data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deep_scaler | [
{
"content": "A positive integer $N$ is a palindrome if the integer obtained by reversing the sequence of digits of $N$ is equal to $N$. The year 1991 is the only year in the current century with the following 2 properties:\n(a) It is a palindrome\n(b) It factors as a product of a 2-digit prime palindrome and a... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "What is the remainder when $2^{19}$ is divided by $7$?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "2",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "What common fraction (that is, a fraction reduced to its lowest terms) is equivalent to $0.1\\overline{35}$?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{67}{495}",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "Find all numbers in the range of\n\\[f(x) = \\arctan x + \\arctan \\frac{1 - x}{1 + x},\\]expressed in radians. Enter all the numbers, separated by commas.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{3 \\pi}{4}, \\frac{\\pi}{4}",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "An icosidodecahedron is a convex polyhedron with 20 triangular faces and 12 pentagonal faces. How many vertices does it have?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "30",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "Let $U = \\{2, 4, 3-a^2\\}$ and $P = \\{2, a^2+2-a\\}$. Given that the complement of $P$ in $U$, denoted as $\\complement_U P$, is $\\{-1\\}$, find the value of $a$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "a = 2",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "What is the largest number of white and black chips that can be placed on a chessboard so that on each horizontal and each vertical, the number of white chips is exactly twice the number of black chips?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
... | math | {
"ground_truth": "48",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "Let $a$ and $b$ be positive integers such that all but $2009$ positive integers are expressible in the form $ma + nb$ , where $m$ and $n$ are nonnegative integers. If $1776 $ is one of the numbers that is not expressible, \ffind $a + b$ .\nPlease reason step by step, and put your fina... | math | {
"ground_truth": "133",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "Let \\( d = \\overline{xyz} \\) be a three-digit number that cannot be divisible by 10. If the sum of \\( \\overline{xyz} \\) and \\( \\overline{zyx} \\) is divisible by \\( c \\), find the largest possible value of this integer \\( d \\).\nPlease reason step by step, and put your final answer wit... | math | {
"ground_truth": "979",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "A telephone number has the form \\text{ABC-DEF-GHIJ}, where each letter represents a different digit. The digits in each part of the number are in decreasing order; that is, $A > B > C$, $D > E > F$, and $G > H > I > J$. Furthermore, $D$, $E$, and $F$ are consecutive even digits; $G$, $H$, $I$, an... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "In Idaho, 472 people were asked what they call soft drinks. The results of the survey are shown in the pie chart. The central angle of the ``Pop'' sector of the graph is $251^\\circ$, to the nearest whole degree. How many of the people surveyed chose ``Pop''? Express your answer as a whole number.... | math | {
"ground_truth": "329",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "Find constants $A$, $B$, and $C$, such that\n$$\\frac{-x^2+3x-4}{x^3+x}= \\frac{A}{x} +\\frac{Bx+C}{x^2+1} $$Enter your answer as the ordered triplet $(A,B,C)$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "(-4,3,3)",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "Two circles of radius 5 are externally tangent to each other and are internally tangent to a circle of radius 13 at points $A$ and $B$, as shown in the diagram. The distance $AB$ can be written in the form $\\tfrac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. What is $m+n$ ?\n... | math | {
"ground_truth": "69",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "How many rectangles can be formed by the vertices of a cube? (Note: square is also a special rectangle).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "12",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "In the diagram, the smaller circles touch the larger circle and touch each other at the center of the larger circle. The radius of the larger circle is $6.$ What is the area of the shaded region?\n\n[asy]\nsize(100);\nimport graph;\nfilldraw(Circle((0,0),2),mediumgray);\nfilldraw(Circle((-1,0),1),... | math | {
