data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the expression \\(\\dfrac{\\sqrt[4]{7}}{\\sqrt[6]{7}}\\)."
}
] | math | {
"style": "rule",
"ground_truth": "7^{\\frac{1}{12}}"
} | {
"index": 8600,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the expression \\[ (a^2+b)^2 - (a^2-b)^2, \\]if $a=4$ and $b=1$."
}
] | math | {
"style": "rule",
"ground_truth": "64"
} | {
"index": 8601,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the expression \\[ \\frac{a+2}{a+1} \\cdot \\frac{b-1}{b-2} \\cdot \\frac{c + 8}{c+6} , \\] given that $c = b-10$, $b = a+2$, $a = 4$, and none of the denominators are zero."
}
] | math | {
"style": "rule",
"ground_truth": "3"
} | {
"index": 8602,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the expression \\[ \\frac{a+3}{a+1} \\cdot \\frac{b-2}{b-3} \\cdot \\frac{c + 9}{c+7} , \\] given that $c = b-11$, $b = a+3$, $a = 5$, and none of the denominators are zero."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{3}"
} | {
"index": 8603,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the expression \\[ \\frac{a^2 + 2a}{a^2 + a} \\cdot \\frac{b^2 - 4}{b^2 - 6b + 8} \\cdot \\frac{c^2 + 16c + 64}{c^2 + 12c + 36} \\]\ngiven that \\(c = b - 20\\), \\(b = a + 4\\), \\(a = 2\\), and ensuring none of the denominators are zero."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3}{4}"
} | {
"index": 8604,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the expression \\[(5^{1001} + 6^{1002})^2 - (5^{1001} - 6^{1002})^2\\] and express it in the form \\(k \\cdot 30^{1001}\\) for some integer \\(k\\)."
}
] | math | {
"style": "rule",
"ground_truth": "24"
} | {
"index": 8605,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the expression given by $$2+\\cfrac{3}{4+\\cfrac{5}{6+\\cfrac{7}{8}}}.$$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{137}{52}"
} | {
"index": 8606,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the expression where the digit 2 appears 2013 times."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{2013}{2014}"
} | {
"index": 8607,
"solution": "Let $f(n)$ denote the corresponding expression with the digit 2 appearing exactly $n$ times. Then $f(1)=\\frac{1}{2}$ and for $n>1, f(n)=\\frac{1}{2-f(n-1)}$. By induction using the identity $\\frac{1}{2-\\frac{N-1}{N}}=\\frac{N}{N+1}$, $f(n)=\\frac{n}{n+1}$ for all $n \\geq 1$, so $f(... |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the expression:\n\\[4(1+4(1+4(1+4(1+4(1+4(1+4(1+4(1))))))))\\]"
}
] | math | {
"style": "rule",
"ground_truth": "87380"
} | {
"index": 8608,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the expression: $2\\log_{2}\\;\\sqrt {2}-\\lg 2-\\lg 5+ \\frac{1}{ 3(\\frac{27}{8})^{2} }$."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{4}{9}"
} | {
"index": 8609,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the expression: $\\left(2\\left(3\\left(2\\left(3\\left(2\\left(3 \\times (2+1) \\times 2\\right)+2\\right)\\times 2\\right)+2\\right)\\times 2\\right)+2\\right)$."
