data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"role": "user",
"content": "Ivan wanted to buy nails. In one store, where 100 grams of nails cost 180 rubles, he couldn't buy the required amount because he was short 1430 rubles. Then he went to another store where 100 grams cost 120 rubles. He bought the required amount and received 490 rubles in change... | math | {
"style": "rule",
"ground_truth": "3.2"
} | {
"split": "train",
"index": 1900,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "An integer $x$ is chosen so that $3x+1$ is an even integer. Which of the following must be an odd integer? (A) $x+3$ (B) $x-3$ (C) $2x$ (D) $7x+4$ (E) $5x+3$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "7x+4"
} | {
"split": "train",
"index": 1901,
"solution": "Solution 1: If $x=1$, then $3x+1=4$, which is an even integer. In this case, the five given choices are (A) $x+3=4$, (B) $x-3=-2$, (C) $2x=2$, (D) $7x+4=11$, (E) $5x+3=8$. Of these, the only odd integer is (D). Therefore, since $x=1$ satisfies the initial criteria, ... |
deepscaler | [
{
"role": "user",
"content": "A parallelogram is generated by the vectors $\\begin{pmatrix} 2 \\\\ 1\\\\ 1 \\end{pmatrix}$ and $\\begin{pmatrix} 1 \\\\ -1 \\\\ - 1 \\end{pmatrix}.$\n\n[asy]\nunitsize(0.4 cm);\n\npair A, B, C, D;\n\nA = (0,0);\nB = (7,2);\nC = (1,3);\nD = B + C;\n\ndraw(A--B,Arrow(6));\ndraw... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{3}"
} | {
"split": "train",
"index": 1902,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The base-ten representation for $19!$ is $121,6T5,100,40M,832,H00$, where $T$, $M$, and $H$ denote digits that are not given. What is $T+M+H$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 1903,
"solution": "1. **Determine the value of $H$:** \n Since $19!$ includes the factors $2^{15}$ and $5^3$ (from the prime factorization of numbers from $1$ to $19$), it has at least three factors of $10$, and thus ends in at least three zeros. Therefore, $H = 0$.\n\n2. **Use the... |
deepscaler | [
{
"role": "user",
"content": "Four foreign guests visit a school and need to be accompanied by two security personnel. Six people enter the school gate in sequence. For safety reasons, the two security personnel must be at the beginning and the end. If the guests A and B must be together, calculate the tota... | math | {
"style": "rule",
"ground_truth": "24"
} | {
"split": "train",
"index": 1904,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the sequence $\\{a_n\\}$ satisfies $a_1=1$, $a_2=4$, $a_3=9$, $a_n=a_{n-1}+a_{n-2}-a_{n-3}$, for $n=4,5,...$, calculate $a_{2017}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "8065"
} | {
"split": "train",
"index": 1905,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A region is bounded by semicircular arcs constructed on the side of a square whose sides measure $2/\\pi$, as shown. What is the perimeter of this region? [asy]\npath a=(10,0)..(5,5)--(5,-5)..cycle;\npath b=(0,10)..(5,5)--(-5,5)..cycle;\npath c=(-10,0)..(-5,5)--(-5,-5)..cycle;\... | math | {
"style": "rule",
"ground_truth": "4"
} | {
"split": "train",
"index": 1906,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the following six statements:\n(1) All women are good drivers\n(2) Some women are good drivers\n(3) No men are good drivers\n(4) All men are bad drivers\n(5) At least one man is a bad driver\n(6) All men are good drivers.\n\nThe statement that negates statement (6) is: Le... | math | {
"style": "rule",
"ground_truth": "(5)"
} | {
"split": "train",
"index": 1907,
"solution": "To find the statement that negates statement (6), we need to understand the logical opposite of the statement:\n\\[\\text{(6) All men are good drivers.}\\]\n\nThe negation of \"All men are good drivers\" is \"There exists at least one man who is not a good driver.\"... |
deepscaler | [
{
"role": "user",
"content": "Find the sum of all real values of $x$ that satisfy\n\\[x = 1 - x + x^2 - x^3 + x^4 - x^5 + \\dotsb.\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{-1 + \\sqrt{5}}{2}"
} | {
"split": "train",
"index": 1908,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The domain of the function \\( f(x) \\) is \\( D \\). If for any \\( x_{1}, x_{2} \\in D \\), when \\( x_{1} < x_{2} \\), it holds that \\( f(x_{1}) \\leq f(x_{2}) \\), then \\( f(x) \\) is called a non-decreasing function on \\( D \\). Suppose that the function \\( f(x) \\) is... | math | {
"style": "rule",
"ground_truth": "\\frac{3}{4}"
} | {
"split": "train",
"index": 1909,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the minimum value for \\(a, b > 0\\) of the expression\n\n$$\n\\frac{|2a - b + 2a(b - a)| + |b + 2a - a(b + 4a)|}{\\sqrt{4a^2 + b^2}}\n$$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{5}}{5}"
} | {
"split": "train",
"index": 1910,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "When the repeating decimal $0.\\overline{12}$ is expressed as a common fraction in lowest terms, what is the sum of its numerator and denominator? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "37"
} | {
"split": "train",
