data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"role": "user",
"content": "There are 7 volunteers to be arranged for community service activities on Saturday and Sunday, with 3 people arranged for each day, calculate the total number of different arrangements. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "140"
} | {
"split": "train",
"index": 21149,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given two-dimensional vectors $\\vec{a}$, $\\vec{b}$, with $|\\vec{a}|=1$, $|\\vec{b}|=2$, and $\\vec{a} \\cdot \\vec{b}=1$. If $\\vec{e}$ is a two-dimensional unit vector, find the maximum value of $|\\vec{a} \\cdot \\vec{e}| + |\\vec{b} \\cdot \\vec{e}|$. Let's think step by ... | math | {
"style": "rule",
"ground_truth": "\\sqrt{7}"
} | {
"split": "train",
"index": 21150,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The numbers from 1 to 150, inclusive, are placed in a bag and a number is randomly selected from the bag. What is the probability it is not a perfect power (integers that can be expressed as $x^{y}$ where $x$ is an integer and $y$ is an integer greater than 1. For example, $2^{... | math | {
"style": "rule",
"ground_truth": "\\frac{133}{150}"
} | {
"split": "train",
"index": 21151,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $S$ be the set of complex numbers of the form $x + yi,$ where $x$ and $y$ are real numbers, such that\n\\[\\frac{\\sqrt{2}}{2} \\le x \\le \\frac{\\sqrt{3}}{2}.\\]Find the smallest positive integer $m$ such that for all positive integers $n \\ge m,$ there exists a complex n... | math | {
"style": "rule",
"ground_truth": "16"
} | {
"split": "train",
"index": 21152,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Selene has 120 cards numbered from 1 to 120, inclusive, and she places them in a box. Selene then chooses a card from the box at random. What is the probability that the number on the card she chooses is a multiple of 2, 4, or 5? Express your answer as a common fraction. Let's ... | math | {
"style": "rule",
"ground_truth": "\\frac{11}{20}"
} | {
"split": "train",
"index": 21153,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Three concentric circles have radii $3,$ $4,$ and $5.$ An equilateral triangle with one vertex on each circle has side length $s.$ The largest possible area of the triangle can be written as $a + \\tfrac{b}{c} \\sqrt{d},$ where $a,$ $b,$ $c,$ and $d$ are positive integers, $b$ ... | math | {
"style": "rule",
"ground_truth": "41"
} | {
"split": "train",
"index": 21154,
"solution": "Reinterpret the problem in the following manner. Equilateral triangle $ABC$ has a point $X$ on the interior such that $AX = 5,$ $BX = 4,$ and $CX = 3.$ A $60^\\circ$ counter-clockwise rotation about vertex $A$ maps $X$ to $X'$ and $B$ to $C.$\n[asy]import cse5; siz... |
deepscaler | [
{
"role": "user",
"content": "There are 10 different mathematics books, 9 different Chinese language books, and 8 different English books. In how many different ways can you take two books of different subjects? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "242"
} | {
"split": "train",
"index": 21155,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the largest possible area of a quadrilateral with sidelengths $1, 4, 7$ and $8$ ? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "18"
} | {
"split": "train",
"index": 21156,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given \\( a_{0}=1, a_{1}=2 \\), and \\( n(n+1) a_{n+1}=n(n-1) a_{n}-(n-2) a_{n-1} \\) for \\( n=1, 2, 3, \\ldots \\), find \\( \\frac{a_{0}}{a_{1}}+\\frac{a_{1}}{a_{2}}+\\frac{a_{2}}{a_{3}}+\\cdots+\\frac{a_{50}}{a_{51}} \\). Let's think step by step and put only the final answ... | math | {
"style": "rule",
"ground_truth": "51"
} | {
"split": "train",
"index": 21157,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $a$ and $b$ be acute angles such that\n\\begin{align*}\n3 \\sin^2 a + 2 \\sin^2 b &= 1, \\\\\n3 \\sin 2a - 2 \\sin 2b &= 0.\n\\end{align*}Find $a + 2b,$ as measured in radians. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\pi}{2}"
} | {
"split": "train",
"index": 21158,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\( P \\) be a regular 2006-sided polygon. A diagonal of \\( P \\) is called a \"good edge\" if both parts of \\( P \\)'s boundary divided by this diagonal contain an odd number of edges. Each side of \\( P \\) is also defined as a \"good edge.\"\n\nGiven that 2003 non-inte... | math | {
"style": "rule",
"ground_truth": "1003"
} | {
"split": "train",
"index": 21159,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many rows of Pascal's Triangle contain the number $43$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1"
} | {
"split": "train",
