data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"role": "user",
"content": "Rectangular prism P Q R S W T U V has a square base P Q R S. Point X is on the face T U V W so that P X = 12, Q X = 10, and R X = 8. Determine the maximum possible area of rectangle P Q U T. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "67.82"
} | {
"split": "train",
"index": 27649,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Five points $A_1,A_2,A_3,A_4,A_5$ lie on a plane in such a way that no three among them lie on a same straight line. Determine the maximum possible value that the minimum value for the angles $\\angle A_iA_jA_k$ can take where $i, j, k$ are distinct integers between $1$ and $5$... | math | {
"style": "rule",
"ground_truth": "36^\\circ"
} | {
"split": "train",
"index": 27650,
"solution": "\nGiven five points \\( A_1, A_2, A_3, A_4, \\) and \\( A_5 \\) in the plane such that no three are collinear, we are tasked with determining the maximum possible minimum value for the angles \\( \\angle A_i A_j A_k \\), where \\( i, j, k \\) are distinct integers ... |
deepscaler | [
{
"role": "user",
"content": "An employee receives an average of two requests per hour. Assuming a simple flow of requests, what is the probability of receiving four requests in four hours? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "0.0572"
} | {
"split": "train",
"index": 27651,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Five friends did gardening for their local community and earned $15, $22, $28, $35, and $50 respectively. They decide to share their total earnings equally. How much money must the friend who earned $50 contribute to the pool?\nA) $10 \nB) $15 \nC) $20 \nD) $25 \nE) $35... | math | {
"style": "rule",
"ground_truth": "20"
} | {
"split": "train",
"index": 27652,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There are 11 of the number 1, 22 of the number 2, 33 of the number 3, and 44 of the number 4 on the blackboard. The following operation is performed: each time, three different numbers are erased, and the fourth number, which is not erased, is written 2 extra times. For example... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 27653,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The segments \\( AP \\) and \\( AQ \\) are tangent to circle \\( O \\) at points \\( P \\) and \\( Q \\), respectively. Moreover, \\( QE \\) is perpendicular to diameter \\( PD \\) of length 4. If \\( PE = 3.6 \\) and \\( AP = 6 \\), what is the length of \\( QE \\)? Let's thin... | math | {
"style": "rule",
"ground_truth": "1.2"
} | {
"split": "train",
"index": 27654,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that ${{a_n}}$ is an arithmetic sequence with a non-zero common difference, and ${{a_9}}$, ${{a_1}}$, ${{a_5}}$ form a geometric sequence, and ${{a_1} + 3{{a_5}} + {{a_9}} = 20}$, determine the value of ${{a_{13}}}$. Let's think step by step and put only the final answer ... | math | {
"style": "rule",
"ground_truth": "28"
} | {
"split": "train",
"index": 27655,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Dima and Sergey were picking berries from a raspberry bush that had 900 berries. Dima alternated his actions: he put one berry in the basket and ate the next one. Sergey also alternated his actions: he put two berries in the basket and ate the next one. It is known that Dima pi... | math | {
"style": "rule",
"ground_truth": "100"
} | {
"split": "train",
"index": 27656,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "New definition: Given that $y$ is a function of $x$, if there exists a point $P(a, a+2)$ on the graph of the function, then point $P$ is called a \"real point\" on the graph of the function. For example, the \"real point\" on the line $y=2x+1$ is $P(1,3)$.\n\n$(1)$ Determine wh... | math | {
"style": "rule",
"ground_truth": "t=-1"
} | {
"split": "train",
"index": 27657,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Evaluate $\\left\\lceil\\left(-\\frac{5}{3}\\right)^2\\right\\rceil$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3"
} | {
"split": "train",
"index": 27658,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Morgan uses a spreadsheet to create a table of values. In the first column, she lists the positive integers from 1 to 400. She then puts integers in the second column in the following way: if the integer in the first column of a given row is $n$, the number in the second column... | math | {
"style": "rule",
"ground_truth": "131"
} | {
"split": "train",
"index": 27659,
"solution": "Since $31=3 \times 10+1$ and $94=3 \times 31+1$ and $331=3 \times 110+1$ and $907=3 \times 302+1$, then each of $31,94,331$, and 907 appear in the second column of Morgan's spreadsheet. Thus, 131 must be the integer that does not appear in Morgan's spreadsheet. (We... |
deepscaler | [
{
"role": "user",
"content": "Given triangle $ABC$ . Let $A_1B_1$ , $A_2B_2$ , $ ...$ , $A_{2008}B_{2008}$ be $2008$ lines parallel to $AB$ which divide triangle $ABC$ into $2009$ equal areas. Calculate the value of $$ \\left\\lfloor \\frac{A_1B_1}{2A_2B_2} + \\frac{A_1B_1}{2A_3B_3} + ... + ... | math | {