"ground_truth": "18\\pi",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "Trapezoid $EFGH$ has sides $EF=100$, $FG=55$, $GH=23$, and $HE=75$, with $EF$ parallel to $GH$. A circle with center $Q$ on $EF$ is drawn tangent to $FG$ and $HE$. Find the length of $EQ$ if it is expressed as a fraction $\\frac{p}{q}$, where $p$ and $q$ are relatively prime integers.\nPlease reas... | math | {
"ground_truth": "\\frac{750}{13}",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "A particular $12$-hour digital clock displays the hour and minute of a day. Unfortunately, whenever it is supposed to display a $1$, it mistakenly displays a $9$. For example, when it is 1:16 PM the clock incorrectly shows 9:96 PM. What fraction of the day will the clock show the correct time?\nPl... | math | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "Let $k$ be a positive real number. In the $X-Y$ coordinate plane, let $S$ be the set of all points of the form $(x,x^2+k)$ where $x\\in\\mathbb{R}$ . Let $C$ be the set of all circles whose center lies in $S$ , and which are tangent to $X$ -axis. Find the minimum value of $k$ such ... | math | {
"ground_truth": "\\frac{1}{4}",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "The Lakers are playing the Celtics in the NBA finals. To win the NBA finals, a team must win 4 games before the other team does. If the Celtics win each game with probability $\\dfrac{2}{3}$ and there are no ties, what is the probability that the Lakers will win the NBA finals but that the contest... | math | {
"ground_truth": "\\frac{160}{2187}",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "Find the largest value of $t$ such that \\[\\frac{13t^2 - 34t + 12}{3t - 2 } + 5t = 6t - 1.\\]\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{5}{2}",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "Let $a$ be a real number. Find the minimum value of $\\int_0^1 |ax-x^3|dx$ .\n\nHow many solutions (including University Mathematics )are there for the problem?\n\nAny advice would be appreciated. :)\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
... | math | {
"ground_truth": "1/8",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "Let the coefficient of \\( x^{1992} \\) in the power series \\( (1 + x)^{\\alpha} = 1 + \\alpha x + \\dots \\) be \\( C(\\alpha) \\). Find \\( \\int_{0}^{1} C(-y-1) \\sum_{k=1}^{1992} \\frac{1}{y+k} \\, dy \\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": ... | math | {
"ground_truth": "1992",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "Given that \\(A, B, C,\\) and \\(D\\) are points on a circle with radius 1, \\(\\overrightarrow{AB} + 2 \\overrightarrow{AC} = \\overrightarrow{AD}\\), and \\(|AC| = 1\\). Find the area of the quadrilateral \\(ABDC\\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
... | math | {
"ground_truth": "\\frac{3 \\sqrt{3}}{4}",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "Let $g(x)$ be a function defined for all positive real numbers such that $g(x) > 0$ for all $x > 0$ and\n\\[g(x + y) = \\sqrt{g(xy) + 3}\\] for all $x > y > 0.$ Determine $g(2023).$\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1 + \\sqrt{13}}{2}",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "The numbers from 1 to 1000 are written in a circle. Starting from the first one, every 15th number (i.e., the numbers 1, 16, 31, etc.) is crossed out, and during subsequent rounds, already crossed-out numbers are also taken into account. The crossing out continues until it turns out that all the n... | math | {
"ground_truth": "800",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "Find one third of 7.2, expressed as a simplified fraction or a mixed number.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "2 \\frac{2}{5}",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "Gerard cuts a large rectangle into four smaller rectangles. The perimeters of three of these smaller rectangles are 16, 18, and 24. What is the perimeter of the fourth small rectangle?\nA) 8\nB) 10\nC) 12\nD) 14\nE) 16\nPlease reason step by step, and put your final answer within \\boxed{}.",
... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "A construction team has 6 projects (A, B, C, D, E, F) that need to be completed separately. Project B must start after project A is completed, project C must start after project B is completed, and project D must immediately follow project C. Determine the number of different ways to schedule thes... | math | {
"ground_truth": "20",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "A binary operation $\\diamondsuit$ has the properties that $a\\,\\diamondsuit\\, (b\\,\\diamondsuit \\,c) = (a\\,\\diamondsuit \\,b)\\cdot c$ and that $a\\,\\diamondsuit \\,a=1$ for all nonzero real numbers $a, b,$ and $c$. (Here $\\cdot$ represents multiplication). Find the solution to the equati... | math | {