"index": 21160,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A group of 50 girls sit in a circle. They throw a ball around the circle. Each girl who gets the ball throws it to the girl sitting six places anticlockwise from her, who catches it. Freda catches the ball 100 times. In that time, how many girls never get to catch the ball? Let... | math | {
"style": "rule",
"ground_truth": "25"
} | {
"split": "train",
"index": 21161,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Evaluate $\\lceil-2.4\\rceil$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-2"
} | {
"split": "train",
"index": 21162,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A frog starts climbing from the bottom of a 12-meter deep well at 8:00 AM. For every 3 meters it climbs up, it slides down 1 meter due to the slippery walls. The time to slide down 1 meter is one-third the time taken to climb up 3 meters. At 8:17 AM, the frog reaches 3 meters f... | math | {
"style": "rule",
"ground_truth": "22"
} | {
"split": "train",
"index": 21163,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Express $0.\\overline{1}+0.\\overline{01}+0.\\overline{0001}$ as a common fraction. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1213}{9999}"
} | {
"split": "train",
"index": 21164,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For any positive integer $x$ , let $f(x)=x^x$ . Suppose that $n$ is a positive integer such that there exists a positive integer $m$ with $m \\neq 1$ such that $f(f(f(m)))=m^{m^{n+2020}}$ . Compute the smallest possible value of $n$ .\n\n*Proposed by Luke Robitaille*... | math | {
"style": "rule",
"ground_truth": "13611"
} | {
"split": "train",
"index": 21165,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Use Horner's method to find the value of the polynomial $f(x) = 5x^5 + 2x^4 + 3.5x^3 - 2.6x^2 + 1.7x - 0.8$ when $x=1$, and find the value of $v_3$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "8.8"
} | {
"split": "train",
"index": 21166,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $\\binom{21}{13}=20349$, $\\binom{21}{14}=11628$, and $\\binom{23}{15}=490314$, find $\\binom{22}{15}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "458337"
} | {
"split": "train",
"index": 21167,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A blackboard contains 68 pairs of nonzero integers. Suppose that for each positive integer $k$ at most one of the pairs $(k, k)$ and $(-k, -k)$ is written on the blackboard. A student erases some of the 136 integers, subject to the condition that no two erased integers may ad... | math | {
"style": "rule",
"ground_truth": "43"
} | {
"split": "train",
"index": 21168,
"solution": "Answer: 43\n \nAttainability: Consider 8 distinct positive numbers. Let there be 5 pairs for each of the numbers including 2 clones of that number. Let there also be 28 pairs that include the negatives of those numbers such that each negative associates with anothe... |
deepscaler | [
{
"role": "user",
"content": "Ellie and Sam run on the same circular track but in opposite directions, with Ellie running counterclockwise and Sam running clockwise. Ellie completes a lap every 120 seconds, while Sam completes a lap every 75 seconds. They both start from the same starting line simultaneousl... | math | {
"style": "rule",
"ground_truth": "\\frac{5}{12}"
} | {
"split": "train",
"index": 21169,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $n$ be the number of ordered quadruples $(x_1,x_2,x_3,x_4)$ of positive odd integers that satisfy $\\sum_{i = 1}^4 x_i = 98.$ Find $\\frac n{100}.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "196"
} | {
"split": "train",
"index": 21170,
"solution": "Define $x_i = 2y_i - 1$. Then $2\\left(\\sum_{i = 1}^4 y_i\\right) - 4 = 98$, so $\\sum_{i = 1}^4 y_i = 51$.\n So we want to find four natural numbers that sum up to 51; we can imagine this as trying to split up 51 on the number line into 4 ranges. This is equivale... |
deepscaler | [
{
"role": "user",
"content": "Three years ago, you invested some money at $12\\%$ interest. You now have $\\$504.32$ in the account. If the interest was compounded yearly, how much did you invest 3 years ago? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "359"
} | {
"split": "train",
"index": 21171,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a certain grade with 1000 students, 100 students are selected as a sample using systematic sampling. All students are numbered from 1 to 1000, and are evenly divided into 100 groups (1-10, 11-20, ..., 991-1000 in order). If the number drawn from the first group is 6, then th... | math | {
"style": "rule",
"ground_truth": "96"
} | {
"split": "train",
"index": 21172,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Compute the number of intersection points of the graphs of\n\\[(x - \\lfloor x \\rfloor)^2 + y^2 = x - \\lfloor x \\rfloor\\]and $y = \\frac{1}{5} x.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "11"