"index": 1911,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the sum of the digits of \\(10^{2008} - 2008\\)? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "18063"
} | {
"split": "train",
"index": 1912,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "We will call a two-digit number power-less if neither of its digits can be written as an integer to a power greater than 1. For example, 53 is power-less, but 54 is not power-less since \\(4 = 2^{2}\\). Which of the following is a common divisor of the smallest and the largest ... | math | {
"style": "rule",
"ground_truth": "11"
} | {
"split": "train",
"index": 1913,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the parabola $y^{2}=2px$ with its directrix equation $x=-2$, let point $P$ be a point on the parabola. Find the minimum distance from point $P$ to the line $y=x+3$. 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": 1914,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the number of ordered integer tuples \\((k_1, k_2, k_3, k_4)\\) that satisfy \\(0 \\leq k_i \\leq 20\\) for \\(i = 1, 2, 3, 4\\), and \\(k_1 + k_3 = k_2 + k_4\\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "6181"
} | {
"split": "train",
"index": 1915,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the Cartesian coordinate system $xOy$, the sum of distances from point $P$ to the two points $(0, -\\sqrt{3})$ and $(0, \\sqrt{3})$ equals $4$. Let the trajectory of point $P$ be $C$.\n\n$(1)$ Write the equation of $C$;\n\n$(2)$ Suppose the line $y=kx+1$ intersects $C$ at po... | math | {
"style": "rule",
"ground_truth": "\\frac{4\\sqrt{65}}{17}"
} | {
"split": "train",
"index": 1916,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Péter sent his son with a message to his brother, Károly, who in turn sent his son to Péter with a message. The cousins met $720 \\, \\text{m}$ away from Péter's house, had a 2-minute conversation, and then continued on their way. Both boys spent 10 minutes at the respective re... | math | {
"style": "rule",
"ground_truth": "1760"
} | {
"split": "train",
"index": 1917,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $$\\overrightarrow {a} = (sinx, \\frac {3}{4})$$, $$\\overrightarrow {b} = (\\frac {1}{3}, \\frac {1}{2}cosx)$$, and $$\\overrightarrow {a}$$ is parallel to $$\\overrightarrow {b}$$. Find the acute angle $x$. Let's think step by step and put only the final answer within \\b... | math | {
"style": "rule",
"ground_truth": "\\frac {\\pi}{4}"
} | {
"split": "train",
"index": 1918,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A hemisphere is placed on a sphere of radius \\(100 \\text{ cm}\\). The second hemisphere is placed on the first one, and the third hemisphere is placed on the second one (as shown below). Find the maximum height of the tower (in cm). Let's think step by step and put only the f... | math | {
"style": "rule",
"ground_truth": "300"
} | {
"split": "train",
"index": 1919,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Observe:\n$$\n\\begin{array}{l}\n1 \\times 2 \\times 3 \\times 4 + 1 = 5^{2} \\\\\n2 \\times 3 \\times 4 \\times 5 + 1 = 11^{2} \\\\\n3 \\times 4 \\times 5 \\times 6 + 1 = 19^{2} \\\\\n\\ldots \\ldots\n\\end{array}\n$$\n\nCalculate $\\sqrt{2020 \\times 2021 \\times 2022 \\times... | math | {
"style": "rule",
"ground_truth": "4086461"
} | {
"split": "train",
"index": 1920,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that the year 2010 corresponds to the Geng-Yin year, determine the year of the previous Geng-Yin year. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1950"
} | {
"split": "train",
"index": 1921,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x)= \\frac{1}{x+1}$, point $O$ is the coordinate origin, point $A_{n}(n,f(n))(n∈N^{})$ where $N^{}$ represents the set of positive integers, vector $ \\overrightarrow{i}=(0,1)$, and $θ_{n}$ is the angle between vector $ \\overrightarrow{OA_{n}}$ and $ \\ov... | math | {
"style": "rule",
"ground_truth": "\\frac{2017}{2018}"
} | {
"split": "train",
"index": 1922,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a toy store, there are large and small plush kangaroos. In total, there are 100 of them. Some of the large kangaroos are female kangaroos with pouches. Each female kangaroo has three small kangaroos in her pouch, and the other kangaroos have empty pouches. Find out how many ... | math | {
"style": "rule",
"ground_truth": "31"
} | {
"split": "train",
"index": 1923,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For any number $x$, we are told that $x\\&=7-x$ and $\\&x = x -7$. What is the value of $\\&(12\\&)$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-12"
} | {
"split": "train",
"index": 1924,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A circle inscribed in triangle \\( ABC \\) touches side \\( AB \\) at point \\( M \\), and \\( AM = 1 \\), \\( BM = 4 \\). Find \\( CM \\) given that \\( \\angle BAC = 120^\\circ \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{273}"
} | {
"split": "train",
