data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"role": "user",
"content": "Let $\\{a_{n}\\}$ and $\\{b_{n}\\}$ be arithmetic sequences, and let $S_{n}$ and $T_{n}$ be the sums of the first $n$ terms of the sequences, respectively. If $\\frac{S_{n}}{T_{n}}=\\frac{3n-1}{n+3}$, then $\\frac{a_{8}}{b_{5}+b_{11}}=\\_\\_\\_\\_\\_\\_$. Let's think step by st... | math | {
"style": "rule",
"ground_truth": "\\frac{11}{9}"
} | {
"split": "train",
"index": 19249,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The sum of the digits of the integer equal to \\( 777777777777777^2 - 222222222222223^2 \\) is Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "74"
} | {
"split": "train",
"index": 19250,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Children get in for half the price of adults. The price for $8$ adult tickets and $7$ child tickets is $42$. If a group buys more than $10$ tickets, they get an additional $10\\%$ discount on the total price. Calculate the cost of $10$ adult tickets and $8$ child tickets. Let's... | math | {
"style": "rule",
"ground_truth": "46"
} | {
"split": "train",
"index": 19251,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Eight circles of diameter 1 are packed in the first quadrant of the coordinate plane as shown. Let region $\\mathcal{R}$ be the union of the eight circular regions. Line $l,$ with slope 3, divides $\\mathcal{R}$ into two regions of equal area. Line $l$'s equation can be express... | math | {
"style": "rule",
"ground_truth": "65"
} | {
"split": "train",
"index": 19252,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A function $f$ is defined on the complex numbers by $f(z)=(a+bi)z,$ where $a$ and $b$ are positive numbers. This function has the property that for each complex number $z$, $f(z)$ is equidistant from both $z$ and the origin. Given that $|a+bi|=8$, find $b^2.$ Let's think step b... | math | {
"style": "rule",
"ground_truth": "\\frac{255}{4}"
} | {
"split": "train",
"index": 19253,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Round to the nearest thousandth and then subtract 0.005: 18.48571. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "18.481"
} | {
"split": "train",
"index": 19254,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "650 students were surveyed about their pasta preferences. The choices were lasagna, manicotti, ravioli and spaghetti. The results of the survey are displayed in the bar graph. What is the ratio of the number of students who preferred spaghetti to the number of students who pref... | math | {
"style": "rule",
"ground_truth": "\\frac{5}{2}"
} | {
"split": "train",
"index": 19255,
"solution": "1. **Identify the number of students who preferred each pasta type:** According to the problem, the number of students who preferred spaghetti is 250 and the number of students who preferred manicotti is 100.\n\n2. **Set up the ratio:** The ratio of the number of s... |
deepscaler | [
{
"role": "user",
"content": "For $x$ a real number, let $f(x)=0$ if $x<1$ and $f(x)=2 x-2$ if $x \\geq 1$. How many solutions are there to the equation $f(f(f(f(x))))=x ?$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2"
} | {
"split": "train",
"index": 19256,
"solution": "Certainly 0,2 are fixed points of $f$ and therefore solutions. On the other hand, there can be no solutions for $x<0$, since $f$ is nonnegative-valued; for $0<x<2$, we have $0 \\leq f(x)<x<2$ (and $f(0)=0$ ), so iteration only produces values below $x$, and for $x>... |
deepscaler | [
{
"role": "user",
"content": "What is the coefficient of $x^4$ when \n$$x^5 - 4x^4 + 6x^3 - 7x^2 + 2x - 1$$ \nis multiplied by \n$$3x^4 - 2x^3 + 5x - 8$$ \nand combining the similar terms? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "27"
} | {
"split": "train",
"index": 19257,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In $\\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. Given that $c \\sin A = \\sqrt{3}a \\cos C$ and $(a-c)(a+c)=b(b-c)$, find the period and the monotonically increasing interval of the function $f(x) = 2 \\sin x \\cos (\\frac... | math | {
"style": "rule",
"ground_truth": "\\frac{5}{2}"
} | {
"split": "train",
"index": 19258,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Compute the unique positive integer $m$ such that\n\\[1 \\cdot 2^1 + 2 \\cdot 2^2 + 3 \\cdot 2^3 + \\dots + m \\cdot 2^m = 2^{m + 8}.\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "129"
} | {
"split": "train",
"index": 19259,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The volume of a given sphere is \\(72\\pi\\) cubic inches. Find the surface area of the sphere. 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": "36\\pi 2^{2/3}"
} | {
"split": "train",
"index": 19260,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The price of each item at the Gauss Gadget Store has been reduced by $20 \\%$ from its original price. An MP3 player has a sale price of $\\$ 112$. What would the same MP3 player sell for if it was on sale for $30 \\%$ off of its original price? Let's think step by step and put... | math | {