"style": "rule",
"ground_truth": "29985"
} | {
"split": "train",
"index": 27660,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle $XYZ$, where $XY = 5$, $YZ = 12$, $XZ = 13$, and $YM$ is the angle bisector from vertex $Y$. If $YM = m \\sqrt{2}$, find $m$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{60}{17}"
} | {
"split": "train",
"index": 27661,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that Anne, Cindy, and Ben repeatedly take turns tossing a die in the order Anne, Cindy, Ben, find the probability that Cindy will be the first one to toss a five. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{30}{91}"
} | {
"split": "train",
"index": 27662,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In Yang's number theory class, Michael K, Michael M, and Michael R take a series of tests. Afterwards, Yang makes the following observations about the test scores:\n\n(a) Michael K had an average test score of $90$ , Michael M had an average test score of $91$ , and Michael R... | math | {
"style": "rule",
"ground_truth": "413"
} | {
"split": "train",
"index": 27663,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the functions $f(x)=x^{2}+ax+3$, $g(x)=(6+a)\\cdot 2^{x-1}$.\n\n(I) If $f(1)=f(3)$, find the value of the real number $a$;\n\n(II) Under the condition of (I), determine the monotonicity of the function $F(x)=\\frac{2}{1+g(x)}$ and provide a proof;\n\n(III) When $x \\in [-... | math | {
"style": "rule",
"ground_truth": "-7"
} | {
"split": "train",
"index": 27664,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In our daily life, we often use passwords, such as when making payments through Alipay. There is a type of password generated using the \"factorization\" method, which is easy to remember. The principle is to factorize a polynomial. For example, the polynomial $x^{3}+2x^{2}-x-2... | math | {
"style": "rule",
"ground_truth": "24121"
} | {
"split": "train",
"index": 27665,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that a, b, and c are the sides opposite to angles A, B, and C respectively in triangle ABC, and c = 2, sinC(cosB - $\\sqrt{3}$sinB) = sinA.\n(1) Find the measure of angle C;\n(2) If cosA = $\\frac{2\\sqrt{2}}{3}$, find the length of side b. Let's think step by step and pu... | math | {
"style": "rule",
"ground_truth": "\\frac{4\\sqrt{2} - 2\\sqrt{3}}{3}"
} | {
"split": "train",
"index": 27666,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the greatest common factor of 40 and 48? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "8"
} | {
"split": "train",
"index": 27667,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $\\cos(x - \\frac{\\pi}{4}) = \\frac{\\sqrt{2}}{10}$, with $x \\in (\\frac{\\pi}{2}, \\frac{3\\pi}{4})$.\n(1) Find the value of $\\sin x$;\n(2) Find the value of $\\cos(2x - \\frac{\\pi}{3})$. Let's think step by step and put only the final answer within \\boxed{}."
... | math | {
"style": "rule",
"ground_truth": "-\\frac{7 + 24\\sqrt{3}}{50}"
} | {
"split": "train",
"index": 27668,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given point $P(0,-2)$, and an ellipse $E$: $\\dfrac{x^{2}}{a^{2}} + \\dfrac{y^{2}}{b^{2}} = 1$ $(a > b > 0)$ with eccentricity $\\dfrac{\\sqrt{2}}{2}$, let $F$ be the right focus of ellipse $E$, and the slope of line $PF$ is $2$, with $O$ being the origin. \n$(1)$ Find the equ... | math | {
"style": "rule",
"ground_truth": "\\dfrac{\\sqrt{2}}{2}"
} | {
"split": "train",
"index": 27669,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "\nIn an olympiad, 2006 students participated. It was found that a student, Vasia, solved only one out of the six problems. Additionally, the number of participants who solved at least 1 problem is 4 times greater than those who solved at least 2 problems;\nthe number who solved... | math | {
"style": "rule",
"ground_truth": "982"
} | {
"split": "train",
"index": 27670,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle $XYZ$, where $\\angle X = 90^\\circ$, the hypotenuse $YZ = 13$, and $\\tan Z = 3\\cos Y$. What is the length of side $XY$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{2\\sqrt{338}}{3}"
} | {
"split": "train",
"index": 27671,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "An equilateral triangle and a square have the same perimeter of 12 inches. What is the ratio of the side length of the triangle to the side length of the square? 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{4}{3}"
} | {
"split": "train",
"index": 27672,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given unit vectors $a$ and $b$ satisfying $|a+3b|=\\sqrt{13}$, find the angle between $a$ and $b$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\pi}{3}"
} | {
"split": "train",
"index": 27673,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If the random variable $X\\sim B(3,p)$ and $Y\\sim N(2,\\delta ^{2})$, and $P(X\\geqslant 1)=0.657$, $P(0 < Y < 2)=p$, then $P(Y > 4)$ is ____. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "0.2"
} | {
"split": "train",