}
] | math | {
"style": "rule",
"ground_truth": "5498"
} | {
"index": 8610,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the expression: \\[ M = \\frac{\\sqrt{\\sqrt{7} + 3} + \\sqrt{\\sqrt{7} - 3}}{\\sqrt{\\sqrt{7} + 2}} + \\sqrt{5 - 2\\sqrt{6}}, \\]\nand determine the value of $M$.\nA) $\\sqrt{9}$\nB) $\\sqrt{2} - 1$\nC) $2\\sqrt{2} - 1$\nD) $\\sqrt{\\frac{7}{2}}$\nE) $1$"
}
] | math | {
"style": "rule",
"ground_truth": "2\\sqrt{2} - 1"
} | {
"index": 8611,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the expression: \\\\( \\frac {\\cos 40 ^{\\circ} +\\sin 50 ^{\\circ} (1+ \\sqrt {3}\\tan 10 ^{\\circ} )}{\\sin 70 ^{\\circ} \\sqrt {1+\\cos 40 ^{\\circ} }}\\\\)"
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt {2}"
} | {
"index": 8612,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the first three digits to the right of the decimal point in the decimal representation of $\\left(10^{987} + 1\\right)^{8/3}$ using the Binomial Expansion."
}
] | math | {
"style": "rule",
"ground_truth": "666"
} | {
"index": 8613,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the following expression as a simplified fraction. $$1+\\cfrac{3}{4+\\cfrac{5}{6}}$$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{47}{29}"
} | {
"index": 8614,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the following expression:\n\n$$\\frac { \\sqrt {3}tan12 ° -3}{sin12 ° (4cos ^{2}12 ° -2)}$$"
}
] | math | {
"style": "rule",
"ground_truth": "-4 \\sqrt {3}"
} | {
"index": 8615,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the following expression: $$ 0 - 1 -2 + 3 - 4 + 5 + 6 + 7 - 8 + ... + 2000 $$ The terms with minus signs are exactly the powers of two."
}
] | math | {
"style": "rule",
"ground_truth": "1996906"
} | {
"index": 8616,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the following product of sequences: $\\frac{1}{3} \\cdot \\frac{9}{1} \\cdot \\frac{1}{27} \\cdot \\frac{81}{1} \\dotsm \\frac{1}{2187} \\cdot \\frac{6561}{1}$."
}
] | math | {
"style": "rule",
"ground_truth": "81"
} | {
"index": 8617,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the greatest integer less than or equal to \\[\\frac{5^{150} + 3^{150}}{5^{147} + 3^{147}}.\\]"
}
] | math | {
"style": "rule",
"ground_truth": "124"
} | {
"index": 8618,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the infinite geometric series:\n$$\\frac{5}{3} - \\frac{5}{4} + \\frac{25}{48} - \\frac{125}{384} + \\dots$$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{20}{21}"
} | {
"index": 8619,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the infinite geometric series: $$\\frac{1}{3}+\\frac{1}{6}+\\frac{1}{12}+\\frac{1}{24}+\\dots$$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{2}{3}"
} | {
"index": 8620,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the infinite geometric series: $$\\frac{3}{2}-\\frac{2}{3}+\\frac{8}{27}-\\frac{32}{243}+\\dots$$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{27}{26}"
} | {
"index": 8621,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the infinite geometric series: $$\\frac{4}{3} - \\frac{3}{4} + \\frac{9}{16} - \\frac{27}{64} + \\dots$$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{64}{75}"
} | {
"index": 8622,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the infinite geometric series: $$\\frac{4}{3} - \\frac{5}{12} + \\frac{25}{144} - \\frac{125}{1728} + \\dots$$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{64}{63}"
} | {
"index": 8623,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the infinite geometric series: $$\\frac{5}{3} - \\frac{3}{5} + \\frac{9}{25} - \\frac{27}{125} + \\dots$$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{125}{102}"
} | {