"ground_truth": "\\frac{25}{84}",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "Simplify and find the value: $4(a^{2}b+ab^{2})-3(a^{2}b-1)+2ab^{2}-6$, where $a=1$, $b=-4$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "89",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "The reciprocal of $-2024$ is ______; $7.8963\\approx$ ______ (rounded to the nearest hundredth).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "7.90",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "Ctibor marked a square land plot on a map with a scale of 1:50000 and calculated that its side corresponds to $1 \\mathrm{~km}$ in reality. He then resized the map on a copier such that the marked square had an area $1.44 \\mathrm{~cm}^{2}$ smaller than the original.\n\nWhat was the scale of the r... | math | {
"ground_truth": "1:62500",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "Jeff has a 50 point quiz at 11 am . He wakes up at a random time between 10 am and noon, then arrives at class 15 minutes later. If he arrives on time, he will get a perfect score, but if he arrives more than 30 minutes after the quiz starts, he will get a 0 , but otherwise, he loses a point for e... | math | {
"ground_truth": "\\frac{55}{2}",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "The faces of an octahedral die are labeled with digits $1$ through $8$. What is the probability, expressed as a common fraction, of rolling a sum of $15$ with a pair of such octahedral dice?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{32}",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "Given the ellipse $C_{1}: \\frac{x^{2}}{a^{2}} + \\frac{y^{2}}{b^{2}} = 1 (a > 0, b > 0)$ and the hyperbola $C_{2}: \\frac{x^{2}}{a^{2}} - \\frac{y^{2}}{b^{2}} = 1$ with asymptote equations $x \\pm \\sqrt{3}y = 0$, determine the product of the eccentricities of $C_{1}$ and $C_{2}$.\nPlease reason ... | math | {
"ground_truth": "\\frac{2\\sqrt{2}}{3}",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "The sides of rectangle $ABCD$ have lengths $12$ and $14$. An equilateral triangle is drawn so that no point of the triangle lies outside $ABCD$. Find the maximum possible area of such a triangle.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "36\\sqrt{3}",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "Scatterbrained Scientist had a sore knee. The doctor prescribed 10 pills for the knee, to be taken one pill daily. These pills help in $90 \\%$ of cases, but in $2 \\%$ of cases, there is a side effect—it eliminates scatterbrainedness, if present.\n\nAnother doctor prescribed the Scientist pills f... | math | {
"ground_truth": "0.69",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "Compute the number of ways to fill each cell in a $8 \\times 8$ square grid with one of the letters $H, M$, or $T$ such that every $2 \\times 2$ square in the grid contains the letters $H, M, M, T$ in some order.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role"... | math | {
"ground_truth": "1076",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "Find the largest natural number \\( n \\) with the following property: for any odd prime number \\( p \\) less than \\( n \\), the difference \\( n - p \\) is also a prime number.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "10",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "Suppose there are 15 dogs including Rex and Daisy. We need to divide them into three groups of sizes 6, 5, and 4. How many ways can we form the groups such that Rex is in the 6-dog group and Daisy is in the 4-dog group?\nPlease reason step by step, and put your final answer within \\boxed{}.",
... | math | {
"ground_truth": "72072",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "In any permutation of the numbers \\(1, 2, 3, \\ldots, 18\\), we can always find a set of 6 consecutive numbers whose sum is at least \\(m\\). Find the maximum value of the real number \\(m\\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "57",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "Assume $n$ is a positive integer. Considers sequences $a_0, a_1, \\ldots, a_n$ for which $a_i \\in \\{1, 2, \\ldots , n\\}$ for all $i$ and $a_n = a_0$. \r\n\r\n(a) Suppose $n$ is odd. Find the number of such sequences if $a_i - a_{i-1} \\not \\equiv i \\pmod{n}$ for all $i = 1, 2, \\ldots, n$.\r\... | math | {