"index": 27674,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There are infinitely many positive integers $k$ which satisfy the equation\n\\[\\cos^2 (k^2 + 6^2)^\\circ = 1.\\]Enter the two smallest solutions, separated by commas. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "18"
} | {
"split": "train",
"index": 27675,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many four-digit numbers, formed using the digits 0, 1, 2, 3, 4, 5 without repetition, are greater than 3410? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "132"
} | {
"split": "train",
"index": 27676,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "An ice ballerina rotates at a constant angular velocity at one particular point. That is, she does not translationally move. Her arms are fully extended as she rotates. Her moment of inertia is $I$ . Now, she pulls her arms in and her moment of inertia is now $\\frac{7}{10}I$... | math | {
"style": "rule",
"ground_truth": "\\dfrac{10}{7}"
} | {
"split": "train",
"index": 27677,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x)=x+ \\frac{1}{x}$, and $g(x)=f^{2}(x)-af(x)+2a$ has four distinct zeros $x\\_1$, $x\\_2$, $x\\_3$, $x\\_4$, determine the value of $[2-f(x\\_1)]\\cdot[2-f(x\\_2)]\\cdot[2-f(x\\_3)]\\cdot[2-f(x\\_4)]$. Let's think step by step and put only the final answe... | math | {
"style": "rule",
"ground_truth": "16"
} | {
"split": "train",
"index": 27678,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the point \\( P(-2,5) \\) lies on the circle \\(\\odot C: x^{2}+y^{2}-2x-2y-23=0\\), and the line \\( l: 3x+4y+8=0 \\) intersects \\(\\odot C\\) at points \\( A \\) and \\( B \\). Find \\(\\overrightarrow{AB} \\cdot \\overrightarrow{BC}\\). Let's think step by step and pu... | math | {
"style": "rule",
"ground_truth": "-32"
} | {
"split": "train",
"index": 27679,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a right triangle with integer length sides, the hypotenuse has length 39 units. How many units is the length of the shorter leg? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "15"
} | {
"split": "train",
"index": 27680,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The opposite of $-23$ is ______; the reciprocal is ______; the absolute value is ______. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "23"
} | {
"split": "train",
"index": 27681,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Regular polygons with $5, 6, 7,$ and $8$ sides are inscribed in the same circle. No two of the polygons share a vertex, and no three of their sides intersect at a common point. At how many points inside the circle do two of their sides intersect? Let's think step by step and pu... | math | {
"style": "rule",
"ground_truth": "68"
} | {
"split": "train",
"index": 27682,
"solution": "1. **Understanding the Intersection Rule**: When two regular polygons with $m$ and $n$ sides ($m > n$) are inscribed in a circle without sharing a vertex, each side of the polygon with $n$ sides intersects with the sides of the polygon with $m$ sides twice. This oc... |
deepscaler | [
{
"role": "user",
"content": "Call a positive real number special if it has a decimal representation that consists entirely of digits $0$ and $7$. For example, $\\frac{700}{99}= 7.\\overline{07}= 7.070707\\cdots$ and $77.007$ are special numbers. What is the smallest $n$ such that $1$ can be written as a su... | math | {
"style": "rule",
"ground_truth": "8"
} | {
"split": "train",
"index": 27683,
"solution": "1. **Understanding the Problem**: We need to find the smallest number of special numbers (numbers with only the digits $0$ and $7$ in their decimal representation) that can sum up to $1$.\n\n2. **Relating to Super-Special Numbers**: We introduce the concept of supe... |
deepscaler | [
{
"role": "user",
"content": "Two lines with slopes $\\dfrac{1}{3}$ and $3$ intersect at $(3,3)$. Find the area of the triangle enclosed by these two lines and the line $x+y=12$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "8.625"
} | {
"split": "train",
"index": 27684,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A rising number, such as $34689$, is a positive integer each digit of which is larger than each of the digits to its left. There are $\\binom{9}{5} = 126$ five-digit rising numbers. When these numbers are arranged from smallest to largest, the $97^{\\text{th}}$ number in the li... | math | {
"style": "rule",
"ground_truth": "5"
} | {
"split": "train",
"index": 27685,
"solution": "1. **Understanding the Problem**: We need to find the $97^{\\text{th}}$ five-digit rising number and identify which digit from the given options it does not contain.\n\n2. **Counting Rising Numbers Starting with '1'**:\n - A five-digit rising number starting with... |
deepscaler | [
{
"role": "user",
"content": "Let the sequence \\(b_1, b_2, b_3, \\dots\\) be defined such that \\(b_1 = 24\\), \\(b_{12} = 150\\), and for all \\(n \\geq 3\\), \\(b_n\\) is the arithmetic mean of the first \\(n - 1\\) terms. Find \\(b_2\\). Let's think step by step and put only the final answer within \\bo... | math | {
"style": "rule",
"ground_truth": "276"
} | {
"split": "train",