} | {
"split": "train",
"index": 21173,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A grocer makes a display of cans in which the top row has one can and each lower row has two more cans than the row above it. If the display contains 100 cans, how many rows does it contain? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 21174,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that the point $(4,7)$ is on the graph of $y=f(x)$, there is one point that must be on the graph of $2y=3f(4x)+5$. What is the sum of the coordinates of that point? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "14"
} | {
"split": "train",
"index": 21175,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The ratio of the measures of two angles of a triangle is 2, and the difference in lengths of the sides opposite to these angles is 2 cm; the length of the third side of the triangle is 5 cm. Calculate the area of the triangle. Let's think step by step and put only the final ans... | math | {
"style": "rule",
"ground_truth": "3.75\\sqrt{7}"
} | {
"split": "train",
"index": 21176,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given $\\sin (30^{\\circ}+\\alpha)= \\frac {3}{5}$, and $60^{\\circ} < \\alpha < 150^{\\circ}$, solve for the value of $\\cos \\alpha$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3-4\\sqrt{3}}{10}"
} | {
"split": "train",
"index": 21177,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A bag contains $4$ identical small balls, of which there is $1$ red ball, $2$ white balls, and $1$ black ball. Balls are drawn from the bag with replacement, randomly taking one each time.\n\n(1) Find the probability of drawing a white ball two consecutive times;\n\n(2) If draw... | math | {
"style": "rule",
"ground_truth": "\\frac{15}{64}"
} | {
"split": "train",
"index": 21178,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the largest four-digit number whose digits add up to 20? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "9920"
} | {
"split": "train",
"index": 21179,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Fill six numbers $1, 3, 5, 7, 9, 11$ into the circles (each circle containing only one number) so that the sum of three numbers on each side of the triangle equals 17. What is the sum of the three numbers in the circles at the vertices of the triangle? Let's think step by step ... | math | {
"style": "rule",
"ground_truth": "15"
} | {
"split": "train",
"index": 21180,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the coordinates of the foci and the eccentricity of the hyperbola $x^{2}-2y^{2}=2$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{6}}{2}"
} | {
"split": "train",
"index": 21181,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many square units are in the area of the parallelogram with vertices at (0, 0), (6, 0), (2, 8) and (8, 8)? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "48"
} | {
"split": "train",
"index": 21182,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A circle is circumscribed about an equilateral triangle with side lengths of $9$ units each. What is the area of the circle, in square units? Express your answer in terms of $\\pi$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "27\\pi"
} | {
"split": "train",
"index": 21183,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the geometric sequence $\\{a_n\\}$, $a_5a_7=2$, $a_2+a_{10}=3$, determine the value of $\\frac{a_{12}}{a_4}$. 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": 21184,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the set \\( M = \\left\\{ x \\ | \\ 5 - |2x - 3| \\in \\mathbf{N}^{*} \\right\\} \\), the number of all non-empty proper subsets of \\( M \\) is? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "510"
} | {
"split": "train",
"index": 21185,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x) = ax^7 + bx - 2$, if $f(2008) = 10$, then the value of $f(-2008)$ is. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-12"
} | {
"split": "train",
"index": 21186,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the points M(2,0) and N(a,b) in the Cartesian coordinate system, with the Manhattan distance between M and N defined as d(M,N) = |x₁ - x₂| + |y₁ - y₂|, and d(M,N) = 2, find the sum of the minimum and maximum values of a² + b² - 4a. Let's think step by step and put only th... | math | {
"style": "rule",
"ground_truth": "-2"
} | {
"split": "train",
"index": 21187,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $x \\%$ of 60 is 12, what is $15 \\%$ of $x$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3"
} | {
"split": "train",
"index": 21188,
"solution": "Since $x \\%$ of 60 is 12, then $\\frac{x}{100} \\cdot 60=12$ or $x=\\frac{12 \\cdot 100}{60}=20$. Therefore, $15 \\%$ of $x$ is $15 \\%$ of 20, or $0.15 \\cdot 20=3$."