"ground_truth": "(n-1)(n-2)^{n-1} - \\frac{2^{n-1} - 1}{n} - 1",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "Determine the smallest positive real number \\(x\\) such that \n\\[\\lfloor x^2 \\rfloor - x \\lfloor x \\rfloor = 7.\\]\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{71}{8}",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "What is the value of $K$ in the equation $16^3\\times8^3=2^K$?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "21",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "A set of 10 distinct integers $S$ is chosen. Let $M$ be the number of nonempty subsets of $S$ whose elements have an even sum. What is the minimum possible value of $M$ ?\n<details><summary>Clarifications</summary>\n\n- $S$ is the ``set of 10 distinct integers'' from the first sentence.\n<... | math | {
"ground_truth": "511",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "A mathematical organization is producing a set of commemorative license plates. Each plate contains a sequence of five characters chosen from the four letters in AIME and the four digits in 2007. No character may appear in a sequence more times than it appears among the four letters in AIME or the... | math | {
"ground_truth": "372",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "A malfunctioning digital clock shows the time $9: 57 \\mathrm{AM}$; however, the correct time is $10: 10 \\mathrm{AM}$. There are two buttons on the clock, one of which increases the time displayed by 9 minutes, and another which decreases the time by 20 minutes. What is the minimum number of butt... | math | {
"ground_truth": "24",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "The product of the positive differences of the sum of eight integers (28) is 6. To what power will it always be divisible?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "6^7",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "There are 22 people standing in a circle, and each of them is either a knight (who always tells the truth) or a liar (who always lies). Each person says: \"The next 10 people clockwise from me are liars.\" How many liars are there among these 22 people?\nPlease reason step by step, and put your fi... | math | {
"ground_truth": "20",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "Given that $α$ is an angle in the first quadrant, it satisfies $\\sin α - \\cos α = \\frac{\\sqrt{10}}{5}$. Find $\\cos 2α$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "- \\frac{4}{5}",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "Given the ellipse $\\frac{x^{2}}{25} + \\frac{y^{2}}{9} = 1$, a line $L$ passing through the right focus $F$ of the ellipse intersects the ellipse at points $A$ and $B$, and intersects the $y$-axis at point $P$. Suppose $\\overrightarrow{PA} = λ_{1} \\overrightarrow{AF}$ and $\\overrightarrow{PB} ... | math | {
"ground_truth": "-\\frac{50}{9}",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "What is the intersection of the lines given by $y=-4x$ and $y-2=12x$? Express your answer as an ordered pair, with both coordinates expressed as common fractions.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "\\left(-\\frac{1}{8}, \\frac{1}{2}\\right)",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "What is the largest possible remainder that is obtained when a two-digit number is divided by the sum of its digits?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "15",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "It is currently 3:15:15 PM on a 12-hour digital clock. After 196 hours, 58 minutes, and 16 seconds, what will the time be in the format $A:B:C$? What is the sum $A + B + C$?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "52",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "The expression $\\frac{4k+8}{4}$ simplifies to an expression of the form $ak+b$ where $a$ and $b$ are integers. Find $\\frac{a}{b}$ .\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "For the Olympic torch relay, it is planned to select 6 cities from 8 in a certain province to establish the relay route, satisfying the following conditions. How many methods are there for each condition?\n(1) Only one of the two cities, A and B, is selected. How many methods are there? How many d... | math | {
"ground_truth": "19440",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "In a right triangle $\\triangle STU$, where $\\angle S = 90^\\circ$, suppose $\\sin T = \\frac{3}{5}$. If the length of $SU$ is 15, find the length of $ST$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "12",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "I have a bag containing red and green marbles. Initially, the ratio of red to green marbles is 3:2. If I remove 18 red marbles and add 15 green marbles, the new ratio becomes 2:5. How many red marbles were there in the bag initially?\nPlease reason step by step, and put your final answer within \\... | math | {