"style": "rule",
"ground_truth": "98"
} | {
"split": "train",
"index": 19261,
"solution": "Since the sale price has been reduced by $20 \\%$, then the sale price of $\\$ 112$ is $80 \\%$ or $\\frac{4}{5}$ of the regular price. Therefore, $\\frac{1}{5}$ of the regular price is $\\$ 112 \\div 4=\\$ 28$. Thus, the regular price is $\\$ 28 \\times 5=\\$ 140$... |
deepscaler | [
{
"role": "user",
"content": "The ferry boat begins transporting tourists to an island every hour starting at 9 AM until its last trip, which starts at 4 PM. On the first trip at 9 AM, there were 120 tourists, and on each successive trip, there were 2 fewer tourists than on the previous trip. Determine the ... | math | {
"style": "rule",
"ground_truth": "904"
} | {
"split": "train",
"index": 19262,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Two circles of radius 3 and 4 are internally tangent to a larger circle. The larger circle circumscribes both the smaller circles. Find the area of the shaded region surrounding the two smaller circles within the larger circle. Express your answer in terms of \\(\\pi\\). Let's ... | math | {
"style": "rule",
"ground_truth": "24\\pi"
} | {
"split": "train",
"index": 19263,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $S_n$ be the sum of the first $n$ terms of the sequence $\\{a_n\\}$. Given that $3S_n=a_{n+1}-2$, and $a_2=1$, find $a_6$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "256"
} | {
"split": "train",
"index": 19264,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Compute\n\\[\n\\frac{(1 + 23) \\left( 1 + \\dfrac{23}{2} \\right) \\left( 1 + \\dfrac{23}{3} \\right) \\dotsm \\left( 1 + \\dfrac{23}{25} \\right)}{(1 + 27) \\left( 1 + \\dfrac{27}{2} \\right) \\left( 1 + \\dfrac{27}{3} \\right) \\dotsm \\left( 1 + \\dfrac{27}{21} \\right)}.\n\... | math | {
"style": "rule",
"ground_truth": "421200"
} | {
"split": "train",
"index": 19265,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A triangle with vertices as $A=(1,3)$, $B=(5,1)$, and $C=(4,4)$ is plotted on a $6\\times5$ grid. What fraction of the grid is covered by the triangle? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{6}"
} | {
"split": "train",
"index": 19266,
"solution": "\nTo find the fraction of the grid covered by the triangle with vertices $A=(1,3)$, $B=(5,1)$, and $C=(4,4)$, we first need to calculate the area of the triangle and then compare it to the area of the grid.\n\n#### Step 1: Calculate the area of the triangle using t... |
deepscaler | [
{
"role": "user",
"content": "A circle with a radius of 3 is centered at the midpoint of one side of an equilateral triangle each side of which has a length of 9. Determine the difference between the area inside the circle but outside the triangle and the area inside the triangle but outside the circle. Let... | math | {
"style": "rule",
"ground_truth": "9\\pi - \\frac{81\\sqrt{3}}{4}"
} | {
"split": "train",
"index": 19267,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the product of the least common multiple (LCM) of $8$ and $6$ and the greatest common divisor (GCD) of $8$ and $6$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "48"
} | {
"split": "train",
"index": 19268,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "At McDonald's restaurants, we can order Chicken McNuggets in packages of 6, 9, or 20 pieces. (For example, we can order 21 pieces because $21=6+6+9$, but there is no way to get 19 pieces.) What is the largest number of pieces that we cannot order? Let's think step by step and p... | math | {
"style": "rule",
"ground_truth": "43"
} | {
"split": "train",
"index": 19269,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Which of the cones below can be formed from a $252^{\\circ}$ sector of a circle of radius 10 by aligning the two straight sides?\n\n[asy]\ndraw((5.8,8.1)..(-10,0)--(0,0)--(3.1,-9.5)..cycle);\nlabel(\"10\",(-5,0),S);\nlabel(\"$252^{\\circ}$\",(0,0),NE);\n[/asy]\n\nA. base radius... | math | {
"style": "rule",
"ground_truth": "C"
} | {
"split": "train",
"index": 19270,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many of the integers between 1 and 1500, inclusive, can be expressed as the difference of the squares of two positive integers? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1124"
} | {
"split": "train",
"index": 19271,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the real solution \\( x, y, z \\) to the equations \\( x + y + z = 5 \\) and \\( xy + yz + zx = 3 \\) such that \\( z \\) is the largest possible value. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{13}{3}"
} | {
"split": "train",
"index": 19272,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "It took $4$ days for $75$ workers, all working together at the same rate, to build an embankment. If only $50$ workers had been available, how many total days would it have taken to build the embankment? Let's think step by step and put only the final answer within \\boxed{}."