"index": 8624,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the infinite series $\\sum_{k = 1}^\\infty \\frac{k^2}{2^k}.$"
}
] | math | {
"style": "rule",
"ground_truth": "6"
} | {
"index": 8625,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the infinite sum $$\\sum_{n=2}^{\\infty} \\log _{2}\\left(\\frac{1-\\frac{1}{n}}{1-\\frac{1}{n+1}}\\right)$$"
}
] | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"index": 8626,
"solution": "Using the identity $\\log _{2}\\left(\\frac{a}{b}\\right)=\\log _{2} a-\\log _{2} b$, the sum becomes $$\\sum_{n=2}^{\\infty} \\log _{2}\\left(\\frac{n-1}{n}\\right)-\\sum_{n=2}^{\\infty} \\log _{2}\\left(\\frac{n}{n+1}\\right)$$ Most of the terms cancel out, except the $\\log _{2}\\le... |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the infinite sum $\\sum_{n=0}^{\\infty}\\binom{2 n}{n} \\frac{1}{5^{n}}$."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{5}"
} | {
"index": 8627,
"solution": "First Solution: Note that $\\binom{2 n}{n} =\\frac{(2 n)!}{n!\\cdot n!}=\\frac{(2 n)(2 n-2)(2 n-4) \\cdots(2)}{n!} \\cdot \\frac{(2 n-1)(2 n-3)(2 n-5) \\cdots(1)}{n!} =2^{n} \\cdot \\frac{(-2)^{n}}{n!}(-\\frac{1}{2})(-\\frac{1}{2}-1)(-\\frac{1}{2}-2) \\cdots(-\\frac{1}{2}-n+1) =(-4)^{n... |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the infinite sum $\\sum_{n=1}^{\\infty} \\frac{n}{n^{4}+4}$."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3}{8}"
} | {
"index": 8628,
"solution": "We have $$\\begin{aligned} \\sum_{n=1}^{\\infty} \\frac{n}{n^{4}+4} & =\\sum_{n=1}^{\\infty} \\frac{n}{\\left(n^{2}+2 n+2\\right)\\left(n^{2}-2 n+2\\right)} \\\\ & =\\frac{1}{4} \\sum_{n=1}^{\\infty}\\left(\\frac{1}{n^{2}-2 n+2}-\\frac{1}{n^{2}+2 n+2}\\right) \\\\ & =\\frac{1}{4} \\sum... |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the infinite sum $\\sum_{n=1}^{\\infty}\\frac{n}{n^4+4}$."
}
] | math | {
"style": "rule",
"ground_truth": "\\dfrac 3 8"
} | {
"index": 8629,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the integral $$\\int_{ -2 }^{ 2 }$$($$\\sqrt {16-x^{2}}$$+sinx)dx=\\_\\_\\_\\_\\_\\_"
}
] | math | {
"style": "rule",
"ground_truth": "4\\sqrt{3} + \\frac{8\\pi}{3}"
} | {
"index": 8630,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the integral $\\int_{0}^{\\frac{\\pi}{2}} \\sin^{2} \\frac{x}{2} dx =$ \\_\\_\\_\\_\\_\\_."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\pi}{4} - \\frac{1}{2}"
} | {
"index": 8631,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the integral $\\int_{2}^{3}{\\frac{x-2}{\\left( x-1 \\right)\\left( x-4 \\right)}dx}=$\n\nA) $-\\frac{1}{3}\\ln 2$\nB) $\\frac{1}{3}\\ln 2$\nC) $-\\ln 2$\nD) $\\ln 2$"
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{1}{3}\\ln 2"
} | {
"index": 8632,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the integral \\(\\int_{0}^{1} \\ln x \\ln (1-x) \\, dx\\)."
}
] | math | {
"style": "rule",
"ground_truth": "2 - \\frac{\\pi^2}{6}"
} | {
"index": 8633,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the limit as \\( n \\) approaches infinity:\n\n$$\n\\lim _{n \\rightarrow \\infty} \\frac{(1+2n)^{3} - 8n^{5}}{(1+2n)^{2} + 4n^{2}}\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"index": 8634,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the limit of the numerical sequence:\n\n\\[\n\\lim _{n \\rightarrow \\infty}\\left(\\frac{n^{2}-6 n+5}{n^{2}-5 n+5}\\right)^{3 n+2}\n\\]"
}
] | math | {
"style": "rule",
"ground_truth": "e^{-3}"
} | {
"index": 8635,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the monotonic intervals of $F(x)=\\int_{0}^{x}(t^{2}+2t-8)dt$ for $x > 0$.\n\n(1) Determine the monotonic intervals of $F(x)$.\n\n(2) Find the maximum and minimum values of the function $F(x)$ on the interval $[1,3]$."