} |
deepscaler | [
{
"role": "user",
"content": "Given that $a > 0$, $b > 0$, and $a + b = 1$, find the minimum value of $\\frac{2}{a} + \\frac{3}{b}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "5 + 2\\sqrt{6}"
} | {
"split": "train",
"index": 21189,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The pairwise products $a b, b c, c d$, and $d a$ of positive integers $a, b, c$, and $d$ are $64,88,120$, and 165 in some order. Find $a+b+c+d$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "42"
} | {
"split": "train",
"index": 21190,
"solution": "The sum $a b+b c+c d+d a=(a+c)(b+d)=437=19 \\cdot 23$, so $\\{a+c, b+d\\}=\\{19,23\\}$ as having either pair sum to 1 is impossible. Then the sum of all 4 is $19+23=42$. (In fact, it is not difficult to see that the only possible solutions are $(a, b, c, d)=(8,8,11... |
deepscaler | [
{
"role": "user",
"content": "Given points P(-2, -2), Q(0, -1), and a point R(2, m) is chosen such that PR + PQ is minimized. What is the value of the real number $m$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-2"
} | {
"split": "train",
"index": 21191,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find all functions $f:\\mathbb{R}\\to\\mathbb{R}$ which satisfy the following conditions: $f(x+1)=f(x)+1$ and $f(x^2)=f(x)^2.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "f(x) = x"
} | {
"split": "train",
"index": 21192,
"solution": "\nLet \\( f: \\mathbb{R} \\to \\mathbb{R} \\) be a function satisfying the following conditions:\n1. \\( f(x+1) = f(x) + 1 \\).\n2. \\( f(x^2) = f(x)^2 \\).\n\nWe aim to find all such functions.\n\n### Step 1: Analyze the First Condition\n\nThe first condition \\( ... |
deepscaler | [
{
"role": "user",
"content": "What is $11111111_2+111111_2$? Write your answer in base $10$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "318"
} | {
"split": "train",
"index": 21193,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A straight line $l$ passes through a vertex and a focus of an ellipse. If the distance from the center of the ellipse to $l$ is one quarter of its minor axis length, calculate the eccentricity of the ellipse. Let's think step by step and put only the final answer within \\boxed... | math | {
"style": "rule",
"ground_truth": "\\dfrac{1}{2}"
} | {
"split": "train",
"index": 21194,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Compute the value of \\[M = 50^2 + 48^2 - 46^2 + 44^2 + 42^2 - 40^2 + \\cdots + 4^2 + 2^2 - 0^2,\\] where the additions and subtractions alternate in triplets. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2600"
} | {
"split": "train",
"index": 21195,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A hexagon has its vertices alternately on two concentric circles with radii 3 units and 5 units and centered at the origin on a Cartesian plane. Each alternate vertex starting from the origin extends radially outward to the larger circle. Calculate the area of this hexagon. Let... | math | {
"style": "rule",
"ground_truth": "\\frac{51\\sqrt{3}}{2}"
} | {
"split": "train",
"index": 21196,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Half of the yellow flowers are tulips, one third of the blue flowers are daisies, and seven tenths of the flowers are yellow. Find the percentage of flowers that are daisies. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "45\\%"
} | {
"split": "train",
"index": 21197,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Simplify $\\sqrt{18} \\times \\sqrt{32} \\times \\sqrt{2}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "24\\sqrt{2}"
} | {
"split": "train",
"index": 21198,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A knight begins on the lower-left square of a standard chessboard. How many squares could the knight end up at after exactly 2009 legal knight's moves? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "32"
} | {
"split": "train",
"index": 21199,
"solution": "The knight goes from a black square to a white square on every move, or vice versa, so after 2009 moves he must be on a square whose color is opposite of what he started on. So he can only land on half the squares after 2009 moves. Note that he can access any of th... |
deepscaler | [
{
"role": "user",
"content": "The digit-sum of $998$ is $9+9+8=26$. How many 3-digit whole numbers, whose digit-sum is $26$, are even? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1"
} | {
"split": "train",
"index": 21200,
"solution": "To find how many 3-digit whole numbers have a digit-sum of 26 and are even, we start by considering the constraints:\n\n1. **Digit-Sum Requirement**: The sum of the digits of the number must be 26.\n2. **Even Number Requirement**: The number must be even, which mea... |
deepscaler | [
{
"role": "user",
"content": "Calculate the value of $\\displaystyle\\frac{245^2-225^2}{20}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "470"
} | {
"split": "train",
"index": 21201,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Carla rotated point $A$ 420 degrees clockwise about point $B$ and it landed at point $C$. Devon rotated the original point $A$ $x$ degrees counterclockwise about point $B$ and it also landed at point $C$. If $x<360$, what is the value of $x$? Let's think step by step and put on... | math | {
"style": "rule",
"ground_truth": "300^{\\circ}"
} | {
"split": "train",
"index": 21202,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a geometric sequence $\\{a_n\\}$ satisfies $a_2a_5=2a_3$, and $a_4$, $\\frac{5}{4}$, $2a_7$ form an arithmetic sequence, the maximum value of $a_1a_2a_3…a_n$ is \\_\\_\\_\\_\\_\\_. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1024"
} | {
"split": "train",
"index": 21203,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The value of $\\sqrt{3^{3}+3^{3}+3^{3}}$ is what? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "9"
} | {
"split": "train",
"index": 21204,
"solution": "Since $3^{3}=3 \\times 3 \\times 3=3 \\times 9=27$, then $\\sqrt{3^{3}+3^{3}+3^{3}}=\\sqrt{27+27+27}=\\sqrt{81}=9$."