... | math | {
"style": "rule",
"ground_truth": "6"
} | {
"split": "train",
"index": 19273,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Express the number one million using numbers that contain only the digit 9 and the algebraic operations of addition, subtraction, multiplication, division, powers, and roots. Determine at least three different solutions. Let's think step by step and put only the final answer wi... | math | {
"style": "rule",
"ground_truth": "1000000"
} | {
"split": "train",
"index": 19274,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $\\sin(α + \\sqrt{2}\\cos(α) = \\sqrt{3})$, find the value of $\\tan(α)$.\n\nA) $\\frac{\\sqrt{2}}{2}$\nB) $\\sqrt{2}$\nC) $-\\frac{\\sqrt{2}}{2}$\nD) $-\\sqrt{2}$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{2}}{2}"
} | {
"split": "train",
"index": 19275,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Convert the base 2 number \\(1011111010_2\\) to its base 4 representation. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "23322_4"
} | {
"split": "train",
"index": 19276,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many 4-digit positive multiples of 4 can be formed from the digits 0, 1, 2, 3, 4, 5, 6 such that each digit appears without repetition? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "176"
} | {
"split": "train",
"index": 19277,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many \"plane-line pairs\" are formed by a line and a plane parallel to each other in a rectangular box, where the line is determined by two vertices and the plane contains four vertices? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "48"
} | {
"split": "train",
"index": 19278,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Masha has an integer multiple of toys compared to Lena, and Lena has the same multiple of toys compared to Katya. Masha gave 3 toys to Lena, and Katya gave 2 toys to Lena. After that, the number of toys each girl had formed an arithmetic progression. How many toys did each girl... | math | {
"style": "rule",
"ground_truth": "105"
} | {
"split": "train",
"index": 19279,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given $a$, $b$, $c \\in \\{1, 2, 3, 4, 5, 6\\}$, if the lengths $a$, $b$, and $c$ can form an isosceles (including equilateral) triangle, then there are \\_\\_\\_\\_\\_\\_ such triangles. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "27"
} | {
"split": "train",
"index": 19280,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In an office at various times during the day, the boss gives the secretary a letter to type, each time putting the letter on top of the pile in the secretary's inbox. When there is time, the secretary takes the top letter off the pile and types it. There are nine letters to be ... | math | {
"style": "rule",
"ground_truth": "704"
} | {
"split": "train",
"index": 19281,
"solution": "Re-stating the problem for clarity, let $S$ be a set arranged in increasing order. At any time an element can be appended to the end of $S$, or the last element of $S$ can be removed. The question asks for the number of different orders in which all of the remainin... |
deepscaler | [
{
"role": "user",
"content": "There are 10 cards, each card is written with two different numbers from $1, 2, 3, 4, 5$, and the numbers on any two cards are not completely the same. These 10 cards are to be placed into five boxes labeled $1, 2, 3, 4, 5$, with the rule that a card with numbers $i, j$ can onl... | math | {
"style": "rule",
"ground_truth": "120"
} | {
"split": "train",
"index": 19282,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Three congruent cones, each with a radius of 8 cm and a height of 8 cm, are enclosed within a cylinder. The base of each cone is consecutively stacked and forms a part of the cylinder’s interior base, while the height of the cylinder is 24 cm. Calculate the volume of the cylind... | math | {
"style": "rule",
"ground_truth": "1024\\pi"
} | {
"split": "train",
"index": 19283,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A 6 m by 8 m rectangular field has a fence around it. There is a post at each of the four corners of the field. Starting at each corner, there is a post every 2 m along each side of the fence. How many posts are there? Let's think step by step and put only the final answer with... | math | {
"style": "rule",
"ground_truth": "14"
} | {
"split": "train",
"index": 19284,
"solution": "A rectangle that is 6 m by 8 m has perimeter $2 \\times(6 \\mathrm{~m}+8 \\mathrm{~m})=28 \\mathrm{~m}$. If posts are put in every 2 m around the perimeter starting at a corner, then we would guess that it will take $\\frac{28 \\mathrm{~m}}{2 \\mathrm{~m}}=14$ post... |
deepscaler | [
{
"role": "user",
"content": "A fair coin is tossed 3 times. What is the probability of at least two consecutive heads? 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": 19285,