"index": 27686,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Two identical rectangular crates are packed with cylindrical pipes, using different methods. Each pipe has diameter 10 cm. A side view of the first four rows of each of the two different methods of packing is shown below.\n\n[asy]\ndraw(circle((1,1),1),black+linewidth(1));\ndr... | math | {
"style": "rule",
"ground_truth": "190-100\\sqrt{3}"
} | {
"split": "train",
"index": 27687,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A teacher received a number of letters from Monday to Friday, which were 10, 6, 8, 5, 6, respectively. The variance $s^2$ of this set of data is \\_\\_\\_\\_\\_\\_. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3.2"
} | {
"split": "train",
"index": 27688,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Two distinct positive integers $a$ and $b$ are factors of 48. If $a\\cdot b$ is not a factor of 48, what is the smallest possible value of $a\\cdot b$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "18"
} | {
"split": "train",
"index": 27689,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $z$ is a complex number such that $z+\\frac 1z=2\\cos 3^\\circ$, find $z^{2000}+\\frac 1{z^{2000}}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"split": "train",
"index": 27690,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $$\\overset{ .}{a_{n}a_{n-1}a_{n-2}\\cdots a_{1}a_{0}}|_{m}$$ be defined as $a_{0}+a_{1}\\times m+\\ldots+a_{n-1}\\times m^{n-1}+a_{n}\\times m^{n}$, where $n\\leq m$, $m$ and $n$ are positive integers, $a_{k}\\in\\{0,1,2,\\ldots,m-1\\}$ ($k=0,1,2,\\ldots,n$) and $a_{n}\\ne... | math | {
"style": "rule",
"ground_truth": "699"
} | {
"split": "train",
"index": 27691,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For a pair of integers \\((a, b)(0 < a < b < 1000)\\), a set \\(S \\subseteq \\{1, 2, \\cdots, 2003\\}\\) is called a \"jump set\" for the pair \\((a, b)\\) if for any pair of elements \\(\\left(s_{1}, s_{2}\\right)\\) in \\(S\\), \\(|s_{1}-s_{2}| \\notin\\{a, b\\}\\).\n\nLet \... | math | {
"style": "rule",
"ground_truth": "668"
} | {
"split": "train",
"index": 27692,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A right triangle is inscribed in the ellipse given by the equation $x^2 + 9y^2 = 9$. One vertex of the triangle is at the point $(0,1)$, and one leg of the triangle is fully contained within the x-axis. Find the squared length of the hypotenuse of the inscribed right triangle, ... | math | {
"style": "rule",
"ground_truth": "11"
} | {
"split": "train",
"index": 27693,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A positive number is called $n$-primable if it is divisible by $n$ and each of its digits is a one-digit prime number. How many 3-primable positive integers are there that are less than 1000? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "28"
} | {
"split": "train",
"index": 27694,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $2x + 5y = 20$ and $5x + 2y = 26$, find $20x^2 + 60xy + 50y^2$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{59600}{49}"
} | {
"split": "train",
"index": 27695,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a division problem, the dividend is 12, and the divisor is a natural number less than 12. What is the sum of all possible different remainders? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "15"
} | {
"split": "train",
"index": 27696,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $f : \\mathbb{R} \\to \\mathbb{R}$ be a function such that\n\\[f(x) f(y) - f(xy) = x + y\\]for all real numbers $x$ and $y.$\n\nLet $n$ be the number of possible values of $f(2),$ and let $s$ be the sum of all possible values of $f(2).$ Find $n \\times s.$ Let's think step... | math | {
"style": "rule",
"ground_truth": "3"
} | {
"split": "train",
"index": 27697,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Complex numbers $p,$ $q,$ and $r$ are zeros of a polynomial $Q(z) = z^3 + sz^2 + tz + u,$ and $|p|^2 + |q|^2 + |r|^2 = 360.$ The points corresponding to $p,$ $q,$ and $r$ in the complex plane are the vertices of a right triangle with hypotenuse $k.$ Find $k^2.$ Let's think step... | math | {
"style": "rule",
"ground_truth": "540"
} | {
"split": "train",
"index": 27698,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Pedrito's lucky number is $34117$ . His friend Ramanujan points out that $34117 = 166^2 + 81^2 = 159^2 + 94^2$ and $166-159 = 7$ , $94- 81 = 13$ . Since his lucky number is large, Pedrito decides to find a smaller one, but that satisfies the same properties, that is, write... | math | {
"style": "rule",
"ground_truth": "545"
} | {
"split": "train",
"index": 27699,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that \\( 169(157 - 77x)^2 + 100(201 - 100x)^2 = 26(77x - 157)(1000x - 2010) \\), find the value of \\( x \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "31"
} | {
"split": "train",
"index": 27700,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A laptop is originally priced at $\\$1200$. It is on sale for $15\\%$ off. John applies two additional coupons: one gives $10\\%$ off the discounted price, and another gives $5\\%$ off the subsequent price. What single percent discount would give the same final price as these t... | math | {