"ground_truth": "33",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "In the diagram, $\\triangle ABF$, $\\triangle BCF$, and $\\triangle CDF$ are right-angled, with $\\angle ABF=\\angle BCF = 90^\\circ$ and $\\angle CDF = 45^\\circ$, and $AF=36$. Find the length of $CF$.\n[asy]\npair A, B, C, D, F;\nA=(0,25);\nB=(0,0);\nC=(0,-12);\nD=(12, -12);\nF=(24,0);\ndraw(A--... | math | {
"ground_truth": "36",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "If the binomial coefficient of only the fourth term in the expansion of $(x^{2} - \\frac {1}{2x})^{n}$ is the largest, then the sum of all the coefficients in the expansion is $\\boxed{\\text{answer}}$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
... | math | {
"ground_truth": "\\frac {1}{64}",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "If $h(x)$ is a function whose domain is $[-8,8]$, and $g(x)=h\\left(\\frac x2\\right)$, then the domain of $g(x)$ is an interval of what width?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "32",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "Given a seminar recording of 495 minutes that needs to be divided into multiple USB sticks, each capable of holding up to 65 minutes of audio, and the minimum number of USB sticks is used, calculate the length of audio that each USB stick will contain.\nPlease reason step by step, and put your fin... | math | {
"ground_truth": "61.875",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "Paint is to be mixed so that the ratio of blue paint to green paint is 5 to 3. If Clara wants to make 45 cans of the mixture and all cans hold the same volume of paint, how many cans of blue paint will she need?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role":... | math | {
"ground_truth": "28",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "An isosceles trapezoid is circumscribed around a circle. The longer base of the trapezoid is $16$, and one of the base angles is $\\arcsin(.8)$. Find the area of the trapezoid.\n$\\textbf{(A)}\\ 72\\qquad \\textbf{(B)}\\ 75\\qquad \\textbf{(C)}\\ 80\\qquad \\textbf{(D)}\\ 90\\qquad \\textbf{(E)}\\... | math | {
"ground_truth": "80",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "Given that $0 < α < \\dfrac {π}{2}$, and $\\cos (2π-α)-\\sin (π-α)=- \\dfrac { \\sqrt {5}}{5}$,\n(1) Find the value of $\\sin α+\\cos α$;\n(2) Find the value of $\\sin (2α- \\dfrac {π}{4})$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "\\dfrac {7 \\sqrt {2}}{10}",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "Triangle $A B C$ has $A B=4, B C=3$, and a right angle at $B$. Circles $\\omega_{1}$ and $\\omega_{2}$ of equal radii are drawn such that $\\omega_{1}$ is tangent to $A B$ and $A C, \\omega_{2}$ is tangent to $B C$ and $A C$, and $\\omega_{1}$ is tangent to $\\omega_{2}$. Find the radius of $\\ome... | math | {
"ground_truth": "\\frac{5}{7}",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "Given the function $f(x)=2 \\sqrt {3}\\sin x\\cos x-\\cos 2x$, where $x\\in R$.\n(1) Find the interval where the function $f(x)$ is monotonically increasing.\n(2) In $\\triangle ABC$, the lengths of the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. If $f(A)=2$, $C=... | math | {
"ground_truth": "\\frac {3+ \\sqrt {3}}{2}",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "Two people agreed to meet at a specific location between 12 PM and 1 PM. The condition is that the first person to arrive will wait for the second person for 15 minutes and then leave. What is the probability that these two people will meet if each of them chooses their moment of arrival at the ag... | math | {
"ground_truth": "7/16",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "Triangle $ABC$ is isosceles with $AB=AC$ . The bisectors of angles $ABC$ and $ACB$ meet at $I$ . If the measure of angle $CIA$ is $130^\\circ$ , compute the measure of angle $CAB$ .\n\n*Proposed by Connor Gordon*\nPlease reason step by step, and put your final answer within \\boxed{}."... | math | {
"ground_truth": "80",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "Joe has a rectangular lawn measuring 120 feet by 180 feet. His lawn mower has a cutting swath of 30 inches, and he overlaps each cut by 6 inches to ensure no grass is missed. Joe mows at a rate of 4000 feet per hour. Calculate the time it will take Joe to mow his entire lawn.\nPlease reason step b... | math | {