"solution": "1. **Total Outcomes**: A fair coin tossed 3 times can result in $2^3 = 8$ possible outcomes. These outcomes are: HHH, HHT, HTH, HTT, THH, THT, TTH, TTT.\n\n2. **Unfavorable Outcomes**: We need to find the outcomes where there are no two consecutive heads. These are... |
deepscaler | [
{
"role": "user",
"content": "Given that $A$, $B$, $C$ are the three internal angles of $\\triangle ABC$, and their respective opposite sides are $a$, $b$, $c$, and $2\\cos ^{2} \\frac {A}{2}+\\cos A=0$.\n(1) Find the value of angle $A$;\n(2) If $a=2 \\sqrt {3},b+c=4$, find the area of $\\triangle ABC$. Let... | math | {
"style": "rule",
"ground_truth": "\\sqrt {3}"
} | {
"split": "train",
"index": 19286,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In $\\triangle PQR,$ the sum of $\\angle P$ and $\\angle Q$ is $60^\\circ.$ What is the measure of $\\angle R?$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "120^\\circ"
} | {
"split": "train",
"index": 19287,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $x + 2y = 30$, what is the value of $\\frac{x}{5} + \\frac{2y}{3} + \\frac{2y}{5} + \\frac{x}{3}$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "16"
} | {
"split": "train",
"index": 19288,
"solution": "Since $x + 2y = 30$, then $\\frac{x}{5} + \\frac{2y}{3} + \\frac{2y}{5} + \\frac{x}{3} = \\frac{x}{5} + \\frac{2y}{5} + \\frac{x}{3} + \\frac{2y}{3} = \\frac{1}{5}x + \\frac{1}{5}(2y) + \\frac{1}{3}x + \\frac{1}{3}(2y) = \\frac{1}{5}(x + 2y) + \\frac{1}{3}(x + 2y) ... |
deepscaler | [
{
"role": "user",
"content": "Consider a number line, with a lily pad placed at each integer point. A frog is standing at the lily pad at the point 0 on the number line, and wants to reach the lily pad at the point 2014 on the number line. If the frog stands at the point $n$ on the number line, it can jump ... | math | {
"style": "rule",
"ground_truth": "0.9102805441016536"
} | {
"split": "train",
"index": 19289,
"solution": "First, we establish a rough upper bound for the probability $p$. Let $q$ be the probability that the frog can reach the lily pad at the point 2014 on the number line if it is allowed to jump from a point $n$ on the number line to the point $n+1$, in addition to the... |
deepscaler | [
{
"role": "user",
"content": "Find the distance between the foci of the hyperbola given by the equation \\(x^2 - 4x - 12y^2 + 24y = -36.\\) Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{2\\sqrt{273}}{3}"
} | {
"split": "train",
"index": 19290,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Quadrilateral $ABCD$ is a rhombus with perimeter $52$ meters. The length of diagonal $\\overline{AC}$ is $24$ meters. What is the area in square meters of rhombus $ABCD$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "120"
} | {
"split": "train",
"index": 19291,
"solution": "1. **Identify the length of each side of the rhombus**: Given that the perimeter of rhombus $ABCD$ is $52$ meters, and knowing that a rhombus has four sides of equal length, we calculate the length of each side as follows:\n \\[\n \\text{Side length} = \\frac{\... |
deepscaler | [
{
"role": "user",
"content": "Given that both $α$ and $β$ are acute angles, and $\\cos(α+β)= \\frac{\\sin α}{\\sin β}$, find the maximum value of $\\tan α$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{ \\sqrt {2}}{4}"
} | {
"split": "train",
"index": 19292,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A positive integer is said to be a \"palindrome\" if it reads the same from left to right as from right to left. For example, 2002 is a palindrome. Find the sum of all 4-digit palindromes. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "495000"
} | {
"split": "train",
"index": 19293,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the least positive integer $n$ such that there are at least $1000$ unordered pairs of diagonals in a regular polygon with $n$ vertices that intersect at a right angle in the interior of the polygon. Let's think step by step and put only the final answer within \\... | math | {
"style": "rule",
"ground_truth": "28"
} | {
"split": "train",
"index": 19294,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Here is a fairly simple puzzle: EH is four times greater than OY. AY is four times greater than OH. Find the sum of all four. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "150"
} | {
"split": "train",
"index": 19295,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A student, Ellie, was supposed to calculate $x-y-z$, but due to a misunderstanding, she computed $x-(y+z)$ and obtained 18. The actual answer should have been 6. What is the value of $x-y$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 19296,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a 12-hour interval (from 0 hours to 12 hours), how many minutes are there when the value of the hour is greater than the value of the minutes? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "66"
} | {
"split": "train",