"style": "rule",
"ground_truth": "27.325\\%"
} | {
"split": "train",
"index": 27701,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Jackie and Alex have two fair coins and a third coin that comes up heads with probability $\\frac{2}{5}$. Jackie flips the three coins, and then Alex flips the same three coins. Determine the probability that Jackie gets the same number of heads as Alex, where the probability i... | math | {
"style": "rule",
"ground_truth": "263"
} | {
"split": "train",
"index": 27702,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a group of 50 children, each of the children in the group have all of their siblings in the group. Each child with no older siblings announces how many siblings they have; however, each child with an older sibling is too embarrassed, and says they have 0 siblings. If the ave... | math | {
"style": "rule",
"ground_truth": "26"
} | {
"split": "train",
"index": 27703,
"solution": "For $i \\geq 1$, let $a_{i}$ be the number of families that have $i$ members in the group. Then, among each family with $i$ children in the group, the oldest child will say $i-1$, and the rest will say 0. Thus, the sum of all the numbers said will be $a_{2}+2 a_{3}... |
deepscaler | [
{
"role": "user",
"content": "How many different positive, five-digit integers can be formed using the digits 2, 2, 2, 9 and 9? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 27704,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In square ABCD, where AB=2, fold along the diagonal AC so that plane ABC is perpendicular to plane ACD, resulting in the pyramid B-ACD. Find the ratio of the volume of the circumscribed sphere of pyramid B-ACD to the volume of pyramid B-ACD. Let's think step by step and put onl... | math | {
"style": "rule",
"ground_truth": "4\\pi:1"
} | {
"split": "train",
"index": 27705,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $\\mathcal{R}$ be the region consisting of the set of points in the coordinate plane that satisfy both $|8 - x| + y \\le 10$ and $3y - x \\ge 15$. When $\\mathcal{R}$ is revolved around the line whose equation is $3y - x = 15$, the volume of the resulting solid is $\\frac {... | math | {
"style": "rule",
"ground_truth": "365"
} | {
"split": "train",
"index": 27706,
"solution": "[asy]size(280); import graph; real min = 2, max = 12; pen dark = linewidth(1); real P(real x) { return x/3 + 5; } real Q(real x) { return 10 - abs(x - 8); } path p = (2,P(2))--(8,P(8))--(12,P(12)), q = (2,Q(2))--(12,Q(12)); pair A = (8,10), B = (4.5,6.5), C= (9.75,... |
deepscaler | [
{
"role": "user",
"content": "\nA random point \\(N\\) on a line has coordinates \\((t, -2-t)\\), where \\(t \\in \\mathbb{R}\\). A random point \\(M\\) on a parabola has coordinates \\(\\left( x, x^2 - 4x + 5 \\right)\\), where \\(x \\in \\mathbb{R}\\). The square of the distance between points \\(M\\) and... | math | {
"style": "rule",
"ground_truth": "\\frac{19\\sqrt{2}}{8}"
} | {
"split": "train",
"index": 27707,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Krzysztof solved the quadratic equation $11x^2-44x-99=0$ by completing the square. In the process, he came up with the equivalent equation $$(x+r)^2 = s,$$where $r$ and $s$ are constants.\n\nWhat is $r+s$? Let's think step by step and put only the final answer within \\boxed{}.... | math | {
"style": "rule",
"ground_truth": "11"
} | {
"split": "train",
"index": 27708,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Write $-\\left(-3\\right)-4+\\left(-5\\right)$ in the form of algebraic sum without parentheses. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3-4-5"
} | {
"split": "train",
"index": 27709,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A classroom is paved with cubic bricks that have an edge length of 0.3 meters, requiring 600 bricks. If changed to cubic bricks with an edge length of 0.5 meters, how many bricks are needed? (Solve using proportions.) Let's think step by step and put only the final answer withi... | math | {
"style": "rule",
"ground_truth": "216"
} | {
"split": "train",
"index": 27710,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many primes less than $100$ have $7$ as the ones digit? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "6"
} | {
"split": "train",
"index": 27711,
"solution": "1. **Identify the numbers with 7 as the ones digit under 100**: \n The numbers are $7, 17, 27, 37, 47, 57, 67, 77, 87, 97$.\n\n2. **Check each number for primality**:\n - $7$ is prime.\n - $17$ is prime.\n - $27$ is not prime (divisible by $3$).\n - $37$ ... |
deepscaler | [
{
"role": "user",
"content": "In this diagram the center of the circle is $O$, the radius is $a$ inches, chord $EF$ is parallel to chord $CD$. $O$,$G$,$H$,$J$ are collinear, and $G$ is the midpoint of $CD$. Let $K$ (sq. in.) represent the area of trapezoid $CDFE$ and let $R$ (sq. in.) represent the area of ... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{\\sqrt{2}}+\\frac{1}{2}"
