data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"role": "user",
"content": "The real numbers $x, y, z, w$ satisfy $$\\begin{aligned} & 2 x+y+z+w=1 \\\\ & x+3 y+z+w=2 \\\\ & x+y+4 z+w=3 \\\\ & x+y+z+5 w=25 \\end{aligned}$$ Find the value of $w$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "11/2"
} | {
"split": "train",
"index": 23949,
"solution": "Multiplying the four equations by $12,6,4,3$ respectively, we get $$\\begin{aligned} 24 x+12 y+12 z+12 w & =12 \\\\ 6 x+18 y+6 z+6 w & =12 \\\\ 4 x+4 y+16 z+4 w & =12 \\\\ 3 x+3 y+3 z+15 w & =75 \\end{aligned}$$ Adding these yields $37 x+37 y+37 z+37 w=111$, or $x+... |
deepscaler | [
{
"role": "user",
"content": "An aluminum can in the shape of a cylinder is closed at both ends. Its surface area is $300 \\mathrm{~cm}^{2}$. If the radius of the can were doubled, its surface area would be $900 \\mathrm{~cm}^{2}$. If instead the height of the can were doubled, what would its surface area b... | math | {
"style": "rule",
"ground_truth": "450 \\mathrm{~cm}^{2}"
} | {
"split": "train",
"index": 23950,
"solution": "Suppose that the original can has radius $r \\mathrm{~cm}$ and height $h \\mathrm{~cm}$. Since the surface area of the original can is $300 \\mathrm{~cm}^{2}$, then $2 \\pi r^{2}+2 \\pi r h=300$. When the radius of the original can is doubled, its new radius is $2 ... |
deepscaler | [
{
"role": "user",
"content": "Read the following material and then answer the following questions: When simplifying algebraic expressions, sometimes we encounter expressions like $\\frac{5}{\\sqrt{3}}$, $\\frac{2}{\\sqrt{3}+1}$, in fact, we can further simplify them:<br/>$($1) $\\frac{5}{\\sqrt{3}}=\\frac{5... | math | {
"style": "rule",
"ground_truth": "\\frac{3\\sqrt{11}-1}{2}"
} | {
"split": "train",
"index": 23951,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A sequence of real numbers $a_{0}, a_{1}, \\ldots, a_{9}$ with $a_{0}=0, a_{1}=1$, and $a_{2}>0$ satisfies $$a_{n+2} a_{n} a_{n-1}=a_{n+2}+a_{n}+a_{n-1}$$ for all $1 \\leq n \\leq 7$, but cannot be extended to $a_{10}$. In other words, no values of $a_{10} \\in \\mathbb{R}$ sat... | math | {
"style": "rule",
"ground_truth": "\\sqrt{2}-1"
} | {
"split": "train",
"index": 23952,
"solution": "Say $a_{2}=a$. Then using the recursion equation, we have $a_{3}=-1, a_{4}=\\frac{a+1}{a-1}, a_{5}=\\frac{-a+1}{a+1}, a_{6}=-\\frac{1}{a}$, $a_{7}=-\\frac{2 a}{a^{2}-1}$, and $a_{8}=1$ Now we have $a_{10} a_{8} a_{7}=a_{10}+a_{8}+a_{7}$. No value of $a_{10}$ can sa... |
deepscaler | [
{
"role": "user",
"content": "Given a pyramid with a vertex and base ABCD, each vertex is painted with one color, ensuring that two vertices on the same edge are of different colors. There are 5 different colors available. Calculate the total number of distinct coloring methods. (Answer with a number) Let's... | math | {
"style": "rule",
"ground_truth": "420"
} | {
"split": "train",
"index": 23953,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given two non-zero vectors $\\overrightarrow {a}$ and $\\overrightarrow {b}$ that satisfy $| \\overrightarrow {a} + \\overrightarrow {b} | = | \\overrightarrow {a} - \\overrightarrow {b} | = \\sqrt {2} | \\overrightarrow {a} |$, find the angle between vector $\\overrightarrow {... | math | {
"style": "rule",
"ground_truth": "\\frac{\\pi}{4}"
} | {
"split": "train",
"index": 23954,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Consider a string of $n$ $7$'s, $7777\\cdots77,$ into which $+$ signs are inserted to produce an arithmetic expression. For example, $7+77+777+7+7=875$ could be obtained from eight $7$'s in this way. For how many values of $n$ is it possible to insert $+$ signs so that the resu... | math | {
"style": "rule",
"ground_truth": "108"
} | {
"split": "train",
"index": 23955,
"solution": "To simplify, replace all the $7$’s with $1$’s. Because the sum is congruent to $n \\pmod 9$ and \\[1000 \\equiv 1 \\pmod 9 \\implies n \\equiv 1 \\pmod 9\\] Also, $n \\leq 1000$. There are \\[\\left \\lfloor \\frac{1000}{9} \\right \\rfloor + 1 = 112 \\textrm{ posi... |
deepscaler | [
{
"role": "user",
"content": "Consider the following function $g(x)$ defined as\\[(x^{2^{2008}-1}-1)g(x) = (x+1)(x^2+1)(x^4+1)\\cdots (x^{2^{2007}}+1) - 1\\]Find $g(2)$.\n Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2"
} | {
"split": "train",
"index": 23956,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $S = {1, 2, \\cdots, 100}.$ $X$ is a subset of $S$ such that no two distinct elements in $X$ multiply to an element in $X.$ Find the maximum number of elements of $X$ . \n\n*2022 CCA Math Bonanza Individual Round #3* Let's think step by step and put only the fina... | math | {
"style": "rule",
"ground_truth": "91"
} | {
"split": "train",
"index": 23957,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The country of HMMTLand has 8 cities. Its government decides to construct several two-way roads between pairs of distinct cities. After they finish construction, it turns out that each city can reach exactly 3 other cities via a single road, and from any pair of distinct cities... | math | {
"style": "rule",
"ground_truth": "875"
} | {
"split": "train",
"index": 23958,
