 1984 as $1984 = 64 \\times 31 = 8^2 \\times 31$. Therefore, $\\sqrt{1984} = \\sqrt{8^2 \\times 31} = 8\\sqrt{31}$.\n\n2. **Rewrite the equation**: The equation $\\sqrt{1984} = ... |
deepscaler | [
{
"role": "user",
"content": "Given the sequence of numbers with only even digits in their decimal representation, determine the $2014^\\text{th}$ number in the sequence. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "62048"
} | {
"split": "train",
"index": 17344,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the matrix $\\mathbf{M}$ that swaps the columns of a matrix. In other words,\n\\[\\mathbf{M} \\begin{pmatrix} a & b \\\\ c & d \\end{pmatrix} = \\begin{pmatrix} b & a \\\\ d & c \\end{pmatrix}.\\]If no such matrix $\\mathbf{M}$ exists, then enter the zero matrix. Let's th... | math | {
"style": "rule",
"ground_truth": "\\begin{pmatrix} 0 & 0 \\\\ 0 & 0 \\end{pmatrix}"
} | {
"split": "train",
"index": 17345,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A new website registered $2000$ people. Each of them invited $1000$ other registered people to be their friends. Two people are considered to be friends if and only if they have invited each other. What is the minimum number of pairs of friends on this website? Let's think step... | math | {
"style": "rule",
"ground_truth": "1000"
} | {
"split": "train",
"index": 17346,
"solution": "\nConsider a new website with \\(2000\\) registered people. Each person invites \\(1000\\) other people from the group to be their friends. According to the rules, two people are actually considered friends if and only if they have invited each other.\n\nWe need to... |
deepscaler | [
{
"role": "user",
"content": "The teacher wrote a two-digit number on the board. Each of the three boys made two statements.\n\n- Andrey: \"This number ends in the digit 6\" and \"This number is divisible by 7.\"\n- Borya: \"This number is greater than 26\" and \"This number ends in the digit 8.\"\n- Sasha:... | math | {
"style": "rule",
"ground_truth": "91"
} | {
"split": "train",
"index": 17347,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Jamie has a jar of coins containing the same number of nickels, dimes and quarters. The total value of the coins in the jar is $\\$$13.20. How many nickels does Jamie have? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "33"
} | {
"split": "train",
"index": 17348,
"solution": ""
} |
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