} | {
"split": "train",
"index": 27712,
"solution": "1. **Identify the given information and setup the problem:**\n - The center of the circle is $O$, and the radius is $a$ inches.\n - Chords $CD$ and $EF$ are parallel, and $O$, $G$, $H$, $J$ are collinear with $G$ as the midpoint of $CD$.\n - $OG = a - 2h$, wh... |
deepscaler | [
{
"role": "user",
"content": "Alicia earns 20 dollars per hour, of which $1.45\\%$ is deducted to pay local taxes. How many cents per hour of Alicia's wages are used to pay local taxes? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "29"
} | {
"split": "train",
"index": 27713,
"solution": "1. **Convert Alicia's hourly wage to cents**: Alicia earns $20$ dollars per hour. Since there are $100$ cents in a dollar, her hourly wage in cents is:\n \\[\n 20 \\text{ dollars} \\times 100 \\text{ cents/dollar} = 2000 \\text{ cents}\n \\]\n\n2. **Calculate... |
deepscaler | [
{
"role": "user",
"content": "The sides of $\\triangle ABC$ measure 11,20, and 21 units. We fold it along $PQ,QR,RP$ where $P,Q,R$ are the midpoints of its sides until $A,B,C$ coincide. What is the volume of the resulting tetrahedron? Let's think step by step and put only the final answer within \\b... | math | {
"style": "rule",
"ground_truth": "45"
} | {
"split": "train",
"index": 27714,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There is a school that offers 10 courses for students to elect. Among them, Courses A, B, and C have conflicting schedules and thus at most one of these can be chosen. The school mandates that each student must elect three courses. How many different elective schemes are availa... | math | {
"style": "rule",
"ground_truth": "98"
} | {
"split": "train",
"index": 27715,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Determine by how many times the number \\((2014)^{2^{2014}} - 1\\) is greater than the number written in the following form:\n\\[\n\\left(\\left((2014)^{2^0} + 1\\right) \\cdot \\left((2014)^{2^1} + 1\\right) \\cdot \\left((2014)^{2^2} + 1\\right) \\ldots \\cdot \\left((2014)^{... | math | {
"style": "rule",
"ground_truth": "2013"
} | {
"split": "train",
"index": 27716,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the Cartesian coordinate system, with the origin as the pole and the positive half-axis of the x-axis as the polar axis, a polar coordinate system is established. The polar equation of curve C is $\\rho - 2\\cos\\theta - 6\\sin\\theta + \\frac{1}{\\rho} = 0$, and the paramet... | math | {
"style": "rule",
"ground_truth": "2\\sqrt{6}"
} | {
"split": "train",
"index": 27717,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given an ellipse $\\frac{x^{2}}{a^{2}} + \\frac{y^{2}}{b^{2}} = 1$ (where $a>0$, $b>0$) with eccentricity $\\frac{\\sqrt{6}}{3}$, the distance from the origin O to the line passing through points A $(0, -b)$ and B $(a, 0)$ is $\\frac{\\sqrt{3}}{2}$. Further, the line $y=kx+m$ (... | math | {
"style": "rule",
"ground_truth": "\\frac{5}{4}"
} | {
"split": "train",
"index": 27718,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The polynomial $-400x^5+2660x^4-3602x^3+1510x^2+18x-90$ has five rational roots. Suppose you guess a rational number which could possibly be a root (according to the rational root theorem). What is the probability that it actually is a root? Let's think step by step and put o... | math | {
"style": "rule",
"ground_truth": "1/36"
} | {
"split": "train",
"index": 27719,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The three-digit even numbers \\( A \\, , B \\, , C \\, , D \\, , E \\) satisfy \\( A < B < C < D < E \\). Given that \\( A + B + C + D + E = 4306 \\), find the smallest value of \\( A \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "326"
} | {
"split": "train",
"index": 27720,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "$\\frac{(.2)^3}{(.02)^2} =$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "20"
} | {
"split": "train",
"index": 27721,
"solution": "1. **Rewrite the expression with powers of 10:** \n We start by expressing $0.2$ and $0.02$ in terms of powers of 10:\n \\[\n 0.2 = \\frac{2}{10} = 2 \\times 10^{-1}, \\quad 0.02 = \\frac{2}{100} = 2 \\times 10^{-2}\n \\]\n\n2. **Calculate the powers:** \... |
deepscaler | [
{
"role": "user",
"content": "Seven standard dice are glued together to make a solid. The pairs of faces of the dice that are glued together have the same number of dots on them. How many dots are on the surface of the solid? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "105"
} | {
"split": "train",
"index": 27722,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Three fair, standard six-sided dice are rolled. What is the probability that the sum of the numbers on the top faces is 18? 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{1}{216}"
} | {
"split": "train",
"index": 27723,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A scientist walking through a forest recorded as integers the heights of $5$ trees standing in a row. She observed that each tree was either twice as tall or half as tall as the one to its right. Unfortunately some of her data was lost when rain fell on her notebook. Her notes ... | math | {