"solution": "Let the cities be numbered $1,2,3,4,5,6,7,8$. WLOG, 1 is connected to 2,3 , and 4 . First suppose 2 and 3 are connected; then 3 and 1 share a second common neighbor, which must be 4 (as 1 is not connected to anything else). Likewise 2 and 4 are connected, and so 5,... |
deepscaler | [
{
"role": "user",
"content": "The increasing sequence $1,3,4,9,10,12,13\\cdots$ consists of all those positive integers which are powers of 3 or sums of distinct powers of 3. Find the $50^{\\mbox{th}}$ term of this sequence. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "327"
} | {
"split": "train",
"index": 23959,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $\\triangle ABC$ be a right triangle at $A$ with circumcircle $\\omega$. The tangents to $\\omega$ at $B$ and $C$ intersect at $T$. Let $X$ and $Y$ be the projections of $T$ onto lines $AB$ and $AC$, respectively. Suppose $BT = CT = 25$, $BC = 34$, and $TX^2 + TY^2 + XY^2 =... | math | {
"style": "rule",
"ground_truth": "987.5"
} | {
"split": "train",
"index": 23960,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Alice is bored in class, so she thinks of a positive integer. Every second after that, she subtracts from her current number its smallest prime divisor, possibly itself. After 2022 seconds, she realizes that her number is prime. Find the sum of all possible values of her initia... | math | {
"style": "rule",
"ground_truth": "8093"
} | {
"split": "train",
"index": 23961,
"solution": "Let $a_{k}$ denote Alice's number after $k$ seconds, and let $p_{k}$ be the smallest prime divisor of $a_{k}$. We are given that $a_{2022}$ is prime, and want to find $a_{0}$. If $a_{0}$ is even, then $a_{n+1}=a_{n}-2$, since every $a_{n}$ is even. Then we need $a_... |
deepscaler | [
{
"role": "user",
"content": "The graph of the function $f(x)=\\sqrt{3}\\cos 2x-\\sin 2x$ can be obtained by translating the graph of the function $f(x)=2\\sin 2x$ by an unspecified distance. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\dfrac{\\pi}{6}"
} | {
"split": "train",
"index": 23962,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Rationalize the denominator of $\\frac{7}{3+\\sqrt{8}}$. The answer can be expressed as $\\frac{P\\sqrt{Q}+R}{S}$, where $P$, $Q$, $R$, and $S$ are integers, $S$ is positive, and $Q$ is not divisible by the square of any prime. If the greatest common divisor of $P$, $R$, and $S... | math | {
"style": "rule",
"ground_truth": "23"
} | {
"split": "train",
"index": 23963,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Calculate the value of $\\sin 135^{\\circ}\\cos (-15^{\\circ}) + \\cos 225^{\\circ}\\sin 15^{\\circ}$. 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": 23964,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Halfway through a 100-shot archery tournament, Chelsea leads by 50 points. For each shot a bullseye scores 10 points, with other possible scores being 8, 4, 2, and 0 points. Chelsea always scores at least 4 points on each shot. If Chelsea's next $n$ shots are bullseyes she will... | math | {
"style": "rule",
"ground_truth": "42"
} | {
"split": "train",
"index": 23965,
"solution": "1. **Identify the current situation**: Chelsea is leading by 50 points after 50 shots. Let $k$ be the number of points Chelsea has scored so far.\n\n2. **Determine the maximum possible score for the opponent**: Since the opponent is 50 points behind Chelsea, if the... |
deepscaler | [
{
"role": "user",
"content": "Given the sequence $\\left\\{a_{n}\\right\\}$ defined by \\(a_{1}=\\frac{2}{3}\\), \\(a_{n+1}=a_{n}^{2}+a_{n-1}^{2}+\\cdots+a_{1}^{2}\\) (where \\(n \\in \\mathbf{N}^{*}\\)), find the smallest value of \\(M\\) such that for any \\(n \\in \\mathbf{N}^{*}\\), the inequality \\(\\... | math | {
"style": "rule",
"ground_truth": "\\frac{57}{20}"
} | {
"split": "train",
"index": 23966,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A number has 6 on both its tens and hundredths places, and 0 on both its ones and tenths places. This number is written as \\_\\_\\_\\_\\_\\_. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "60.06"
} | {
"split": "train",
"index": 23967,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the least positive integer that is divisible by the primes 7, 11, and 13? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1001"
} | {
"split": "train",
"index": 23968,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Dean is playing a game with calculators. The 42 participants (including Dean) sit in a circle, and Dean holds 3 calculators. One calculator reads 1, another 0, and the last one -1. Dean starts by pressing the cube button on the calculator that shows 1, pressing the square butto... | math | {
"style": "rule",
"ground_truth": "0"
} | {
"split": "train",
"index": 23969,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the minimum (identical) number of pencils that need to be placed in each of the 6 boxes so that in any 4 boxes there are pencils of any of the 26 pre-specified colors (assuming there are enough pencils available)? Let's think step by step and put only the final answer w... | math | {
"style": "rule",
"ground_truth": "13"
} | {
"split": "train",
"index": 23970,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many perfect squares are between 100 and 400? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "11"
} | {
"split": "train",