} |
deepscaler | [
{
"role": "user",
"content": "The segment \\( PQ \\) is divided into several smaller segments. On each of them, a square is constructed (see illustration).\n\nWhat is the length of the path along the arrows if the length of the segment \\( PQ \\) is 73? If necessary, round your answer to 0.01 or write the a... | math | {
"style": "rule",
"ground_truth": "219"
} | {
"split": "train",
"index": 21205,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Patrick tosses four four-sided dice, each numbered $1$ through $4$ . What's the probability their product is a multiple of four? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{13}{16}"
} | {
"split": "train",
"index": 21206,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the quadrilateral \\(ABCD\\), it is known that \\(\\angle BAC = \\angle CAD = 60^\\circ\\), and \\(AB + AD = AC\\). Additionally, it is known that \\(\\angle ACD = 23^\\circ\\). What is the measure of angle \\(ABC\\) in degrees? Let's think step by step and put only the fina... | math | {
"style": "rule",
"ground_truth": "83"
} | {
"split": "train",
"index": 21207,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the smallest positive integer $n$ such that $\\frac{n}{n+53}$ is equal to a terminating decimal? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "11"
} | {
"split": "train",
"index": 21208,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find all solutions to\n\\[\\sqrt[4]{47 - 2x} + \\sqrt[4]{35 + 2x} = 4.\\]Enter all the solutions, separated by commas. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "23,-17"
} | {
"split": "train",
"index": 21209,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If the sum of the first $3n$ positive integers is $150$ more than the sum of the first $n$ positive integers, then the sum of the first $4n$ positive integers is Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "300"
} | {
"split": "train",
"index": 21210,
"solution": "1. **Set up the equation based on the problem statement:**\n The sum of the first $3n$ positive integers is given by the formula $\\frac{3n(3n+1)}{2}$, and the sum of the first $n$ positive integers is given by $\\frac{n(n+1)}{2}$. According to the problem, the s... |
deepscaler | [
{
"role": "user",
"content": "A standard die is rolled consecutively two times. Calculate the probability that the face-up numbers are adjacent natural numbers. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{5}{18}"
} | {
"split": "train",
"index": 21211,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the minimum number of equilateral triangles, of side length 1 unit, needed to cover an equilateral triangle of side length 15 units? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "225"
} | {
"split": "train",
"index": 21212,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a recent test, $15\\%$ of the students scored $60$ points, $20\\%$ got $75$ points, $30\\%$ scored $85$ points, $10\\%$ scored $90$ points, and the rest scored $100$ points. Find the difference between the mean and the median score on this test. Let's think step by step and ... | math | {
"style": "rule",
"ground_truth": "-1.5"
} | {
"split": "train",
"index": 21213,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a sequence $\\{a_n\\}$ where each term is a positive number and satisfies the relationship $a_{n+1}^2 = ta_n^2 +(t-1)a_na_{n+1}$, where $n\\in \\mathbb{N}^*$. \n\n(1) If $a_2 - a_1 = 8$, $a_3 = a$, and the sequence $\\{a_n\\}$ is unique:\n ① Find the value of $a$.\n ②... | math | {
"style": "rule",
"ground_truth": "32"
} | {
"split": "train",
"index": 21214,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $(a_1,a_2,a_3,\\ldots,a_{14})$ be a permutation of $(1,2,3,\\ldots,14)$ where $a_1 > a_2 > a_3 > a_4 > a_5 > a_6 > a_7$ and $a_7 < a_8 < a_9 < a_{10} < a_{11} < a_{12} < a_{13} < a_{14}$. An example of such a permutation is $(7,6,5,4,3,2,1,8,9,10,11,12,13,14)$. Determine th... | math | {