"index": 19297,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Suppose $f(x)=\\frac{3}{2-x}$. If $g(x)=\\frac{1}{f^{-1}(x)}+9$, find $g(3)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 19298,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the sequence ${a_n}$ that satisfies: $a_1=3$, $a_{n+1}=9\\cdot 3a_{n} (n\\geqslant 1)$, find $\\lim\\limits_{n\\to∞}a_{n}=$ \\_\\_\\_\\_\\_\\_. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "27"
} | {
"split": "train",
"index": 19299,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The operation $\\star$ is defined as $a \\star b = a + \\frac{a}{b}$. What is the value of $12 \\star 3$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "16"
} | {
"split": "train",
"index": 19300,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Alice, Bob, and Carol play a game in which each of them chooses a real number between 0 and 1. The winner of the game is the one whose number is between the numbers chosen by the other two players. Alice announces that she will choose her number uniformly at random from all the... | math | {
"style": "rule",
"ground_truth": "\\frac{13}{24}"
} | {
"split": "train",
"index": 19301,
"solution": "Let $a$, $b$, and $c$ be the numbers that Alice, Bob, and Carol choose, respectively. Alice chooses $a$ uniformly from $[0,1]$, Bob chooses $b$ uniformly from $[\\frac{1}{2}, \\frac{2}{3}]$, and Carol aims to choose $c$ optimally.\n\nCarol wins if her number $c$ is... |
deepscaler | [
{
"role": "user",
"content": "The lateral surface area of a regular triangular pyramid is 3 times the area of its base. The area of the circle inscribed in the base is numerically equal to the radius of this circle. Find the volume of the pyramid. Let's think step by step and put only the final answer withi... | math | {
"style": "rule",
"ground_truth": "\\frac{2 \\sqrt{6}}{\\pi^3}"
} | {
"split": "train",
"index": 19302,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Xiao Ming participated in the \"Inheriting Classics, Building the Future\" themed speech competition. His scores for speech image, speech content, and speech effect were 9, 8, and 9 respectively. If the scores for speech image, speech content, and speech effect are determined i... | math | {
"style": "rule",
"ground_truth": "8.5"
} | {
"split": "train",
"index": 19303,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The value of the expression \\(10 - 10.5 \\div [5.2 \\times 14.6 - (9.2 \\times 5.2 + 5.4 \\times 3.7 - 4.6 \\times 1.5)]\\) is Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "9.3"
} | {
"split": "train",
"index": 19304,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $z_1,z_2,z_3,\\dots,z_{12}$ be the 12 zeroes of the polynomial $z^{12}-2^{36}$. For each $j$, let $w_j$ be one of $z_j$ or $i z_j$. Then the maximum possible value of the real part of $\\sum_{j=1}^{12} w_j$ can be written as $m+\\sqrt{n}$ where $m$ and $n$ are positive inte... | math | {
"style": "rule",
"ground_truth": "784"
} | {
"split": "train",
"index": 19305,
"solution": "Use De Moivre's Theorem to brute force all the roots out. Then choose the greater value of $\\operatorname{Re}(z), \\operatorname{Re}(iz)$. After adeding everything up, you get $\\boxed{784}$.\n ~hastapasta"
} |
deepscaler | [
{
"role": "user",
"content": "Compute the number of distinct pairs of the form (first three digits of $x$, first three digits of $x^{4}$ ) over all integers $x>10^{10}$. For example, one such pair is $(100,100)$ when $x=10^{10^{10}}$. Let's think step by step and put only the final answer within \\boxed{}."... | math | {
"style": "rule",
"ground_truth": "4495"
} | {
"split": "train",
"index": 19306,
"solution": "Graph these points on an $x, y$-plane. We claim that there are integers $100=a_{0}<a_{1}<$ $a_{2}<a_{3}<a_{4}=999$, for which the locus of these points is entirely contained in four taxicab (up/right movement by 1 unit) paths from $\\left(a_{i}, 100\\right)$ to $\\... |
deepscaler | [
{
"role": "user",
"content": "Circles $A,B$, and $C$ are externally tangent to each other and internally tangent to circle $D$. Circles $B$ and $C$ are congruent. Circle $A$ has radius 1 and passes through the center of $D$. What is the radius of circle $B$?\n\n[asy]unitsize(1cm);\npair A,B,C,D;\nA=(-1,0);\... | math | {
"style": "rule",
"ground_truth": "\\frac{8}{9}"
} | {
"split": "train",
"index": 19307,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $h(x) = x - 3$ and $k(x) = x / 4$. Also denote the inverses to these functions as $h^{-1}$ and $k^{-1}$. Compute \\[h(k^{-1}(h^{-1}(h^{-1}(k(h(27)))))).\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "45"
} | {
"split": "train",
"index": 19308,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a sequence $ \\{a_n\\} $ with the first term $ \\dfrac{3}{5} $, and the sequence $ \\{a_n\\} $ satisfies $ a_{n+1} = 2 - \\dfrac{1}{a_n} $, calculate $ a_{2018} $. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\dfrac{4031}{4029}"
} | {
"split": "train",