"index": 1925,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "On the number line, points $M$ and $N$ divide $L P$ into three equal parts. What is the value at $M$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{9}"
} | {
"split": "train",
"index": 1926,
"solution": "The difference between $\\frac{1}{6}$ and $\\frac{1}{12}$ is $\\frac{1}{6}-\\frac{1}{12}=\\frac{2}{12}-\\frac{1}{12}=\\frac{1}{12}$, so $L P=\\frac{1}{12}$. Since $L P$ is divided into three equal parts, then this distance is divided into three equal parts, each equ... |
deepscaler | [
{
"role": "user",
"content": "Determine all integers $k$ such that there exists infinitely many positive integers $n$ [b]not[/b] satisfying \n\\[n+k |\\binom{2n}{n}\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "k \\neq 1"
} | {
"split": "train",
"index": 1927,
"solution": "\nDetermine all integers \\( k \\) such that there exist infinitely many positive integers \\( n \\) not satisfying \n\\[\nn + k \\mid \\binom{2n}{n}.\n\\]\n\nWe claim that all integers \\( k \\neq 1 \\) satisfy the desired property.\n\nFirst, recall that \\(\\frac{... |
deepscaler | [
{
"role": "user",
"content": "Compute $\\lim _{n \\rightarrow \\infty} \\frac{1}{\\log \\log n} \\sum_{k=1}^{n}(-1)^{k}\\binom{n}{k} \\log k$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1"
} | {
"split": "train",
"index": 1928,
"solution": "Answer: 1. The idea is that if $f(k)=\\int g^{k}$, then $\\sum(-1)^{k}\\binom{n}{k} f(k)=\\int(1-g)^{n}$. To relate this to logarithm, we may use the Frullani integrals $\\int_{0}^{\\infty} \\frac{e^{-x}-e^{-k x}}{x} d x=\\lim _{c \\rightarrow+0} \\int_{c}^{\\infty}... |
deepscaler | [
{
"role": "user",
"content": "What is the least integer whose square is 48 more than its double? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-6"
} | {
"split": "train",
"index": 1929,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A rectangular board of 12 columns and 12 rows has squares numbered beginning in the upper left corner and moving left to right so row one is numbered 1 through 12, row two is 13 through 24, and so on. Determine which number of the form $n^2$ is the first to ensure that at least... | math | {
"style": "rule",
"ground_truth": "144"
} | {
"split": "train",
"index": 1930,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In this Number Wall, you add the numbers next to each other and write the sum in the block directly above the two numbers. Which number will be the block labeled '$n$'? [asy]\ndraw((0,0)--(8,0)--(8,2)--(0,2)--cycle);\ndraw((2,0)--(2,2));\ndraw((4,0)--(4,2));\ndraw((6,0)--(6,2))... | math | {
"style": "rule",
"ground_truth": "3"
} | {
"split": "train",
"index": 1931,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For how many values of $k$ is $12^{12}$ the least common multiple of the positive integers $6^6$, $8^8$, and $k$?\n Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "25"
} | {
"split": "train",
"index": 1932,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a right square prism \\( P-ABCD \\) with side edges and base edges both equal to 4, determine the total length of all the curves formed on its surface by points that are 3 units away from vertex \\( P \\). Let's think step by step and put only the final answer within \\boxed... | math | {
"style": "rule",
"ground_truth": "6\\pi"
} | {
"split": "train",
"index": 1933,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Convert the following radians to degrees: convert degrees to radians:\n(1) $\\frac{\\pi}{12} =$ \\_\\_\\_\\_\\_\\_ ; (2) $\\frac{13\\pi}{6} =$ \\_\\_\\_\\_\\_\\_ ; (3) $- \\frac{5}{12}\\pi =$ \\_\\_\\_\\_\\_\\_ .\n(4) $36^{\\circ} =$ \\_\\_\\_\\_\\_\\_ $rad$ ; (5) $-105^{\\circ... | math | {
"style": "rule",
"ground_truth": "-\\frac{7\\pi}{12}"
} | {
"split": "train",
"index": 1934,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Points \\(A\\) and \\(B\\) are connected by two arcs of circles, convex in opposite directions: \\(\\cup A C B = 117^\\circ 23'\\) and \\(\\cup A D B = 42^\\circ 37'\\). The midpoints \\(C\\) and \\(D\\) of these arcs are connected to point \\(A\\). Find the angle \\(C A D\\). ... | math | {
"style": "rule",
"ground_truth": "80"
} | {
"split": "train",
"index": 1935,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Calculate the length of the arc of the astroid given by \\(x=\\cos^{3} t\\), \\(y=\\sin^{3} t\\), where \\(0 \\leq t \\leq 2\\pi\\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 1936,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let point P be the intersection point in the first quadrant of the hyperbola $\\frac{x^{2}}{a^{2}}- \\frac{y^{2}}{b^{2}}=1 (a > 0, b > 0)$ and the circle $x^{2}+y^{2}=a^{2}+b^{2}$. F\\1 and F\\2 are the left and right foci of the hyperbola, respectively, and $|PF_1|=3|PF_2|$. F... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{10}}{2}"
} | {
"split": "train",
"index": 1937,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the equation of the directrix of the parabola $y = -2x^2 + 4x - 8.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "y = -\\frac{47}{8}"
} | {
"split": "train",