"index": 23971,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the equation of a line is $Ax+By=0$, choose two different numbers from the set $\\{1, 2, 3, 4, 5\\}$ to be the values of $A$ and $B$ each time, and find the number of different lines obtained. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "18"
} | {
"split": "train",
"index": 23972,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Egor wrote a number on the board and encrypted it according to the rules of letter puzzles (different letters correspond to different digits, identical letters - identical digits). The result was the word \"GWATEMALA\". How many different numbers could Egor have originally writ... | math | {
"style": "rule",
"ground_truth": "114240"
} | {
"split": "train",
"index": 23973,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Cory has $4$ apples, $2$ oranges, and $1$ banana. If Cory eats one piece of fruit per day for a week, and must consume at least one apple before any orange, how many different orders can Cory eat these fruits? The fruits within each category are indistinguishable. Let's think s... | math | {
"style": "rule",
"ground_truth": "105"
} | {
"split": "train",
"index": 23974,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle $ABC,\\,$ angle $C$ is a right angle and the altitude from $C\\,$ meets $\\overline{AB}\\,$ at $D.\\,$ The lengths of the sides of $\\triangle ABC\\,$ are integers, $BD=29^3,\\,$ and $\\cos B=m/n\\,$, where $m\\,$ and $n\\,$ are relatively prime positive integers. F... | math | {
"style": "rule",
"ground_truth": "450"
} | {
"split": "train",
"index": 23975,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In how many ways can the number 5 be expressed as the sum of one or more positive integers? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "16"
} | {
"split": "train",
"index": 23976,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a tetrahedron \\(ABCD\\), \\(AD = \\sqrt{2}\\) and all other edge lengths are 1. Find the shortest path distance from the midpoint \\(M\\) of edge \\(AB\\) to the midpoint \\(N\\) of edge \\(CD\\) along the surface of the tetrahedron. Let's think step by step and put only th... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{3}}{2}"
} | {
"split": "train",
"index": 23977,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Robert has 4 indistinguishable gold coins and 4 indistinguishable silver coins. Each coin has an engraving of one face on one side, but not on the other. He wants to stack the eight coins on a table into a single stack so that no two adjacent coins are face to face. Find the nu... | math | {
"style": "rule",
"ground_truth": "630"
} | {
"split": "train",
"index": 23978,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the correct ordering of the three numbers $\\frac{5}{19}$, $\\frac{7}{21}$, and $\\frac{9}{23}$, in increasing order? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{5}{19} < \\frac{7}{21} < \\frac{9}{23}"
} | {
"split": "train",
"index": 23979,
"solution": "To find the correct ordering of the fractions $\\frac{5}{19}$, $\\frac{7}{21}$, and $\\frac{9}{23}$, we can compare each pair of fractions.\n\n1. **Simplify $\\frac{7}{21}$:**\n \\[\\frac{7}{21} = \\frac{1}{3}\\]\n\n2. **Compare $\\frac{5}{19}$ and $\\frac{7}{21}... |
deepscaler | [
{
"role": "user",
"content": "In a 24-hour format digital watch that displays hours and minutes, calculate the largest possible sum of the digits in the display if the sum of the hour digits must be even. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "22"
} | {
"split": "train",
"index": 23980,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $\\left\\{a_{n}\\right\\}$ be the number of subsets of the set $\\{1,2, \\ldots, n\\}$ with the following properties:\n- Each subset contains at least two elements.\n- The absolute value of the difference between any two elements in the subset is greater than 1.\n\nFind $\\... | math | {
"style": "rule",
"ground_truth": "133"
} | {
"split": "train",
"index": 23981,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that \\( n \\) is a positive integer and \\( n \\leq 144 \\), ten questions of the type \"Is \\( n \\) smaller than \\( a \\)?\" are allowed. The answers are provided with a delay such that the answer to the \\( i \\)-th question is given only after the \\((i+1)\\)-st que... | math | {
"style": "rule",
"ground_truth": "144"
} | {
"split": "train",
"index": 23982,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Recall that a perfect square is the square of some integer. How many perfect squares less than 10,000 can be represented as the difference of two consecutive perfect squares? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "50"
} | {
"split": "train",
"index": 23983,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For some complex number $z$ with $|z| = 3,$ there is some real $\\lambda > 1$ such that $z,$ $z^2,$ and $\\lambda z$ form an equilateral triangle in the complex plane. Find $\\lambda.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1 + \\sqrt{33}}{2}"
} | {
"split": "train",
"index": 23984,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "(1) Find the value of $\\cos\\frac{5\\pi}{3}$.\n\n(2) Given that $\\frac{\\sin\\alpha + 2\\cos\\alpha}{5\\cos\\alpha - \\sin\\alpha} = \\frac{5}{16}$, find the value of $\\tan\\alpha$.\n\n(3) Given that $\\sin\\theta = \\frac{1}{3}$ and $\\theta \\in (0, \\frac{\\pi}{2})$, find... | math | {