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{28}{3}"
} | {
"index": 8636,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the polynomial \\[ p(x) = x^4 - 3x^3 - 9x^2 + 27x - 8, \\] where $x$ is a positive number such that $x^2 - 3x - 9 = 0$."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{65 + 81\\sqrt{5}}{2}"
} | {
"index": 8637,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the polynomial \\[ x^3 - 2 x^2 - 8 x + 4, \\]where $x$ is the positive number such that $x^2 - 2x - 8 = 0$."
}
] | math | {
"style": "rule",
"ground_truth": "4"
} | {
"index": 8638,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the polynomial \\[ x^3 - 3x^2 - 12x + 9, \\] where \\(x\\) is the positive number such that \\(x^2 - 3x - 12 = 0\\) and \\(x \\neq -2\\)."
}
] | math | {
"style": "rule",
"ground_truth": "-23"
} | {
"index": 8639,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the product $\\frac{1}{2} \\times \\frac{3}{2} \\times \\frac{4}{3} \\times \\frac{5}{4} \\times \\cdots \\times \\frac{2010}{2009}$."
}
] | math | {
"style": "rule",
"ground_truth": "502.5"
} | {
"index": 8640,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the product $\\frac{1}{2}\\cdot\\frac{4}{1}\\cdot\\frac{1}{8}\\cdot\\frac{16}{1} \\dotsm \\frac{1}{16384}\\cdot\\frac{32768}{1}$."
}
] | math | {
"style": "rule",
"ground_truth": "256"
} | {
"index": 8641,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the product $\\frac{1}{3} \\cdot \\frac{9}{1} \\cdot \\frac{1}{27} \\cdot \\frac{81}{1} \\dotsm \\frac{1}{6561} \\cdot \\frac{19683}{1}$."
}
] | math | {
"style": "rule",
"ground_truth": "729"
} | {
"index": 8642,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the product \\[ (a-10) \\cdot (a-9) \\cdot \\dotsm \\cdot (a-1) \\cdot a, \\] where $a=2$."
}
] | math | {
"style": "rule",
"ground_truth": "0"
} | {
"index": 8643,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the product \\[ (n-1) \\cdot n \\cdot (n+1) \\cdot (n+2) \\cdot (n+3), \\] where $n=2$."
}
] | math | {
"style": "rule",
"ground_truth": "120"
} | {
"index": 8644,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the product \\[\\left(\\sqrt{5}+\\sqrt{6}+\\sqrt{7}\\right)\\left(\\sqrt{5}+\\sqrt{6}-\\sqrt{7}\\right)\\left(\\sqrt{5}-\\sqrt{6}+\\sqrt{7}\\right)\\left(-\\sqrt{5}+\\sqrt{6}+\\sqrt{7}\\right).\\]"
}
] | math | {
"style": "rule",
"ground_truth": "104"
} | {
"index": 8645,
"solution": "We group the first and last factors as well as the two middle factors, then apply the difference of squares repeatedly: \\begin{align*} \\left(\\left(\\sqrt{6} + \\sqrt{7}\\right)^2 - \\sqrt{5}^2\\right)\\left(\\sqrt{5}^2 - \\left(\\sqrt{6} - \\sqrt{7}\\right)^2\\right) &= \\left(13 + ... |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the ratio $\\frac{10^{3000} + 10^{3004}}{10^{3001} + 10^{3003}}$ and determine which whole number it is closest to."