"style": "rule",
"ground_truth": "24.2"
} | {
"split": "train",
"index": 27724,
"solution": "1. **Identify the relationship between the trees' heights:** Each tree is either twice as tall or half as tall as the one to its right. This means that for any tree $i$ and tree $i+1$, the height of tree $i$ is either $2 \\times \\text{height of tree } i+1$ or $\\f... |
deepscaler | [
{
"role": "user",
"content": "Let $a_{1}, a_{2}, \\cdots, a_{6}$ be any permutation of $\\{1,2, \\cdots, 6\\}$. If the sum of any three consecutive numbers is not divisible by 3, how many such permutations exist? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "96"
} | {
"split": "train",
"index": 27725,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Rationalize the denominator of $\\frac{\\sqrt[3]{27} + \\sqrt[3]{2}}{\\sqrt[3]{3} + \\sqrt[3]{2}}$ and express your answer in simplest form. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "7 - \\sqrt[3]{54} + \\sqrt[3]{6}"
} | {
"split": "train",
"index": 27726,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Among the nine fractions\n\n$$\n\\frac{5}{4}, \\frac{17}{6}, \\frac{-5}{4}, \\frac{10}{7}, \\frac{2}{3}, \\frac{14}{8}, \\frac{-1}{3}, \\frac{5}{3} \\text { and } \\frac{-3}{2}\n$$\n\nwe have eight with the following properties:\n\n- 2 fractions whose sum is $\\frac{2}{5}$\n- 2... | math | {
"style": "rule",
"ground_truth": "-\\frac{3}{2}"
} | {
"split": "train",
"index": 27727,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Christine must buy at least $45$ fluid ounces of milk at the store. The store only sells milk in $200$ milliliter bottles. If there are $33.8$ fluid ounces in $1$ liter, then what is the smallest number of bottles that Christine could buy? (You may use a calculator on this pro... | math | {
"style": "rule",
"ground_truth": "7"
} | {
"split": "train",
"index": 27728,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a right triangle where one leg has length $4x + 2$ feet and the other leg has length $(x-3)^2$ feet, find the value of $x$ if the hypotenuse is $5x + 1$ feet. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{\\frac{3}{2}}"
} | {
"split": "train",
"index": 27729,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\( E(n) \\) denote the largest integer \\( k \\) such that \\( 5^{k} \\) divides the product \\( 1^{1} \\cdot 2^{2} \\cdot 3^{3} \\cdot 4^{4} \\cdots \\cdots n^{n} \\). What is the value of \\( E(150) \\)? Let's think step by step and put only the final answer within \\box... | math | {
"style": "rule",
"ground_truth": "2975"
} | {
"split": "train",
"index": 27730,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If for a number \\( x \\) you calculate the sum of its digits and repeat this process two more times with the resulting number, you get a sequence of four numbers. Find the smallest \\( x \\) for which all four numbers are distinct and the last number is 2. Let's think step by ... | math | {
"style": "rule",
"ground_truth": "2999"
} | {
"split": "train",
"index": 27731,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In bridge, a standard 52-card deck is dealt in the usual way to 4 players. By convention, each hand is assigned a number of \"points\" based on the formula $$4 \\times(\\# \\mathrm{~A} \\text { 's })+3 \\times(\\# \\mathrm{~K} \\text { 's })+2 \\times(\\# \\mathrm{Q} \\text { '... | math | {
"style": "rule",
"ground_truth": "\\frac{197}{1820}"
} | {
"split": "train",
"index": 27732,
"solution": "Obviously, we can ignore the cards lower than J. Simply enumerate the ways to get at least 13 points: AAAA (1), AAAK (16), AAAQ (16), AAAJ (16), AAKK (36), AAKQ (96), AKKK (16). The numbers in parentheses represent the number of ways to choose the suits, given the ... |
deepscaler | [
{
"role": "user",
"content": "In trapezoid $PQRS$, the parallel sides $PQ$ and $RS$ have lengths of 10 and 30 units, respectively, and the altitude is 18 units. Points $T$ and $U$ are the midpoints of sides $PR$ and $QS$, respectively. What is the area of quadrilateral $TURS$? Let's think step by step and p... | math | {
"style": "rule",
"ground_truth": "225"
} | {
"split": "train",
"index": 27733,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A bear is in the center of the left down corner of a $100*100$ square .we call a cycle in this grid a bear cycle if it visits each square exactly ones and gets back to the place it started.Removing a row or column with compose the bear cycle into number of pathes.Find the min... | math | {
"style": "rule",
"ground_truth": "5000"
} | {
"split": "train",
"index": 27734,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given an ellipse $C$: $\\frac{x^{2}}{a^{2}} + \\frac{y^{2}}{b^{2}} = 1 (a > b > 0)$ passing through the point $(0,4)$, with an eccentricity of $\\frac{3}{5}$\n1. Find the equation of $C$;\n2. Find the length of the line segment intercepted by $C$ on the line passing through poi... | math | {
"style": "rule",
"ground_truth": "\\frac{41}{5}"
} | {
"split": "train",