"style": "rule",
"ground_truth": "2\\sqrt{2}"
} | {
"split": "train",
"index": 23985,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a specific year, a \"prime date\" occurs when both the month and the day are prime numbers. Determine the total number of prime dates in a non-leap year where February has 28 days, and March, May, and July have 31 days, while November has 30 days. Let's think step by step an... | math | {
"style": "rule",
"ground_truth": "52"
} | {
"split": "train",
"index": 23986,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For what value of the parameter \\( p \\) will the sum of the squares of the roots of the equation\n\n\\[ \nx^{2}+(3 p-2) x-7 p-1=0 \n\\]\n\nbe minimized? What is this minimum value? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{53}{9}"
} | {
"split": "train",
"index": 23987,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find all primes $p$ such that there exist positive integers $x,y$ that satisfy $x(y^2-p)+y(x^2-p)=5p$ . Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2, 3, 7"
} | {
"split": "train",
"index": 23988,
"solution": "Rearrange the original equation to get \\begin{align*} 5p &= xy^2 + x^2 y - xp - yp \\\\ &= xy(x+y) -p(x+y) \\\\ &= (xy-p)(x+y) \\end{align*} Since $5p$ , $xy-p$ , and $x+y$ are all integers, $xy-p$ and $x+y$ must be a factor of $5p$ . Now there are four cases to c... |
deepscaler | [
{
"role": "user",
"content": "A park is in the shape of a regular hexagon $2$ km on a side. Starting at a corner, Alice walks along the perimeter of the park for a distance of $5$ km. How many kilometers is she from her starting point? Let's think step by step and put only the final answer within \\boxed{}.... | math | {
"style": "rule",
"ground_truth": "\\sqrt{13}"
} | {
"split": "train",
"index": 23989,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There are three pairs of real numbers $(x_1,y_1)$, $(x_2,y_2)$, and $(x_3,y_3)$ that satisfy both $x^3-3xy^2=2005$ and $y^3-3x^2y=2004$. Compute $\\left(1-\\frac{x_1}{y_1}\\right)\\left(1-\\frac{x_2}{y_2}\\right)\\left(1-\\frac{x_3}{y_3}\\right)$. Let's think step by step and p... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{1002}"
} | {
"split": "train",
"index": 23990,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If \\( N \\) is the smallest positive integer whose digits have a product of 1728, what is the sum of the digits of \\( N \\)? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "28"
} | {
"split": "train",
"index": 23991,
"solution": "Since the product of the digits of \\( N \\) is 1728, we find the prime factorization of 1728 to help us determine what the digits are: \\( 1728=9 \\times 192=3^{2} \\times 3 \\times 64=3^{3} \\times 2^{6} \\). We must try to find a combination of the smallest numb... |
deepscaler | [
{
"role": "user",
"content": "After finding the average of $35$ scores, a student carelessly included the average with the $35$ scores and found the average of these $36$ numbers. The ratio of the second average to the true average was Let's think step by step and put only the final answer within \\boxed{}.... | math | {
"style": "rule",
"ground_truth": "1:1"
} | {
"split": "train",
"index": 23992,
"solution": "1. **Calculate the True Average of the Original Scores**:\n Let the $35$ scores be denoted as $x_1, x_2, \\dots, x_{35}$. The true average of these scores is given by:\n \\[\n \\text{True Average} = \\frac{x_1 + x_2 + \\cdots + x_{35}}{35}\n \\]\n Let's d... |
deepscaler | [
{
"role": "user",
"content": "In right triangle $DEF$, $DE=15$, $DF=9$ and $EF=12$ units. What is the distance from $F$ to the midpoint of segment $DE$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "7.5"
} | {
"split": "train",
"index": 23993,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the area bounded by the graph of $ y\\equal{}\\sqrt[3]{x\\plus{}\\sqrt{x^2\\plus{}1}}\\plus{}\\sqrt[3]{x\\minus{}\\sqrt{x^2\\plus{}1}}$ , the line $ x\\minus{}y\\minus{}1\\equal{}0$ and the $ x$ axis. Let's think step by step and put only the final answer within \\box... | math | {
"style": "rule",
"ground_truth": "5/8"
} | {
"split": "train",
"index": 23994,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A number $x$ is equal to $7\\cdot24\\cdot48$. What is the smallest positive integer $y$ such that the product $xy$ is a perfect cube? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "588"
} | {
"split": "train",
"index": 23995,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There are five people in a room. They each simultaneously pick two of the other people in the room independently and uniformly at random and point at them. Compute the probability that there exists a group of three people such that each of them is pointing at the other two in t... | math | {
"style": "rule",
"ground_truth": "\\frac{5}{108}"
} | {
"split": "train",
"index": 23996,
"solution": "The desired probability is the number of ways to pick the two isolated people times the probability that the remaining three point at each other. So, $$P=\\binom{5}{2} \\cdot\\left(\\frac{\\binom{2}{2}}{\\binom{4}{2}}\\right)^{3}=10 \\cdot\\left(\\frac{1}{6}\\right... |
deepscaler | [
{
"role": "user",