"style": "rule",
"ground_truth": "1716"
} | {
"split": "train",
"index": 21215,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Calculate: $\\sqrt[3]{27}+|-\\sqrt{2}|+2\\sqrt{2}-(-\\sqrt{4})$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "5 + 3\\sqrt{2}"
} | {
"split": "train",
"index": 21216,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle $A B C, \\angle A B C$ is obtuse. Point $D$ lies on side $A C$ such that \\angle A B D$ is right, and point $E$ lies on side $A C$ between $A$ and $D$ such that $B D$ bisects \\angle E B C$. Find $C E$, given that $A C=35, B C=7$, and $B E=5$. Let's think step by st... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 21217,
"solution": "Reflect $A$ and $E$ over $B D$ to $A^{\\prime}$ and $E^{\\prime}$ respectively. Note that the angle conditions show that $A^{\\prime}$ and $E^{\\prime}$ lie on $A B$ and $B C$ respectively. $B$ is the midpoint of segment $A A^{\\prime}$ and $C E^{\\prime}=$ $B C-B ... |
deepscaler | [
{
"role": "user",
"content": "What is the intersection point of the line $y = 2x + 5$ and the line perpendicular to it that passes through the point $(5, 5)$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "(1, 7)"
} | {
"split": "train",
"index": 21218,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A line $x=k$ intersects the graph of $y=\\log_5 x$ and the graph of $y=\\log_5 (x + 4)$. The distance between the points of intersection is $0.5$. Given that $k = a + \\sqrt{b}$, where $a$ and $b$ are integers, what is $a+b$? Let's think step by step and put only the final answ... | math | {
"style": "rule",
"ground_truth": "6"
} | {
"split": "train",
"index": 21219,
"solution": "1. **Identify the points of intersection**: The line $x=k$ intersects the graphs of $y=\\log_5 x$ and $y=\\log_5 (x+4)$. The points of intersection are $(k, \\log_5 k)$ and $(k, \\log_5 (k+4))$ respectively.\n\n2. **Set up the equation for the distance between the ... |
deepscaler | [
{
"role": "user",
"content": "In the sum $K A N$ each letter stands for a different digit.\n$$\n\\frac{+G A}{R O O}\n$$\n\nWhat is the answer to the subtraction $R N$ ?\n$$\n\\underline{-K G}\n$$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "11"
} | {
"split": "train",
"index": 21220,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A set containing three real numbers can be represented as $\\{a,\\frac{b}{a},1\\}$, or as $\\{a^{2}, a+b, 0\\}$. Find the value of $a^{2023}+b^{2024}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"split": "train",
"index": 21221,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "\"My phone number,\" said the trip leader to the kids, \"is a five-digit number. The first digit is a prime number, and the last two digits are obtained from the previous pair (which represents a prime number) by rearrangement, forming a perfect square. The number formed by rev... | math | {
"style": "rule",
"ground_truth": "26116"
} | {
"split": "train",
"index": 21222,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Define $||x||$ $(x\\in R)$ as the integer closest to $x$ (when $x$ is the arithmetic mean of two adjacent integers, $||x||$ takes the larger integer). Let $G(x)=||x||$. If $G(\\frac{4}{3})=1$, $G(\\frac{5}{3})=2$, $G(2)=2$, and $G(2.5)=3$, then $\\frac{1}{G(1)}+\\frac{1}{G(2)}+... | math | {
"style": "rule",
"ground_truth": "\\frac{1334}{15}"
} | {
"split": "train",
"index": 21223,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The value of $\\sin 210^\\circ$ is equal to $\\frac{-\\sqrt{3}}{2}$. 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": 21224,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let numbers $x$ and $y$ be chosen independently at random from the intervals $[0, \\pi]$ and $[-\\frac{\\pi}{2}, \\frac{\\pi}{2}]$, respectively. Define $P(\\alpha)$ as the probability that\n\\[\\cos^2{x} + \\cos^2{y} < \\alpha\\]\nwhere $\\alpha$ is a constant with $1 < \\alph... | math | {