"index": 1938,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The radius $r$ of a circle inscribed within three mutually externally tangent circles of radii $a$, $b$ and $c$ is given by\n\\[\\frac{1}{r} = \\frac{1}{a} + \\frac{1}{b} + \\frac{1}{c} + 2 \\sqrt{\\frac{1}{ab} + \\frac{1}{ac} + \\frac{1}{bc}}.\\]What is the value of $r$ when $... | math | {
"style": "rule",
"ground_truth": "\\frac{9}{7}"
} | {
"split": "train",
"index": 1939,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The set of $x$-values satisfying the inequality $2 \\leq |x-1| \\leq 5$ is: Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-4\\leq x\\leq-1\\text{ or }3\\leq x\\leq 6"
} | {
"split": "train",
"index": 1940,
"solution": "The inequality given is $2 \\leq |x-1| \\leq 5$. We can interpret this as the absolute value of $x-1$ being at least 2 and at most 5. To solve this, we break it into two separate inequalities based on the definition of absolute value:\n\n1. **Case 1: $x-1 \\geq 0$**... |
deepscaler | [
{
"role": "user",
"content": "A sports league consists of 16 teams divided into 2 divisions of 8 teams each. Throughout the season, each team plays every other team in its own division three times and every team in the other division twice. How many games are in a complete season for the league? Let's think... | math | {
"style": "rule",
"ground_truth": "296"
} | {
"split": "train",
"index": 1941,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Anca and Bruce left Mathville at the same time. They drove along a straight highway towards Staton. Bruce drove at $50 \\mathrm{~km} / \\mathrm{h}$. Anca drove at $60 \\mathrm{~km} / \\mathrm{h}$, but stopped along the way to rest. They both arrived at Staton at the same time. ... | math | {
"style": "rule",
"ground_truth": "40 \\text{ minutes}"
} | {
"split": "train",
"index": 1942,
"solution": "Since Bruce drove 200 km at a speed of $50 \\mathrm{~km} / \\mathrm{h}$, this took him $\\frac{200}{50}=4$ hours. Anca drove the same 200 km at a speed of $60 \\mathrm{~km} / \\mathrm{h}$ with a stop somewhere along the way. Since Anca drove 200 km at a speed of $60... |
deepscaler | [
{
"role": "user",
"content": "Find the solution to $x|x| = 2x+1$ which has the smallest value. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"split": "train",
"index": 1943,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Steve guesses randomly on a 15-question multiple choice test in which each problem has two choices, a correct one and an incorrect one. What is the probability that he gets at least half of the questions correct? Express your answer as a common fraction. Let's think step by ste... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"split": "train",
"index": 1944,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the integer $n,$ $-180 < n < 180,$ such that $\\tan n^\\circ = \\tan 345^\\circ.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-15"
} | {
"split": "train",
"index": 1945,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Consider the 100th, 101st, and 102nd rows of Pascal's triangle, denoted as sequences $(p_i)$, $(q_i)$, and $(r_i)$ respectively. Calculate:\n\\[\n\\sum_{i = 0}^{100} \\frac{q_i}{r_i} - \\sum_{i = 0}^{99} \\frac{p_i}{q_i}.\n\\] Let's think step by step and put only the final ans... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"split": "train",
"index": 1946,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The natural number \\(a\\) is divisible by 35 and has 75 different divisors, including 1 and \\(a\\). Find the smallest such \\(a\\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "490000"
} | {
"split": "train",
"index": 1947,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "You have a whole pizza in the refrigerator. On your first trip to the refrigerator, you eat half the pizza. On each successive trip, you eat half of the remaining pizza. After five trips to the refrigerator, what fractional part of the pizza have you eaten? Let's think step by ... | math | {
"style": "rule",
"ground_truth": "\\frac{31}{32}"
} | {
"split": "train",
"index": 1948,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that \\( A \\) and \\( B \\) are two distinct points on the parabola \\( y = 3 - x^2 \\) that are symmetric with respect to the line \\( x + y = 0 \\), calculate the distance |AB|. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3\\sqrt{2}"
} | {
"split": "train",
"index": 1949,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The number of triangles with vertices' coordinates $(x, y)$ that satisfy $1 \\leqslant x \\leqslant 4, 1 \\leqslant y \\leqslant 4$, and where $x$ and $y$ are integers is $\\qquad$ . Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "516"
} | {
"split": "train",
"index": 1950,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the set \\( A = \\{1,2,3,4\\} \\), Ander randomly selects a number from \\( A \\) every second (with replacement). The selection stops when the sum of the last two selected numbers is a prime number. What is the probability that the last number selected is \"1\"? Let's th... | math | {
"style": "rule",