"content": "Person A and Person B start from points $A$ and $B$ simultaneously and move towards each other. It is known that the speed ratio of Person A to Person B is 6:5. When they meet, they are 5 kilometers from the midpoint between $A$ and $B$. How many kilometers away is Person B fro... | math | {
"style": "rule",
"ground_truth": "5/3"
} | {
"split": "train",
"index": 23997,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $f(\\alpha)= \\frac{\\sin(\\pi - \\alpha)\\cos(-\\alpha)\\cos(-\\alpha + \\frac{3\\pi}{2})}{\\cos(\\frac{\\pi}{2} - \\alpha)\\sin(-\\pi - \\alpha)}$.\n(1) Find the value of $f(-\\frac{41\\pi}{6})$;\n(2) If $\\alpha$ is an angle in the third quadrant and $\\cos(\\alph... | math | {
"style": "rule",
"ground_truth": "\\frac{2\\sqrt{2}}{3}"
} | {
"split": "train",
"index": 23998,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the greatest prime factor of 221? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "17"
} | {
"split": "train",
"index": 23999,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The average age of the 10 females in a choir is 30 years. The average age of the 15 males in the same choir is 35 years. What is the average age, in years, of the 25 people in the choir? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "33"
} | {
"split": "train",
"index": 24000,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $a$ and $b$ are nonzero real numbers such that $\\left| a \\right| \\ne \\left| b \\right|$ , compute the value of the expression\n\\[\n \\left( \\frac{b^2}{a^2} + \\frac{a^2}{b^2} - 2 \\right) \\times\n \\left( \\frac{a + b}{b - a} + \\frac{b - a}{a + b} \\right) \\t... | math | {
"style": "rule",
"ground_truth": "-8"
} | {
"split": "train",
"index": 24001,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Marissa constructs a large spherical snow sculpture by placing smaller snowballs inside it with radii of 4 inches, 6 inches, and 8 inches. Assuming all snowballs are perfectly spherical and fit exactly inside the sculpture, and the sculpture itself is a sphere whose radius is s... | math | {
"style": "rule",
"ground_truth": "\\sqrt[3]{792}"
} | {
"split": "train",
"index": 24002,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the smallest positive integer with exactly 18 positive divisors? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "288"
} | {
"split": "train",
"index": 24003,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The perpendicular bisectors of the sides of triangle $ABC$ meet its circumcircle at points $A',$ $B',$ and $C',$ as shown. If the perimeter of triangle $ABC$ is 35 and the radius of the circumcircle is 8, then find the area of hexagon $AB'CA'BC'.$\n\n[asy]\nunitsize(2 cm);\n\n... | math | {
"style": "rule",
"ground_truth": "140"
} | {
"split": "train",
"index": 24004,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Four cats, four dogs, and four mice are placed in 12 cages. If a cat and a mouse are in the same column, the cat will meow non-stop; if a mouse is surrounded by two cats on both sides, the mouse will squeak non-stop; if a dog is flanked by a cat and a mouse, the dog will bark n... | math | {
"style": "rule",
"ground_truth": "28"
} | {
"split": "train",
"index": 24005,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that the slant height of a certain cone is $4$ and the height is $2\\sqrt{3}$, calculate the total surface area of the cone. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "12\\pi"
} | {
"split": "train",
"index": 24006,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The sum of the lengths of all the edges of a cube is 60 cm. Find the number of cubic centimeters in the volume of the cube. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "125"
} | {
"split": "train",
"index": 24007,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the distance from Boguli to Bolifoyn? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 24008,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Doraemon and Nobita are playing the game \"rock, paper, scissors.\" The rules state that the winner of each round receives two dorayakis, while the loser gets none. If there is a tie, each player receives one dorayaki. Nobita knows that Doraemon can only play \"rock,\" but he s... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 24009,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The sum of the coefficients of the expanded form of $(x+ \\frac{a}{x})(2x- \\frac{1}{x})^{5}$ is 2. Find the constant term in the expanded form. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "40"
} | {
"split": "train",
"index": 24010,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A particular integer is the smallest multiple of 72, each of whose digits is either 0 or 1. How many digits does this integer have? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 24011,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the 18 th digit after the decimal point of $\\frac{10000}{9899}$ ? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "5"
} | {
"split": "train",
"index": 24012,
"solution": "$\\frac{10000}{9899}$ satisfies $100(x-1)=1.01 x$, so each pair of adjacent digits is generated by adding the previous two pairs of digits. So the decimal is $1.01020305081321345590 \\ldots$, and the 18 th digit is 5."