"index": 19309,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Fold a 10m long rope in half 5 times, then cut it in the middle with scissors. How many segments is the rope cut into? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "33"
} | {
"split": "train",
"index": 19310,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The line $\\sqrt{2}ax+by=1$ intersects the circle $x^{2}+y^{2}=1$ at points $A$ and $B$ (where $a$ and $b$ are real numbers), and $\\triangle AOB$ is a right-angled triangle (where $O$ is the origin). The maximum distance between point $P(a,b)$ and point $(0,1)$ is ______. Let'... | math | {
"style": "rule",
"ground_truth": "\\sqrt{2} + 1"
} | {
"split": "train",
"index": 19311,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given \\( S = [\\sqrt{1}] + [\\sqrt{2}] + \\cdots + [\\sqrt{1988}] \\), find \\( [\\sqrt{S}] \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "241"
} | {
"split": "train",
"index": 19312,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Suppose \\(A, B\\) are the foci of a hyperbola and \\(C\\) is a point on the hyperbola. Given that the three sides of \\(\\triangle ABC\\) form an arithmetic sequence, and \\(\\angle ACB = 120^\\circ\\), determine the eccentricity of the hyperbola. Let's think step by step and ... | math | {
"style": "rule",
"ground_truth": "7/2"
} | {
"split": "train",
"index": 19313,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given an obtuse triangle \\(ABC\\) with obtuse angle \\(C\\). Points \\(P\\) and \\(Q\\) are marked on its sides \\(AB\\) and \\(BC\\) respectively, such that \\(\\angle ACP = CPQ = 90^\\circ\\). Find the length of segment \\(PQ\\) if it is known that \\(AC = 25\\), \\(CP = 20\... | math | {
"style": "rule",
"ground_truth": "16"
} | {
"split": "train",
"index": 19314,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The recruits stood in a row one behind the other, all facing the same direction. Among them were three brothers: Peter, Nicholas, and Denis. Ahead of Peter, there were 50 people; ahead of Nicholas, there were 100; ahead of Denis, there were 170. When the command \"About-face!\"... | math | {
"style": "rule",
"ground_truth": "211"
} | {
"split": "train",
"index": 19315,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A rectangular box has a volume of 108 cubic feet. How many cubic yards are in the volume of this box? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4"
} | {
"split": "train",
"index": 19316,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Suppose the curve C has the polar coordinate equation $ρ\\sin^2θ - 8\\cos θ = 0$. Establish a rectangular coordinate system $xoy$ with the pole as the origin and the non-negative semi-axis of the polar axis as the $x$-axis. A line $l$, with an inclination angle of $α$, passes t... | math | {
"style": "rule",
"ground_truth": "16\\sqrt{2}"
} | {
"split": "train",
"index": 19317,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\( M_n \\) be the set of \\( n \\)-digit pure decimals in decimal notation \\( 0.\\overline{a_1a_2\\cdots a_n} \\), where \\( a_i \\) can only take the values 0 or 1 for \\( i=1,2,\\cdots,n-1 \\), and \\( a_n = 1 \\). Let \\( T_n \\) be the number of elements in \\( M_n \\... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{18}"
} | {
"split": "train",
"index": 19318,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the sum of all the solutions of $x = \\left|2x-|60-2x|\\right|$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "92"
} | {
"split": "train",
"index": 19319,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $ S $ be the set of all sides and diagonals of a regular hexagon. A pair of elements of $ S $ are selected at random without replacement. What is the probability that the two chosen segments have the same length? Let's think step by step and put only the final answer within... | math | {
"style": "rule",
"ground_truth": "\\frac{33}{105}"
} | {
"split": "train",
"index": 19320,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Two cross sections of a right hexagonal pyramid are obtained by cutting the pyramid with planes parallel to the hexagonal base. The areas of the cross sections are $216\\sqrt{3}$ square feet and $486\\sqrt{3}$ square feet. The two planes are $8$ feet apart. How far from the ape... | math | {
"style": "rule",
"ground_truth": "24"
} | {
"split": "train",
"index": 19321,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the maximum of the expression\n$$\n|| \\ldots|| x_{1}-x_{2}\\left|-x_{3}\\right|-\\ldots\\left|-x_{2023}\\right|,\n$$\nwhere \\( x_{1}, x_{2}, \\ldots, x_{2023} \\) are distinct natural numbers between 1 and 2023. Let's think step by step and put only the final answer with... | math | {
"style": "rule",
"ground_truth": "2022"
} | {
"split": "train",