"ground_truth": "\\frac{15}{44}"
} | {
"split": "train",
"index": 1951,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $\\{a_{n}\\}$ be an arithmetic sequence with a common difference of $d$, and $d \\gt 1$. Define $b_{n}=\\frac{{n}^{2}+n}{{a}_{n}}$, and let $S_{n}$ and $T_{n}$ be the sums of the first $n$ terms of the sequences $\\{a_{n}\\}$ and $\\{b_{n}\\}$, respectively. \n$(1)$ If $3a... | math | {
"style": "rule",
"ground_truth": "\\frac{51}{50}"
} | {
"split": "train",
"index": 1952,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the expression $(xy - \\frac{1}{2})^2 + (x - y)^2$ for real numbers $x$ and $y$, find the least possible value. 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": 1953,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the sequence $\\{{a_{n}}\\}$, the adjacent terms ${a_{n}}$ and ${a_{n+1}}$ are the roots of the equation ${x^{2}}+3nx+{{b_{n}}=0}$. Given that ${{a_{10}}=-17}$, find the value of ${{b_{51}}}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "5840"
} | {
"split": "train",
"index": 1954,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\( a, b, c \\) be real numbers satisfying \\( 9a^2 + 4b^2 + 36c^2 = 4 \\). Find the minimum value of \\( 3a + 6b + 12c \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-2\\sqrt{14}"
} | {
"split": "train",
"index": 1955,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $(1+x+x^2)^n=a_0 + a_1x+a_2x^2+ \\cdots + a_{2n}x^{2n}$ be an identity in $x$. If we let $s=a_0+a_2+a_4+\\cdots +a_{2n}$, then $s$ equals: Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3^n+1}{2}"
} | {
"split": "train",
"index": 1956,
"solution": "1. **Define the function and expand**: Let $f(x) = (1+x+x^2)^n$. We can express $f(x)$ as a polynomial in $x$:\n \\[\n f(x) = a_0 + a_1x + a_2x^2 + \\cdots + a_{2n}x^{2n}\n \\]\n\n2. **Evaluate $f(x)$ at $x=1$**: Substitute $x = 1$ into $f(x)$:\n \\[\n f(1... |
deepscaler | [
{
"role": "user",
"content": "What is the remainder when $2024 \\cdot 3047$ is divided by $800$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "728"
} | {
"split": "train",
"index": 1957,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Harry Potter is creating an enhanced magical potion called \"Elixir of Life\" (this is a very potent sleeping potion composed of powdered daffodil root and wormwood infusion. The concentration of the \"Elixir of Life\" is the percentage of daffodil root powder in the entire pot... | math | {
"style": "rule",
"ground_truth": "11"
} | {
"split": "train",
"index": 1958,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Three fair six-sided dice are rolled. What is the probability that the values shown on two of the dice sum to the value shown on the remaining die? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{5}{24}"
} | {
"split": "train",
"index": 1959,
"solution": "1. **Total Outcomes**: When three six-sided dice are rolled, each die has 6 possible outcomes. Therefore, the total number of outcomes when rolling three dice is:\n \\[\n 6 \\times 6 \\times 6 = 216\n \\]\n\n2. **Favorable Outcomes**: We need to count the numb... |
deepscaler | [
{
"role": "user",
"content": "A natural number \\( n \\) is called \"cubowat\" if \\( n^{3} + 13n - 273 \\) is a cube of a natural number. Find the sum of all cubowat numbers. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "29"
} | {
"split": "train",
"index": 1960,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $A, B, C, D, E$ be five points on a circle; some segments are drawn between the points so that each of the $\\binom{5}{2}=10$ pairs of points is connected by either zero or one segments. Determine the number of sets of segments that can be drawn such that: - It is possible ... | math | {
"style": "rule",
"ground_truth": "195"
} | {
"split": "train",
"index": 1961,
"solution": "First we show that we can divide the five points into sets $S$ and $T$ according to the second condition in only one way. Assume that we can divide the five points into $S \\cup T$ and $S^{\\prime} \\cup T^{\\prime}$. Then, let $A=S^{\\prime} \\cap S, B=S^{\\prime} ... |
deepscaler | [
{
"role": "user",
"content": "Joshua chooses five distinct numbers. In how many different ways can he assign these numbers to the variables $p, q, r, s$, and $t$ so that $p<s, q<s, r<t$, and $s<t$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "8"
} | {
"split": "train",
"index": 1962,
"solution": "Suppose that the five distinct numbers that Joshua chooses are $V, W, X, Y, Z$, and that $V<W<X<Y<Z$. We want to assign these to $p, q, r, s, t$ so that $p<s$ and $q<s$ and $r<t$ and $s<t$. First, we note that $t$ must be the largest of $p, q, r, s, t$. This is beca... |
deepscaler | [
{
"role": "user",
"content": "Count all the distinct anagrams of the word \"YOANN\". Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "60"
} | {
"split": "train",
"index": 1963,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The function $f(x)$ satisfies\n\\[xf(y) = yf(x)\\]for all real numbers $x$ and $y.$ If $f(15) = 20,$ find $f(3).$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4"