"style": "rule",
"ground_truth": "\\frac{\\pi}{2}"
} | {
"split": "train",
"index": 21225,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the \"five rows by six columns\" examination room, if two students A and B from the same school are to be seated with no two adjacent seats in any direction (front, back, left, right), calculate the number of different seating arrangements for students A and B. Let's think s... | math | {
"style": "rule",
"ground_truth": "772"
} | {
"split": "train",
"index": 21226,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Choose one of the following conditions from (1) $a\\sin \\left(B+C\\right)+c\\sin C-b\\sin B=2a\\sin C\\sin B$, (2) $\\frac{cosB}{cosC}+\\frac{b}{c-\\sqrt{2}a}=0$, (3) $2a^{2}=(a^{2}+b^{2}-c^{2})(1+\\tan C)$, and fill in the blank in the question below, and answer the correspon... | math | {
"style": "rule",
"ground_truth": "\\frac{3\\sqrt{2}}{5}"
} | {
"split": "train",
"index": 21227,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Al, Bert, Carl, and Dan are the winners of a school contest for a pile of books, which they are to divide in a ratio of $4:3:2:1$, respectively. Due to some confusion, they come at different times to claim their prizes, and each assumes he is the first to arrive. If each takes ... | math | {
"style": "rule",
"ground_truth": "\\frac{1701}{2500}"
} | {
"split": "train",
"index": 21228,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For a positive integer $n>1$ , let $g(n)$ denote the largest positive proper divisor of $n$ and $f(n)=n-g(n)$ . For example, $g(10)=5, f(10)=5$ and $g(13)=1,f(13)=12$ . Let $N$ be the smallest positive integer such that $f(f(f(N)))=97$ . Find the largest integer not... | math | {
"style": "rule",
"ground_truth": "19"
} | {
"split": "train",
"index": 21229,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A penny, nickel, dime, and quarter are simultaneously flipped. What is the expected value of the amount of the coins which come up heads? Express your answer in cents, rounded to the nearest tenth of a cent. Let's think step by step and put only the final answer within \\boxe... | math | {
"style": "rule",
"ground_truth": "20.5"
} | {
"split": "train",
"index": 21230,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the positive real number $x$ such that $\\lfloor x \\rfloor \\cdot x = 70$. Express $x$ as a decimal. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "8.75"
} | {
"split": "train",
"index": 21231,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $S = \\{2^0,2^1,2^2,\\ldots,2^{10}\\}$. Consider all possible positive differences of pairs of elements of $S$. Let $N$ be the sum of all of these differences. Find the remainder when $N$ is divided by $1000$. Let's think step by step and put only the final answer within \\... | math | {
"style": "rule",
"ground_truth": "398"
} | {
"split": "train",
"index": 21232,
"solution": "Find the positive differences in all $55$ pairs and you will get $\\boxed{398}$."
} |
deepscaler | [
{
"role": "user",
"content": "Let $S$ be a subset of the set $\\{1,2,3, \\ldots, 2015\\}$ such that for any two elements $a, b \\in S$, the difference $a-b$ does not divide the sum $a+b$. Find the maximum possible size of $S$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "672"
} | {
"split": "train",
"index": 21233,
"solution": "From each of the sets $\\{1,2,3\\},\\{4,5,6\\},\\{7,8,9\\}, \\ldots$ at most 1 element can be in $S$. This leads to an upper bound of $\\left\\lceil\\frac{2015}{3}\\right\\rceil=672$ which we can obtain with the set $\\{1,4,7, \\ldots, 2014\\}$."