} |
deepscaler | [
{
"role": "user",
"content": "Determine the area enclosed by the curve of $y = \\arccos(\\cos x)$ and the $x$-axis over the interval $\\frac{\\pi}{4} \\le x \\le \\frac{9\\pi}{4}.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3\\pi^2}{2}"
} | {
"split": "train",
"index": 24013,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $x$ is real and $x^3+\\frac{1}{x^3}=52$, find $x+\\frac{1}{x}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4"
} | {
"split": "train",
"index": 24014,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a magic square, the sum of the three entries in any row, column, or diagonal is the same value. The figure below shows four of the entries of a magic square. Find $x$.\n[asy]\nsize(2cm);\nfor (int i=0; i<=3; ++i) draw((i,0)--(i,3)^^(0,i)--(3,i));\nlabel(\"$x$\",(0.5,2.5));la... | math | {
"style": "rule",
"ground_truth": "200"
} | {
"split": "train",
"index": 24015,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\( A \\) and \\( B \\) be two sets, and \\((A, B)\\) be called a \"pair\". If \\( A \\neq B \\), then \\((A, B)\\) and \\((B, A)\\) are considered different \"pairs\". Find the number of different pairs \\((A, B)\\) that satisfy the condition \\( A \\cup B = \\{1,2,3,4\\} ... | math | {
"style": "rule",
"ground_truth": "81"
} | {
"split": "train",
"index": 24016,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Flat Albert and his buddy Mike are watching the game on Sunday afternoon. Albert is drinking lemonade from a two-dimensional cup which is an isosceles triangle whose height and base measure 9 cm and 6 cm; the opening of the cup corresponds to the base, which points upwards. Eve... | math | {
"style": "rule",
"ground_truth": "26"
} | {
"split": "train",
"index": 24017,
"solution": "Let $A_{0}=\\frac{1}{2}(6)(9)=27$ denote the area of Albert's cup; since area varies as the square of length, at time $n$ Mike adds $$A\\left(1-\\left(1-\\frac{1}{9 n^{2}}\\right)^{2}\\right)$$ whence in all, he adds $$A_{0} \\sum_{n=1}^{\\infty}\\left(\\frac{2}{9 ... |
deepscaler | [
{
"role": "user",
"content": "The circumradius R of triangle △ABC is $\\sqrt{3}$. The sides opposite to angles A, B, and C are a, b, c respectively, and it is given that $\\frac{2\\sin A-\\sin C}{\\sin B} = \\frac{\\cos C}{\\cos B}$. \n(1) Find the angle B and the side length b. \n(2) Find the maximum val... | math | {
"style": "rule",
"ground_truth": "\\frac{9\\sqrt{3}}{4}"
} | {
"split": "train",
"index": 24018,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $S=\\{1,2, \\ldots, 2014\\}$. For each non-empty subset $T \\subseteq S$, one of its members is chosen as its representative. Find the number of ways to assign representatives to all non-empty subsets of $S$ so that if a subset $D \\subseteq S$ is a disjoint union of non-em... | math | {
"style": "rule",
"ground_truth": "108 \\cdot 2014!"
} | {
"split": "train",
"index": 24019,
"solution": "Answer: $108 \\cdot 2014$ !. For any subset $X$ let $r(X)$ denotes the representative of $X$. Suppose that $x_{1}=r(S)$. First, we prove the following fact: $$ \\text { If } x_{1} \\in X \\text { and } X \\subseteq S \\text {, then } x_{1}=r(X) $$ If $|X| \\leq 201... |
deepscaler | [
{
"role": "user",
"content": "In a novel that consists of 530 pages, each page number is printed once, starting from page 1 up to page 530. How many more 3's are printed than 7's throughout the book? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "100"
} | {
"split": "train",
"index": 24020,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Calculate \\(3^{18} \\div 27^2\\) and multiply the result by 7. Write your answer as an integer. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3720087"
} | {
"split": "train",
"index": 24021,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A semicircle of diameter 3 sits at the top of a semicircle of diameter 4, as shown. The shaded area inside the smaller semicircle and outside the larger semicircle is called a $\\textit{lune}$. Determine the area of this lune. Express your answer in terms of $\\pi$ and in simpl... | math | {
"style": "rule",
"ground_truth": "\\frac{11}{24}\\pi"
} | {
"split": "train",
"index": 24022,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find\n\\[\n\\sum_{n = 1}^\\infty \\frac{3^n}{1 + 3^n + 3^{n + 1} + 3^{2n + 1}}.\n\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{4}"
} | {
"split": "train",
"index": 24023,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "To calculate $41^2$, David mentally figures the value $40^2$ and adds 81. David subtracts a number from $40^2$ to calculate $39^2$. What number does he subtract? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "79"
} | {
"split": "train",
"index": 24024,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the diagram, rectangle \\(P Q R S\\) has \\(P Q = 30\\) and rectangle \\(W X Y Z\\) has \\(Z Y = 15\\). If \\(S\\) is on \\(W X\\) and \\(X\\) is on \\(S R\\), such that \\(S X = 10\\), then \\(W R\\) equals: Let's think step by step and put only the final answer within \\bo... | math | {