"ground_truth": "2.7",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "Given that the year 2010 corresponds to the Geng-Yin year, determine the year of the previous Geng-Yin year.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "1950",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "Let $S$ denote the value of the sum\n\\[\\sum_{n = 1}^{9800} \\frac{1}{\\sqrt{n + \\sqrt{n^2 - 1}}}\\]\n$S$ can be expressed as $p + q \\sqrt{r}$, where $p, q,$ and $r$ are positive integers and $r$ is not divisible by the square of any prime. Determine $p + q + r$.\nPlease reason step by step, an... | math | {
"ground_truth": "121",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "Evaluate $\\frac{2016!^{2}}{2015!2017!}$. Here $n$ ! denotes $1 \\times 2 \\times \\cdots \\times n$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{2016}{2017}",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "Determine the appropriate value of $h$ so that the following equation in base $h$ is accurate:\n$$\\begin{array}{c@{}c@{}c@{}c@{}c@{}c}\n&&8&6&7&4_h \\\\\n&+&4&3&2&9_h \\\\\n\\cline{2-6}\n&1&3&0&0&3_h.\n\\end{array}$$\nPlease reason step by step, and put your final answer within \\boxed{}.",
"... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "On Namek, each hour has 100 minutes. On the planet's clocks, the hour hand completes one full circle in 20 hours and the minute hand completes one full circle in 100 minutes. How many hours have passed on Namek from 0:00 until the next time the hour hand and the minute hand overlap?\nPlease reason... | math | {
"ground_truth": "20/19",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "Using each of the digits 1-9 exactly once, form a two-digit perfect square, a three-digit perfect square, and a four-digit perfect square. What is the smallest four-digit perfect square among them?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "1369",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "The total price of 4 floppy disks and 5 CDs is not less than 20 yuan, and the total price of 6 floppy disks and 3 CDs is not more than 24 yuan. What is the minimum amount of money needed to buy 3 floppy disks and 9 CDs?\nPlease reason step by step, and put your final answer within \\boxed{}.",
... | math | {
"ground_truth": "22",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "Given the function $y=ax^{2}+bx+c$, where $a$, $b$, $c\\in R$.<br/>$(Ⅰ)$ If $a \\gt b \\gt c$ and $a+b+c=0$, and the distance between the graph of this function and the $x$-axis is $l$, find the range of values for $l$;<br/>$(Ⅱ)$ If $a \\lt b$ and the solution set of the inequality $y \\lt 0$ is $... | math | {
"ground_truth": "6+4\\sqrt{3}",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "King Qi and Tian Ji are competing in a horse race. Tian Ji's top horse is better than King Qi's middle horse, worse than King Qi's top horse; Tian Ji's middle horse is better than King Qi's bottom horse, worse than King Qi's middle horse; Tian Ji's bottom horse is worse than King Qi's bottom horse... | math | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "Express $\\frac{165_7}{11_2}+\\frac{121_6}{21_3}$ in base 10.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "39",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "We have an equilateral triangle with circumradius $1$ . We extend its sides. Determine the point $P$ inside the triangle such that the total lengths of the sides (extended), which lies inside the circle with center $P$ and radius $1$ , is maximum.\n(The total distance of the point P from the... | math | {
"ground_truth": "3\\sqrt{3}",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "Find the largest value of the parameter \\(a\\) for which the equation:\n\n\\[ (|x-2| + 2a)^2 - 3(|x-2| + 2a) + 4a(3-4a) = 0 \\]\n\nhas exactly three solutions. Indicate the largest value in the answer.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
... | math | {
"ground_truth": "0.5",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "Mark and Sandy are walking to the convenience store at the midpoint of their coordinates. Mark is standing at $(0,7)$, and Sandy is standing at $(-4,-1)$. At what coordinate will they meet?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "(-2,3)",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "What is the least five-digit positive integer which is congruent to 6 (mod 17)?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "10,017",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "Determine the area of the smallest square that can contain a circle with a radius of 6.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "144",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "Consider the ellipse $C\\_1$: $\\frac{x^{2}}{2}+y^{2}=1$ and the ellipse $C\\_2$: $\\frac{x^{2}}{a^{2}}+\\frac{y^{2}}{b^{2}}=1$ ($a > b > 0$). One focus of ellipse $C\\_2$ has the coordinates $(\\sqrt{5},0)$. The line $l$ with slope $1$ intersects ellipse $C\\_2$ at points $A$ and $B$, and the mid... | math | {