} |
deepscaler | [
{
"role": "user",
"content": "How many ounces of pure water must be added to $30$ ounces of a $30\\%$ solution of acid to yield a solution that is $20\\%$ acid? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "15"
} | {
"split": "train",
"index": 21234,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Rationalize the denominator: $$\\frac{1}{\\sqrt[3]{3}+\\sqrt[3]{27}}$$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt[3]{9}}{12}"
} | {
"split": "train",
"index": 21235,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Define the lengths of intervals $(m, n)$, $[m, n)$, $(m, n]$, and $[m, n]$ to be $n - m$ ($n, m \\in \\mathbf{R}$ and $n > m$). Find the sum of the lengths of the intervals for real numbers $x$ that satisfy the inequality\n\\[\n\\frac{1}{x-20}+\\frac{1}{x-17} \\geqslant \\frac{... | math | {
"style": "rule",
"ground_truth": "1024"
} | {
"split": "train",
"index": 21236,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There is a magical tree with 58 fruits. On the first day, 1 fruit falls from the tree. From the second day onwards, the number of fruits falling each day increases by 1 compared to the previous day. However, if on any given day the number of fruits on the tree is less than the ... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 21237,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Suppose $x$ is in the interval $[0, \\pi/2]$ and $\\log_{24\\sin x} (24\\cos x)=\\frac{3}{2}$. Find $24\\cot^2 x$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "192"
} | {
"split": "train",
"index": 21238,
"solution": "Like Solution 1, we can rewrite the given expression as \\[24\\sin^3x=\\cos^2x\\] Divide both sides by $\\sin^3x$. \\[24 = \\cot^2x\\csc x\\] Square both sides. \\[576 = \\cot^4x\\csc^2x\\] Substitute the identity $\\csc^2x = \\cot^2x + 1$. \\[576 = \\cot^4x(\\cot^... |
deepscaler | [
{
"role": "user",
"content": "The graph of $y = \\frac{p(x)}{q(x)}$ is shown below, where $p(x)$ is linear and $q(x)$ is quadratic. (Assume that the grid lines are at integers.)\n\n[asy]\nunitsize(0.6 cm);\n\nreal func (real x) {\n return (2*x/((x - 2)*(x + 3)));\n}\n\nint i;\n\nfor (i = -5; i <= 5; ++i) ... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{3}"
} | {
"split": "train",
"index": 21239,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a \\(10 \\times 10\\) grid (where the sides of the cells have a unit length), \\(n\\) cells are selected, and a diagonal is drawn in each of them with an arrow pointing in one of two directions. It turns out that for any two arrows, either the end of one coincides with the b... | math | {
"style": "rule",
"ground_truth": "48"
} | {
"split": "train",
"index": 21240,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A point \\((x, y)\\) is a distance of 14 units from the \\(x\\)-axis. It is a distance of 8 units from the point \\((1, 8)\\). Given that \\(x > 1\\), what is the distance \\(n\\) from this point to the origin? Let's think step by step and put only the final answer within \\box... | math | {
"style": "rule",
"ground_truth": "15"
} | {
"split": "train",
"index": 21241,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There is an equilateral triangle $ABC$ on the plane. Three straight lines pass through $A$ , $B$ and $C$ , respectively, such that the intersections of these lines form an equilateral triangle inside $ABC$ . On each turn, Ming chooses a two-line intersection inside $ABC... | math | {
"style": "rule",
"ground_truth": "45853"
} | {
"split": "train",
"index": 21242,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the units digit of the decimal expansion of $\\left(15 + \\sqrt{220}\\right)^{19} + \\left(15 + \\sqrt{220}\\right)^{82}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "9"
} | {
"split": "train",
"index": 21243,
"solution": "1. **Define the expressions**:\n Let $A = 15 + \\sqrt{220}$ and $B = 15 - \\sqrt{220}$. \n\n2. **Use the properties of conjugates**:\n Note that $A$ and $B$ are conjugates, and any even power of $\\sqrt{220}$ in their binomial expansions will result in rational... |
deepscaler | [
{
"role": "user",
"content": "Given a random variable $\\xi \\sim N(1,4)$, and $P(\\xi < 3)=0.84$, then $P(-1 < \\xi < 1)=$ \\_\\_\\_\\_\\_\\_. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "0.34"
} | {
"split": "train",
"index": 21244,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $\\mathbf{v}$ be a vector such that\n\\[\\left\\| \\mathbf{v} + \\begin{pmatrix} 3 \\\\ -1 \\end{pmatrix} \\right\\| = 8.\\]Find the smallest possible value of $\\|\\mathbf{v}\\|.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "8 - \\sqrt{10}"
} | {
"split": "train",
"index": 21245,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The average (mean) of a list of 10 numbers is 17. When one number is removed from the list, the new average is 16. What number was removed? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "26"
} | {
"split": "train",
"index": 21246,
"solution": "When 10 numbers have an average of 17, their sum is $10 \\times 17=170$. When 9 numbers have an average of 16, their sum is $9 \\times 16=144$. Therefore, the number that was removed was $170-144=26$."
} |
deepscaler | [
{
"role": "user",
"content": "A box contains 5 white balls and 6 black balls. Five balls are drawn out of the box at random. What is the probability that they all are white? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\dfrac{1}{462}"
} | {
"split": "train",
"index": 21247,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the only real number that can be expressed in the form \\[(a + bi)^3 - 107i,\\]where $i^2 = -1,$ and $a$ and $b$ are positive integers. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "198"
} | {
"split": "train",
"index": 21248,
"solution": ""
} |
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