"style": "rule",
"ground_truth": "35"
} | {
"split": "train",
"index": 24025,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If you set the clock back by 10 minutes, the number of radians the minute hand has turned is \\_\\_\\_\\_\\_\\_. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\pi}{3}"
} | {
"split": "train",
"index": 24026,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For every $3^\\circ$ rise in temperature, the volume of a certain gas expands by $4$ cubic centimeters. If the volume of the gas is $24$ cubic centimeters when the temperature is $32^\\circ$, what was the volume of the gas in cubic centimeters when the temperature was $20^\\ci... | math | {
"style": "rule",
"ground_truth": "8"
} | {
"split": "train",
"index": 24027,
"solution": "1. **Identify the relationship between temperature and volume**: \n Given that for every $3^\\circ$ rise in temperature, the volume of the gas expands by $4$ cubic centimeters. This implies that for every $3^\\circ$ decrease in temperature, the volume of the gas ... |
deepscaler | [
{
"role": "user",
"content": "Let rectangle $A B C D$ have lengths $A B=20$ and $B C=12$. Extend ray $B C$ to $Z$ such that $C Z=18$. Let $E$ be the point in the interior of $A B C D$ such that the perpendicular distance from $E$ to \\overline{A B}$ is 6 and the perpendicular distance from $E$ to \\overline... | math | {
"style": "rule",
"ground_truth": "72"
} | {
"split": "train",
"index": 24028,
"solution": "Draw the line parallel to \\overline{A D}$ through $E$, intersecting \\overline{A B}$ at $F$ and \\overline{C D}$ at $G$. It is clear that $X F E$ and $Y G E$ are congruent, so the area of $A X Y D$ is equal to that of $A F G D$. But $A F G D$ is simply a 12 by 6 r... |
deepscaler | [
{
"role": "user",
"content": "If $x, y$ and $2x + \\frac{y}{2}$ are not zero, then\n$\\left( 2x + \\frac{y}{2} \\right)^{-1} \\left[(2x)^{-1} + \\left( \\frac{y}{2} \\right)^{-1} \\right]$ equals Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{xy}"
} | {
"split": "train",
"index": 24029,
"solution": "1. **Rewrite the expression**:\n Given the expression $\\left( 2x + \\frac{y}{2} \\right)^{-1} \\left[(2x)^{-1} + \\left( \\frac{y}{2} \\right)^{-1} \\right]$, we start by simplifying each component:\n \\[\n \\left( 2x + \\frac{y}{2} \\right)^{-1} = \\left( \... |
deepscaler | [
{
"role": "user",
"content": "There is a magical tree with 123 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 the number of fruits on the tree is less than the number of fruits... | math | {
"style": "rule",
"ground_truth": "17"
} | {
"split": "train",
"index": 24030,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Tommy takes a 25-question true-false test. He answers each question correctly with independent probability $\\frac{1}{2}$ . Tommy earns bonus points for correct streaks: the first question in a streak is worth 1 point, the second question is worth 2 points, and so on. For in... | math | {
"style": "rule",
"ground_truth": "50"
} | {
"split": "train",
"index": 24031,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A trapezoid is given where the ratio of the lengths of its bases is 2. If the trapezoid is rotated $360^\\circ$ around the longer base, the resulting solid is $\\Phi_1$. If the trapezoid is rotated $360^\\circ$ around the shorter base, the resulting solid is $\\Phi_2$. Find the... | math | {
"style": "rule",
"ground_truth": "5/4"
} | {
"split": "train",
"index": 24032,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The reciprocal of the opposite number of \\(-(-3)\\) is \\(\\frac{1}{3}\\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{1}{3}"
} | {
"split": "train",
"index": 24033,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For each natural number from 1 to 999, Damir subtracted the last digit from the first digit and wrote all the resulting 1000 differences on the board. For example, for the number 7, Damir wrote 0; for the number 105, he wrote (-4); for the number 61, he wrote 5.\n\nWhat is the ... | math | {
"style": "rule",
"ground_truth": "495"
} | {
"split": "train",
"index": 24034,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A club has 12 members - 6 boys and 6 girls. Each member is also categorized either as a senior or junior with equal distribution among genders. Two of the members are chosen at random. What is the probability that they are both girls where one girl is a senior and the other is ... | math | {
"style": "rule",
"ground_truth": "\\frac{9}{66}"
} | {
"split": "train",
"index": 24035,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A coordinate system and parametric equations problem (4-4):\n\nIn the rectangular coordinate system $x0y$, the parametric equations of line $l$ are given by $\\begin{cases} x = \\frac{1}{2}t \\ y = \\frac{\\sqrt{2}}{2} + \\frac{\\sqrt{3}}{2}t \\end{cases}$, where $t$ is the par... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{10}}{2}"