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"index": 8646,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the series $$\\frac{2^1}{8^1 - 1} + \\frac{2^2}{8^2 - 1} + \\frac{2^3}{8^3 - 1} + \\frac{2^4}{8^4 - 1} + \\cdots.$$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{3}"
} | {
"index": 8647,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the sum\n$$\n\\cos \\left(\\frac{2\\pi}{18}\\right) + \\cos \\left(\\frac{4\\pi}{18}\\right) + \\cdots + \\cos \\left(\\frac{34\\pi}{18}\\right).\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"index": 8648,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the sum\n\\[\n\\sum_{k=1}^{50} (-1)^k \\cdot \\frac{k^3 + k^2 + 1}{(k+1)!}.\n\\]\nDetermine the form of the answer as a difference between two terms, where each term is a fraction involving factorials."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{126001}{51!}"
} | {
"index": 8649,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the sum $$\\frac{1}{2\\lfloor\\sqrt{1}\\rfloor+1}+\\frac{1}{2\\lfloor\\sqrt{2}\\rfloor+1}+\\frac{1}{2\\lfloor\\sqrt{3}\\rfloor+1}+\\cdots+\\frac{1}{2\\lfloor\\sqrt{100}\\rfloor+1}$$"
}
] | math | {
"style": "rule",
"ground_truth": "190/21"
} | {
"index": 8650,
"solution": "The first three terms all equal $1 / 3$, then the next five all equal $1 / 5$; more generally, for each $a=1,2, \\ldots, 9$, the terms $1 /(2\\lfloor\\sqrt{a^{2}}\\rfloor+1)$ to $1 /(2\\lfloor\\sqrt{a^{2}+2 a}\\rfloor+1)$ all equal $1 /(2 a+1)$, and there are $2 a+1$ such terms. Thus o... |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the sum $$\\frac{3^1}{9^1 - 1} + \\frac{3^2}{9^2 - 1} + \\frac{3^4}{9^4 - 1} + \\frac{3^8}{9^8 - 1} + \\cdots.$$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"index": 8651,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the sum $$\\lceil\\sqrt{10}\\rceil + \\lceil\\sqrt{11}\\rceil + \\lceil\\sqrt{12}\\rceil + \\cdots + \\lceil\\sqrt{40}\\rceil$$"
}
] | math | {
"style": "rule",
"ground_truth": "170"
} | {
"index": 8652,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the sum $$\\lceil\\sqrt{5}\\rceil + \\lceil\\sqrt{6}\\rceil + \\lceil\\sqrt{7}\\rceil + \\cdots + \\lceil\\sqrt{39}\\rceil$$\nNote: For a real number $x,$ $\\lceil x \\rceil$ denotes the smallest integer that is greater than or equal to $x.$"
}
] | math | {
"style": "rule",
"ground_truth": "175"
} | {
"index": 8653,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the sum $2345 + 3452 + 4523 + 5234$ and then subtract $1234$ from the result."
}
] | math | {
"style": "rule",
"ground_truth": "14320"
} | {
"index": 8654,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the sum \\[\\frac{1}{2^1} + \\frac{2}{2^2} + \\frac{3}{2^3} + \\cdots + \\frac{k}{2^k} + \\cdots \\]"
}
] | math | {
"style": "rule",
"ground_truth": "2"
} | {
"index": 8655,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the sum \\[\\frac{1}{3^1} + \\frac{2}{3^2} + \\frac{3}{3^3} + \\cdots + \\frac{k}{3^k} + \\cdots \\]"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3}{4}"
} | {
"index": 8656,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the sum of $1001101_2$ and $111000_2$, and then add the decimal equivalent of $1010_2$. Write your final answer in base $10$."
}
] | math | {
"style": "rule",
"ground_truth": "143"
} | {
"index": 8657,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the sum:\n\\[\n\\sum_{n=1}^\\infty \\frac{n^3 + n^2 - n}{(n+3)!}.\n\\]"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{6}"
} | {
"index": 8658,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the sum: 1 - 2 + 3 - 4 + $\\cdots$ + 100 - 101"
}
] | math | {
"style": "rule",
"ground_truth": "-151"
} | {
"index": 8659,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the value of $3^2 \\times 4 \\times 6^3 \\times 7!$."