} | {
"split": "train",
"index": 1964,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Triangle \\(ABC\\) is isosceles with \\(AB = AC\\) and \\(BC = 65 \\, \\text{cm}\\). \\(P\\) is a point on \\(BC\\) such that the perpendicular distances from \\(P\\) to \\(AB\\) and \\(AC\\) are \\(24 \\, \\text{cm}\\) and \\(36 \\, \\text{cm}\\), respectively. Find the area o... | math | {
"style": "rule",
"ground_truth": "2535"
} | {
"split": "train",
"index": 1965,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Determine the value of\n\\[2002 + \\frac{1}{2} \\left( 2001 + \\frac{1}{2} \\left( 2000 + \\dots + \\frac{1}{2} \\left( 3 + \\frac{1}{2} \\cdot 2 \\right) \\right) \\dotsb \\right).\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4002"
} | {
"split": "train",
"index": 1966,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the graph of the function $y=\\cos (x+\\frac{4\\pi }{3})$ is translated $\\theta (\\theta > 0)$ units to the right, and the resulting graph is symmetrical about the $y$-axis, determine the smallest possible value of $\\theta$. Let's think step by step and put only the fin... | math | {
"style": "rule",
"ground_truth": "\\frac{\\pi }{3}"
} | {
"split": "train",
"index": 1967,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A conical glass is in the form of a right circular cone. The slant height is $21$ and the radius of the top rim of the glass is $14$ . An ant at the mid point of a slant line on the outside wall of the glass sees a honey drop diametrically opposite to it on the inside wall o... | math | {
"style": "rule",
"ground_truth": "18"
} | {
"split": "train",
"index": 1968,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Six soccer teams play at most one match between any two teams. If each team plays exactly 2 matches, how many possible arrangements of these matches are there? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "70"
} | {
"split": "train",
"index": 1969,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given triangle $\\triangle ABC$, the sides opposite to the internal angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. Given $9\\sin ^{2}B=4\\sin ^{2}A$ and $\\cos C=\\frac{1}{4}$, calculate $\\frac{c}{a}$. Let's think step by step and put only the final answer within... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{10}}{3}"
} | {
"split": "train",
"index": 1970,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The sum of the coefficients of all terms except the constant term in the expansion of $\\left(\\frac{2}{\\sqrt{x}} - x\\right)^9$ is ______. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "5377"
} | {
"split": "train",
"index": 1971,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Segments \\(AA', BB'\\), and \\(CC'\\), each of length 2, all intersect at a point \\(O\\). If \\(\\angle AOC'=\\angle BOA'=\\angle COB'=60^{\\circ}\\), find the maximum possible value of the sum of the areas of triangles \\(AOC', BOA'\\), and \\(COB'\\). Let's think step by st... | math | {
"style": "rule",
"ground_truth": "\\sqrt{3}"
} | {
"split": "train",
"index": 1972,
"solution": "Extend \\(OA\\) to \\(D\\) and \\(OC'\\) to \\(E\\) such that \\(AD=OA'\\) and \\(C'E=OC\\). Since \\(OD=OE=2\\) and \\(\\angle DOE=60^{\\circ}\\), we have \\(ODE\\) is an equilateral triangle. Let \\(F\\) be the point on \\(DE\\) such that \\(DF=OB\\) and \\(EF=OB'... |
deepscaler | [
{
"role": "user",
"content": "In $\\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. Given that $(2c-a)\\cos B=b\\cos A$.\n(1) Find angle $B$;\n(2) If $b=6$ and $c=2a$, find the area of $\\triangle ABC$. Let's think step by step and put only the final answer ... | math | {
"style": "rule",
"ground_truth": "6 \\sqrt{3}"
} | {
"split": "train",
"index": 1973,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For any integer $a$ , let $f(a) = |a^4 - 36a^2 + 96a - 64|$ . What is the sum of all values of $f(a)$ that are prime?\n\n*Proposed by Alexander Wang* Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "22"
} | {
"split": "train",
"index": 1974,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The points $A$, $B$ and $C$ lie on the surface of a sphere with center $O$ and radius $20$. It is given that $AB=13$, $BC=14$, $CA=15$, and that the distance from $O$ to $\\triangle ABC$ is $\\frac{m\\sqrt{n}}k$, where $m$, $n$, and $k$ are positive integers, $m$ and $k$ are re... | math | {
"style": "rule",
"ground_truth": "118"
} | {
"split": "train",
"index": 1975,
"solution": "Let $D$ be the foot of the perpendicular from $O$ to the plane of $ABC$. By the Pythagorean Theorem on triangles $\\triangle OAD$, $\\triangle OBD$ and $\\triangle OCD$ we get:\n\\[DA^2=DB^2=DC^2=20^2-OD^2\\]\n It follows that $DA=DB=DC$, so $D$ is the circumcenter ... |
deepscaler | [
{
"role": "user",
"content": "Given the ellipse $\\frac{x^2}{4} + y^2 = 1$ with points A and B symmetric about the line $4x - 2y - 3 = 0$, find the magnitude of the vector sum of $\\overrightarrow{OA}$ and $\\overrightarrow{OB}$. Let's think step by step and put only the final answer within \\boxed{}."