"index": 19322,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A deck of 100 cards is numbered from 1 to 100, each card having the same number printed on both sides. One side of each card is red and the other side is yellow. Barsby places all the cards, red side up, on a table. He first turns over every card that has a number divisible by ... | math | {
"style": "rule",
"ground_truth": "49"
} | {
"split": "train",
"index": 19323,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Ara and Shea were once the same height. Since then Shea has grown 20% while Ara has grown half as many inches as Shea. Shea is now 60 inches tall. How tall, in inches, is Ara now? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "55"
} | {
"split": "train",
"index": 19324,
"solution": "1. **Determine Shea's original height**: \n Given that Shea has grown by 20% and is now 60 inches tall, we can set up the equation for her original height $x$:\n \\[\n 1.2x = 60\n \\]\n Solving for $x$, we divide both sides by 1.2:\n \\[\n x = \\frac{... |
deepscaler | [
{
"role": "user",
"content": "What is the largest 4-digit integer congruent to $7 \\pmod{19}$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "9982"
} | {
"split": "train",
"index": 19325,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Evaluate $\\log_5625$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4"
} | {
"split": "train",
"index": 19326,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $x_1< x_2 < x_3$ be the three real roots of the equation $\\sqrt{100} x^3 - 210x^2 + 3 = 0$. Find $x_2(x_1+x_3)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "21"
} | {
"split": "train",
"index": 19327,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A sequence begins with 3, and each subsequent term is triple the sum of all preceding terms. Determine the first term in the sequence that exceeds 15000. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "36864"
} | {
"split": "train",
"index": 19328,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If \\( \\sqrt{\\frac{3}{x} + 3} = \\frac{5}{3} \\), solve for \\( x \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{27}{2}"
} | {
"split": "train",
"index": 19329,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Oleg drew an empty $50 \\times 50$ table and wrote a number above each column and to the left of each row. It turned out that all 100 written numbers are different, with 50 being rational and the remaining 50 being irrational. Then, in each cell of the table, he recorded the su... | math | {
"style": "rule",
"ground_truth": "1250"
} | {
"split": "train",
"index": 19330,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "An [i]animal[/i] with $n$ [i]cells[/i] is a connected figure consisting of $n$ equal-sized cells[1].\n\nA [i]dinosaur[/i] is an animal with at least $2007$ cells. It is said to be [i]primitive[/i] it its cells cannot be partitioned into two or more dinosaurs. Find with proof th... | math | {
"style": "rule",
"ground_truth": "4n-3"
} | {
"split": "train",
"index": 19331,
"solution": "\nA **dinosaur** is a **polyomino** having at least 2007 cells that is also **primitive**, meaning it cannot be split into smaller dinosaurs. We need to determine the maximum number of cells in a primitive dinosaur.\n\nTo tackle this problem, let's consider a primi... |
deepscaler | [
{
"role": "user",
"content": "The values of $y$ which will satisfy the equations $2x^{2}+6x+5y+1=0$, $2x+y+3=0$ may be found by solving: Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "y^{2}+10y-7=0"
} | {
"split": "train",
"index": 19332,
"solution": "1. **Substitute $x$ from the second equation into the first equation:**\n Given the equations:\n \\[ 2x^2 + 6x + 5y + 1 = 0 \\]\n \\[ 2x + y + 3 = 0 \\]\n Solve the second equation for $x$:\n \\[ 2x = -y - 3 \\]\n \\[ x = -\\frac{y+3}{2} \\]\n\n2. **Sub... |
deepscaler | [
{
"role": "user",
"content": "In the Cartesian coordinate plane $(xOy)$, if the line $ax + y - 2 = 0$ intersects the circle centered at $C$ with the equation $(x - 1)^2 + (y - a)^2 = 16$ at points $A$ and $B$, and $\\triangle ABC$ is a right triangle, then the value of the real number $a$ is _____. Let's th... | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"split": "train",
"index": 19333,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many whole numbers from $1$ through $46$ are divisible by either $3$ or $5$ or both? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "21"
} | {
"split": "train",
"index": 19334,
"solution": "1. **Count numbers divisible by 3**: \n To find how many numbers between 1 and 46 are divisible by 3, we calculate:\n \\[\n \\left\\lfloor \\frac{46}{3} \\right\\rfloor = 15\n \\]\n This means there are 15 numbers divisible by 3.\n\n2. **Count numbers div... |
deepscaler | [
{
"role": "user",
"content": "How many points on the hyperbola \\( y = \\frac{2013}{x} \\) are there such that the tangent line at those points intersects both coordinate axes at points with integer coordinates? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "48"
} | {
"split": "train",