} | {
"split": "train",
"index": 24036,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Solve the equations: \n(1) $x^2-4x+3=0$ \n(2) $4(2y-5)^2=(3y-1)^2$． Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{11}{7}"
} | {
"split": "train",
"index": 24037,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A certain shopping mall's sales volume (unit: ten thousand pieces) for five consecutive years is as shown in the table below:\n\n| $x$(year) | 1 | 2 | 3 | 4 | 5 |\n|-----------|---|---|---|---|---|\n| $y$(sales volume) | 5 | 5 | 6 | 7 | 7 |\n\n$(1)$ Find the linear regression e... | math | {
"style": "rule",
"ground_truth": "\\frac{2}{5}"
} | {
"split": "train",
"index": 24038,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $x$ and $y$ be two-digit positive integers with mean $60$. What is the maximum value of the ratio $\\frac{x}{y}$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{33}{7}"
} | {
"split": "train",
"index": 24039,
"solution": "1. **Given Information and Equation Setup:**\n - Let $x$ and $y$ be two-digit positive integers.\n - The mean of $x$ and $y$ is given as $60$. Therefore, we have:\n \\[\n \\frac{x+y}{2} = 60\n \\]\n - Multiplying both sides by $2$ to eliminate the... |
deepscaler | [
{
"role": "user",
"content": "In the figure, the outer equilateral triangle has area $16$, the inner equilateral triangle has area $1$, and the three trapezoids are congruent. What is the area of one of the trapezoids? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "5"
} | {
"split": "train",
"index": 24040,
"solution": "1. **Identify the total area of the large triangle**: Given in the problem, the area of the outer equilateral triangle is $16$ square units.\n\n2. **Identify the area of the inner triangle**: The area of the inner equilateral triangle is given as $1$ square unit.\n... |
deepscaler | [
{
"role": "user",
"content": "Let \\( O \\) be an interior point of \\( \\triangle ABC \\). Extend \\( AO \\) to meet \\( BC \\) at \\( D \\). Similarly, extend \\( BO \\) and \\( CO \\) to meet \\( CA \\) and \\( AB \\) respectively at \\( E \\) and \\( F \\). Given \\( AO = 30 \\), \\( FO = 20 \\), \\( BO... | math | {
"style": "rule",
"ground_truth": "20"
} | {
"split": "train",
"index": 24041,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $A$, $B$, $C$ and $D$ be the vertices of a regular tetrahedron each of whose edges measures 1 meter. A bug, starting from vertex $A$, observes the following rule: at each vertex it chooses one of the three edges meeting at that vertex, each edge being equally likely to be c... | math | {
"style": "rule",
"ground_truth": "182"
} | {
"split": "train",
"index": 24042,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is $a-2b$, where $a=4-2i$ and $b=3+2i$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-2-6i"
} | {
"split": "train",
"index": 24043,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Compute $\\begin{pmatrix} 1 & 0 \\\\ 1 & 1 \\end{pmatrix}^{2018}.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\begin{pmatrix} 1 & 0 \\\\ 2018 & 1 \\end{pmatrix}"
} | {
"split": "train",
"index": 24044,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Daniel wrote all the positive integers from 1 to $n$ inclusive on a piece of paper. After careful observation, he realized that the sum of all the digits that he wrote was exactly 10,000. Find $n$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "799"
} | {
"split": "train",
"index": 24045,
"solution": "Let $S(n)$ denote the sum of the digits of $n$, and let $f(x)=\\sum_{n=0}^{x} S(n)$. (We may add $n=0$ because $S(0)=0$.) Observe that: $$f(99)=\\sum_{a=0}^{9}\\left(\\sum_{b=0}^{9}(a+b)\\right)=10 \\sum_{b=0}^{9} b+10 \\sum_{a=0}^{9} a=900$$ If $a$ is an integer b... |
deepscaler | [
{
"role": "user",
"content": "Let's consider two positive real numbers $a$ and $b$, where an operation $a \\, \\blacktriangle \\, b$ is defined such that $(ab) \\, \\blacktriangle \\, b = a(b \\, \\blacktriangle \\, b)$ and $(a \\, \\blacktriangle \\, 1) \\, \\blacktriangle \\, a = a \\, \\blacktriangle \\,... | math | {
"style": "rule",
"ground_truth": "2070"
} | {
"split": "train",
"index": 24046,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "When the binary number $100101110010_2$ is divided by 4, what is the remainder (give your answer in base 10)? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2"
} | {
"split": "train",
"index": 24047,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A sequence of two distinct numbers is extended in two ways: one to form a geometric progression and the other to form an arithmetic progression. The third term of the geometric progression coincides with the tenth term of the arithmetic progression. With which term of the arith... | math | {
"style": "rule",
"ground_truth": "74"
} | {
"split": "train",
"index": 24048,
"solution": ""
} |
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