"ground_truth": "-\\frac{1}{2}",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "If a number eight times as large as $x$ is increased by two, then one fourth of the result equals\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "2x + \\frac{1}{2}",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "Given that $E$ and $F$ are a chord of the circle $C: x^{2}+y^{2}-2x-4y+1=0$, and $CE\\bot CF$, $P$ is the midpoint of $EF$. When the chord $EF$ moves on the circle $C$, there exist two points $A$ and $B$ on the line $l: x-y-3=0$ such that $∠APB≥\\frac{π}{2}$ always holds. Determine the minimum val... | math | {
"ground_truth": "4\\sqrt{2}",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "How many distinct sequences of four letters can be made from the letters in PROBLEM if each letter can be used only once and each sequence must begin with L and not end with P?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "100",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "Simplify $\\dfrac{5+12i}{2-3i}$. Your answer should be of the form $a+bi$, where $a$ and $b$ are both real numbers and written as improper fractions (if necessary).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "-2+3i",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "What is the area of the region defined by the equation $x^2+y^2 + 2x - 4y - 8 = 3y - 6x + 9$?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{153\\pi}{4}",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "Two distinct integers, $x$ and $y$, are randomly chosen from the set $\\{1,2,3,4,5,6,7,8,9,10\\}$. What is the probability that $xy-x-y$ is even?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{2}{9}",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "Two \\(10 \\times 24\\) rectangles are inscribed in a circle as shown. Find the shaded area.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "169\\pi - 380",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "In a grade, Class 1, Class 2, and Class 3 each select two students (one male and one female) to form a group of high school students. Two students are randomly selected from this group to serve as the chairperson and vice-chairperson. Calculate the probability of the following events:\n- The two s... | math | {
"ground_truth": "\\dfrac{2}{5}",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "Given that in triangle $\\triangle ABC$, the sides opposite angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively, and $2\\sin A + \\sin B = 2\\sin C\\cos B$ and the area of $\\triangle ABC$ is $S = \\frac{\\sqrt{3}}{2}c$, find the minimum value of $ab$.\nPlease reason step by step, and put ... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "Given an arithmetic sequence $\\{a_n\\}$ with a common difference $d \\neq 0$, and $S_n$ as the sum of its first $n$ terms, if $a_2$, $a_3$, and $a_6$ form a geometric sequence and $a_{10} = -17$, determine the minimum value of $\\frac{S_n}{2^n}$.\nPlease reason step by step, and put your final an... | math | {
"ground_truth": "-\\frac{1}{2}",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "Select 4 students from 5 female and 4 male students to participate in a speech competition. \n(1) If 2 male and 2 female students are to be selected, how many different selections are there? \n(2) If at least 1 male and 1 female student must be selected, and male student A and female student B c... | math | {
"ground_truth": "99",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "A boy has the following seven coins in his pocket: $2$ pennies, $2$ nickels, $2$ dimes, and $1$ quarter. He takes out two coins, records the sum of their values, and then puts them back with the other coins. He continues to take out two coins, record the sum of their values, and put them back. How... | math | {
"ground_truth": "9",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "Barry picks infinitely many points inside a unit circle, each independently and uniformly at random, $P_{1}, P_{2}, \\ldots$ Compute the expected value of $N$, where $N$ is the smallest integer such that $P_{N+1}$ is inside the convex hull formed by the points $P_{1}, P_{2}, \\ldots, P_{N}$. Submi... | math | {
"ground_truth": "6.54",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
deep_scaler | [
{
"content": "The hypotenuse of a right triangle whose legs are consecutive even numbers is 34 units. What is the sum of the lengths of the two legs?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "46",
"style": "rule"
} | {
"dataset": "deepscaler"
} |
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