"index": 27735,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Compute the sum of all positive integers $n$ such that $n^{2}-3000$ is a perfect square. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1872"
} | {
"split": "train",
"index": 27736,
"solution": "Suppose $n^{2}-3000=x^{2}$, so $n^{2}-x^{2}=3000$. This factors as $(n-x)(n+x)=3000$. Thus, we have $n-x=2a$ and $n+x=2b$ for some positive integers $a, b$ such that $ab=750$ and $a<b$. Therefore, we have $n=a+b$, so the sum will be just the sum of divisors of $750... |
deepscaler | [
{
"role": "user",
"content": "Given a pyramid $P-ABC$ where $PA=PB=2PC=2$, and $\\triangle ABC$ is an equilateral triangle with side length $\\sqrt{3}$, the radius of the circumscribed sphere of the pyramid $P-ABC$ is _______. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\dfrac{\\sqrt{5}}{2}"
} | {
"split": "train",
"index": 27737,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many of the base-ten numerals for the positive integers less than or equal to $2017$ contain the digit $0$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "469"
} | {
"split": "train",
"index": 27738,
"solution": "To solve this problem, we need to count the number of integers from 1 to 2017 that contain at least one digit '0'. We will break this down by the number of digits in the integers.\n\n1. **One-digit integers (1 to 9):**\n - None of these integers contain the digit... |
deepscaler | [
{
"role": "user",
"content": "How many integers satisfy the inequality $(x+3)^{2}\\leq1$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3"
} | {
"split": "train",
"index": 27739,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For transportation between points located hundreds of kilometers apart on the Earth's surface, people of the future will likely dig straight tunnels through which capsules will travel frictionlessly under the influence of Earth's gravity. Let points \\( A, B, \\) and \\( C \\) ... | math | {
"style": "rule",
"ground_truth": "42"
} | {
"split": "train",
"index": 27740,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The sequence consists of 19 ones and 49 zeros arranged in a random order. A group is defined as the maximal subsequence of identical symbols. For example, in the sequence 110001001111, there are five groups: two ones, then three zeros, then one one, then two zeros, and finally ... | math | {
"style": "rule",
"ground_truth": "2.83"
} | {
"split": "train",
"index": 27741,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the diagram, \\(PQRS\\) is a square with side length 8. Points \\(T\\) and \\(U\\) are on \\(PS\\) and \\(QR\\) respectively with \\(QU = TS = 1\\). The length of \\(TU\\) is closest to Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 27742,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Compute the number of ordered pairs of integers $(x,y)$ with $1\\le x<y\\le 100$ such that $i^x+i^y$ is a real number. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1850"
} | {
"split": "train",
"index": 27743,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $f(\\alpha) = \\left(\\sqrt{\\frac{1 - \\sin{\\alpha}}{1 + \\sin{\\alpha}}} + \\sqrt{\\frac{1 + \\sin{\\alpha}}{1 - \\sin{\\alpha}}}\\right)\\cos^3{\\alpha} + 2\\sin{\\left(\\frac{\\pi}{2} + \\alpha\\right)}\\cos{\\left(\\frac{3\\pi}{2} + \\alpha\\right)}$ (where $\\... | math | {
"style": "rule",
"ground_truth": "\\frac{3}{4}"
} | {
"split": "train",
"index": 27744,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A cashier from Aeroflot has to deliver tickets to five groups of tourists. Three of these groups live in the hotels \"Druzhba\", \"Rossiya\", and \"Minsk\". The fourth group's address will be given by tourists from \"Rossiya\", and the fifth group's address will be given by tou... | math | {
"style": "rule",
"ground_truth": "30"
} | {
"split": "train",
"index": 27745,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $ABCD$ be a parallelogram such that $\\angle BAD = 60^{\\circ}.$ Let $K$ and $L$ be the midpoints of $BC$ and $CD,$ respectively. Assuming that $ABKL$ is a cyclic quadrilateral, find $\\angle ABD.$ Let's think step by step and put only the final answer with... | math | {
"style": "rule",
"ground_truth": "75"
} | {
"split": "train",
"index": 27746,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "From the digits 0, 1, 2, 3, 4, 5, 6, select 2 even numbers and 1 odd number to form a three-digit number without repeating digits. The number of such three-digit numbers that are divisible by 5 is ____. (Answer with a number) Let's think step by step and put only the final answ... | math | {
"style": "rule",
"ground_truth": "27"
} | {
"split": "train",
"index": 27747,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Can we find \\( N \\) such that all \\( m \\times n \\) rectangles with \\( m, n > N \\) can be tiled with \\( 4 \\times 6 \\) and \\( 5 \\times 7 \\) rectangles? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "840"
} | {
"split": "train",
"index": 27748,
"solution": ""
} |
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