}
... | math | {
"style": "rule",
"ground_truth": "\\sqrt {5}"
} | {
"split": "train",
"index": 1976,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given an arithmetic sequence $\\{a_n\\}$ with the common difference $d$ being an integer, and $a_k=k^2+2$, $a_{2k}=(k+2)^2$, where $k$ is a constant and $k\\in \\mathbb{N}^*$ \n$(1)$ Find $k$ and $a_n$ \n$(2)$ Let $a_1 > 1$, the sum of the first $n$ terms of $\\{a_n\\}$ is $S... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{13}-1}{2}"
} | {
"split": "train",
"index": 1977,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A $25$ foot ladder is placed against a vertical wall of a building. The foot of the ladder is $7$ feet from the base of the building. If the top of the ladder slips $4$ feet, then the foot of the ladder will slide: Let's think step by step and put only the final answer within \... | math | {
"style": "rule",
"ground_truth": "8"
} | {
"split": "train",
"index": 1978,
"solution": "1. **Identify the initial setup**: A $25$ foot ladder is placed against a vertical wall, with the foot of the ladder $7$ feet from the base of the building. This forms a right triangle where the ladder acts as the hypotenuse.\n\n2. **Calculate the initial height of ... |
deepscaler | [
{
"role": "user",
"content": "Let \\( x \\) be a positive integer, and write \\( a = \\left\\lfloor \\log_{10} x \\right\\rfloor \\) and \\( b = \\left\\lfloor \\log_{10} \\frac{100}{x} \\right\\rfloor \\). Here \\( \\lfloor c \\rfloor \\) denotes the greatest integer less than or equal to \\( c \\). Find t... | math | {
"style": "rule",
"ground_truth": "24"
} | {
"split": "train",
"index": 1979,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "By partial fractions,\n\\[\\frac{1}{x(x + 1)(x + 2)(x + 3)(x + 4)} = \\frac{A}{x} + \\frac{B}{x + 1} + \\frac{C}{x + 2} + \\frac{D}{x + 3} + \\frac{E}{x + 4}\\]for some constants $A,$ $B,$ $C,$ $D,$ and $E.$ Find $A + B + C + D + E.$ Let's think step by step and put only the f... | math | {
"style": "rule",
"ground_truth": "0"
} | {
"split": "train",
"index": 1980,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "On a line, 5 points \\( P, Q, R, S, T \\) are marked in that order. It is known that the sum of the distances from \\( P \\) to the other 4 points is 67, and the sum of the distances from \\( Q \\) to the other 4 points is 34. Find the length of segment \\( PQ \\). Let's think ... | math | {
"style": "rule",
"ground_truth": "11"
} | {
"split": "train",
"index": 1981,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The line RS does not intersect with △ABC. Perpendiculars are drawn from the vertices A, B, and C of △ABC to line RS, and the corresponding feet of the perpendiculars are D, E, and F respectively. It is given that AD = 10, BE = 6, and CF = 24. Let H be the foot of the perpendicu... | math | {
"style": "rule",
"ground_truth": "\\frac{40}{3}"
} | {
"split": "train",
"index": 1982,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Elective 4-4: Coordinate System and Parametric Equations\n\nIn the Cartesian coordinate system $xOy$, the curve $C$ is given by the parametric equations $\\begin{cases} & x=2\\sqrt{3}\\cos \\alpha \\\\ & y=2\\sin \\alpha \\end{cases}$, where $\\alpha$ is the parameter, $\\alpha... | math | {
"style": "rule",
"ground_truth": "6 \\sqrt{2}"
} | {
"split": "train",
"index": 1983,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A 10 by 10 checkerboard has alternating black and white squares. How many distinct squares, with sides on the grid lines of the checkerboard (both horizontal and vertical) and containing at least 7 black squares, can be drawn on the checkerboard? Let's think step by step and pu... | math | {
"style": "rule",
"ground_truth": "140"
} | {
"split": "train",
"index": 1984,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Compute without using a calculator: $12!/11!$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 1985,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Suppose $\\overline{AB}$ is a segment of unit length in the plane. Let $f(X)$ and $g(X)$ be functions of the plane such that $f$ corresponds to rotation about $A$ $60^\\circ$ counterclockwise and $g$ corresponds to rotation about $B$ $90^\\circ$ clockwise. Let... | math | {
"style": "rule",
"ground_truth": "\\frac{1 + \\sqrt{3}}{2}"
} | {
"split": "train",
"index": 1986,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The product of two positive integers is 18. The positive difference of these two integers is 3. What is the sum of the two integers? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "9"
} | {
"split": "train",