"index": 19335,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Calculate: $(10 \\times 19 \\times 20 \\times 53 \\times 100 + 601) \\div 13 = \\ ?$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1549277"
} | {
"split": "train",
"index": 19336,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many natural numbers between 200 and 400 are divisible by 8? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "25"
} | {
"split": "train",
"index": 19337,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the greatest integer $x$ such that $|6x^2-47x+15|$ is prime? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "8"
} | {
"split": "train",
"index": 19338,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given \\( x \\) satisfies \\(\\log _{5 x} 2 x = \\log _{625 x} 8 x\\), find the value of \\(\\log _{2} x\\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\ln 5}{2 \\ln 2 - 3 \\ln 5}"
} | {
"split": "train",
"index": 19339,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Little Pang, Little Dingding, Little Ya, and Little Qiao's four families, totaling 8 parents and 4 children, went to the amusement park together. The ticket prices are as follows: adult tickets are 100 yuan per person; children's tickets are 50 yuan per person; if there are 10 ... | math | {
"style": "rule",
"ground_truth": "800"
} | {
"split": "train",
"index": 19340,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In $\\triangle ABC$, $AC = BC$, and point $D$ is on $\\overline{BC}$ so that $CD = 3\\cdot BD$. Let $E$ be the midpoint of $\\overline{AD}$. Given that $CE = \\sqrt{7}$ and $BE = 3$, the area of $\\triangle ABC$ can be expressed in the form $m\\sqrt{n}$, where $m$ and $n$ are p... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 19341,
"solution": "Let the coordinates of A, B and C be (-a, 0), (a, 0) and (0, h) respectively. Then $D = (\\frac{3a}{4}, \\frac{h}{4})$ and $E = (-\\frac{a}{8},\\frac{h}{8}).$ $EC^2 = 7$ implies $a^2 + 49h^2 = 448$; $EB^2 = 9$ implies $81a^2 + h^2 = 576.$ Solve this system of equat... |
deepscaler | [
{
"role": "user",
"content": "Given that $\\operatorname{log}_{8}(p) = \\operatorname{log}_{12}(q) = \\operatorname{log}_{18}(p-q)$, calculate the value of $\\frac{q}{p}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{5} - 1}{2}"
} | {
"split": "train",
"index": 19342,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the real numbers \\( x \\) and \\( y \\) that satisfy \\( xy + 6 = x + 9y \\) and \\( y \\in (-\\infty, 1) \\), find the maximum value of \\((x+3)(y+1)\\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "27 - 12\\sqrt{2}"
} | {
"split": "train",
"index": 19343,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $\\cos 60^{\\circ} = \\cos 45^{\\circ} \\cos \\theta$ with $0^{\\circ} \\leq \\theta \\leq 90^{\\circ}$, what is the value of $\\theta$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "45^{\\circ}"
} | {
"split": "train",
"index": 19344,
"solution": "Since $\\cos 60^{\\circ}=\\frac{1}{2}$ and $\\cos 45^{\\circ}=\\frac{1}{\\sqrt{2}}$, then the given equation $\\cos 60^{\\circ}=\\cos 45^{\\circ} \\cos \\theta$ becomes $\\frac{1}{2}=\\frac{1}{\\sqrt{2}} \\cos \\theta$. Therefore, $\\cos \\theta=\\frac{\\sqrt{2}}{2... |
deepscaler | [
{
"role": "user",
"content": "Given Jasmine has two types of bottles, one that can hold 45 milliliters and another that can hold 675 milliliters, and a vase that can hold 95 milliliters, determine the total number of small bottles she must buy to fill the large bottle as much as possible and the vase. Let's... | math | {
"style": "rule",
"ground_truth": "18"
} | {
"split": "train",
"index": 19345,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $\\mathbf{Z}$ denote the set of all integers. Find all real numbers $c > 0$ such that there exists a labeling of the lattice points $ ( x, y ) \\in \\mathbf{Z}^2$ with positive integers for which: \n[list]\n[*] only finitely many distinct labels occur, and\n[*] for each lab... | math | {
"style": "rule",
"ground_truth": "c < \\sqrt{2}"
} | {
"split": "train",
"index": 19346,
"solution": "\nTo solve this problem, we need to determine all real numbers \\( c > 0 \\) such that there exists a labeling of the lattice points \\( (x, y) \\in \\mathbf{Z}^2 \\) with positive integers while satisfying the given conditions:\n- Only finitely many distinct label... |
deepscaler | [
{
"role": "user",
"content": "Find the greatest common divisor of $5616$ and $11609$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "13"
} | {
"split": "train",
"index": 19347,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given $a \\neq 0,$ solve for $x$ in\n\\[\\begin{vmatrix} x + a & x & x \\\\ x & x + a & x \\\\ x & x & x + a \\end{vmatrix} = 0.\\]Give your answer in terms of $a.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{a}{3}"
} | {
"split": "train",
"index": 19348,
"solution": ""
} |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.