"index": 1987,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the second smallest four-digit number in Pascal's triangle? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1001"
} | {
"split": "train",
"index": 1988,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What are the last 8 digits of $$11 \\times 101 \\times 1001 \\times 10001 \\times 100001 \\times 1000001 \\times 111 ?$$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "19754321"
} | {
"split": "train",
"index": 1989,
"solution": "Multiply terms in a clever order. $$\\begin{aligned} 11 \\cdot 101 \\cdot 10001 & =11,111,111 \\\\ 111 \\cdot 1001 \\cdot 1000001 & =111,111,111,111 \\end{aligned}$$ The last eight digits of $11,111,111 \\cdot 111,111,111,111$ are 87654321. We then just need to comp... |
deepscaler | [
{
"role": "user",
"content": "Find the remainder when $x^4 + 2$ is divided by $(x - 2)^2.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "32x - 46"
} | {
"split": "train",
"index": 1990,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A two-row triangle is created with a total of 15 pieces: nine unit rods and six connectors, as shown. What is the total number of pieces that would be used to create an eight-row triangle?\n\n[asy]\ndraw((0,0)--(4,0)--(2,2sqrt(3))--(0,0)--cycle,linewidth(1));\ndraw((2,0)--(3,sq... | math | {
"style": "rule",
"ground_truth": "153"
} | {
"split": "train",
"index": 1991,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Determine the sum of all positive even factors of the number $720$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2340"
} | {
"split": "train",
"index": 1992,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many four-digit numbers have at least one 6 or at least one 8 as digits? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "5416"
} | {
"split": "train",
"index": 1993,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the rectangular coordinate system $(xOy)$, if the initial side of angle $\\alpha$ is the non-negative semi-axis of $x$, and the terminal side is the ray $l$: $y=2x(x\\leqslant 0)$.\n\n(1) Find the value of $\\tan \\alpha$;\n\n(2) Find the value of $\\frac{\\cos \\left(\\alph... | math | {
"style": "rule",
"ground_truth": "-3"
} | {
"split": "train",
"index": 1994,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Rationalize the denominator of $\\frac{1+\\sqrt{3}}{1-\\sqrt{3}}$. When you write your answer in the form $A+B\\sqrt{C}$, where $A$, $B$, and $C$ are integers, what is $ABC$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "6"
} | {
"split": "train",
"index": 1995,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many nonzero complex numbers $z$ have the property that $0, z,$ and $z^3,$ when represented by points in the complex plane, are the three distinct vertices of an equilateral triangle? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4"
} | {
"split": "train",
"index": 1996,
"solution": "1. **Convert to Polar Form and Apply De Moivre's Theorem**:\n Let $z = r \\text{cis}(\\theta)$, where $r$ is the modulus and $\\theta$ is the argument of $z$. By De Moivre's Theorem, $z^3 = r^3 \\text{cis}(3\\theta)$.\n\n2. **Equilateral Triangle Condition**:\n ... |
deepscaler | [
{
"role": "user",
"content": "Households A, B, and C plan to subscribe to newspapers. There are 5 different types of newspapers available. Each household subscribes to two different newspapers. It is known that each pair of households shares exactly one common newspaper. How many different subscription ways... | math | {
"style": "rule",
"ground_truth": "180"
} | {
"split": "train",
"index": 1997,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A teacher gave a test to a class in which $10\\%$ of the students are juniors and $90\\%$ are seniors. The average score on the test was $84.$ The juniors all received the same score, and the average score of the seniors was $83.$ What score did each of the juniors receive on t... | math | {
"style": "rule",
"ground_truth": "93"
} | {
"split": "train",
"index": 1998,
"solution": "1. **Assume the total number of students**: Let's assume there are $10$ students in the class for simplicity, as $10\\%$ of any number of students being juniors will always be $10\\%$ of that number. This assumption makes calculations straightforward without loss of... |
deepscaler | [
{
"role": "user",
"content": "How many rectangles can be formed where each vertex is a point on a 4x4 grid of equally spaced points? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "36"
} | {
"split": "train",
"index": 1999,
"solution": ""
} |
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