}
] | math | {
"style": "rule",
"ground_truth": "39191040"
} | {
"index": 8660,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the value of $\\frac{(2210-2137)^2 + (2137-2028)^2}{64}$."
}
] | math | {
"style": "rule",
"ground_truth": "268.90625"
} | {
"index": 8661,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the value of $\\frac{1}{4}\\cdot\\frac{8}{1}\\cdot\\frac{1}{32}\\cdot\\frac{64}{1} \\dotsm \\frac{1}{1024}\\cdot\\frac{2048}{1}$."
}
] | math | {
"style": "rule",
"ground_truth": "32"
} | {
"index": 8662,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the value of the expression \\((5(5(5(5+1)+1)+1)+1)\\)."
}
] | math | {
"style": "rule",
"ground_truth": "781"
} | {
"index": 8663,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate the volume of solid $T$ defined by the inequalities $|x| + |y| \\leq 2$, $|x| + |z| \\leq 2$, and $|y| + |z| \\leq 2$."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{32}{3}"
} | {
"index": 8664,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate: $(12345679^2 \\times 81 - 1) \\div 11111111 \\div 10 \\times 9 - 8$ in billions. (Answer in billions)"
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"index": 8665,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate: $(2^2)^3$."
}
] | math | {
"style": "rule",
"ground_truth": "64"
} | {
"index": 8666,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate: $(723)(723)-(722)(724)$."
}
] | math | {
"style": "rule",
"ground_truth": "1"
} | {
"index": 8667,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate: $-\\left(14\\div 2\\cdot 9-60+3\\cdot 9\\right)$."
}
] | math | {
"style": "rule",
"ground_truth": "-30"
} | {
"index": 8668,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate: $5-7\\left(8-3^2\\right)4.$"
}
] | math | {
"style": "rule",
"ground_truth": "33"
} | {
"index": 8669,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate: $6 - 5\\left[7 - (\\sqrt{16} + 2)^2\\right] \\cdot 3.$"
}
] | math | {
"style": "rule",
"ground_truth": "-429"
} | {
"index": 8670,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate: $6 - 8\\left(9 - 4^2\\right) \\div 2 - 3.$"
}
] | math | {
"style": "rule",
"ground_truth": "31"
} | {
"index": 8671,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate: $64^2-36^2$"
}
] | math | {
"style": "rule",
"ground_truth": "2800"
} | {
"index": 8672,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate: $81^2 - (x+9)^2$ where $x=45$."
}
] | math | {
"style": "rule",
"ground_truth": "3645"
} | {
"index": 8673,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate: $\\frac{10^{-2}5^0}{10^{-3}}$"
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"index": 8674,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate: \\( \\frac {\\tan 150^{\\circ} \\cos (-210^{\\circ}) \\sin (-420^{\\circ})}{\\sin 1050^{\\circ} \\cos (-600^{\\circ})} \\)."
}
] | math | {
"style": "rule",
"ground_truth": "-\\sqrt{3}"
} | {
"index": 8675,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Evaluate: \\(\\sin 37^{\\circ} \\cos ^{2} 34^{\\circ} + 2 \\sin 34^{\\circ} \\cos 37^{\\circ} \\cos 34^{\\circ} - \\sin 37^{\\circ} \\sin ^{2} 34^{\\circ}\\)."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{6} + \\sqrt{2}}{4}"
} | {
"index": 8676,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Every 1 kilogram of soybeans can produce 0.8 kilograms of soybean oil. With 20 kilograms of soybeans, you can produce \\_\\_\\_\\_\\_\\_ kilograms of soybean oil. To obtain 20 kilograms of soybean oil, you need \\_\\_\\_\\_\\_\\_ kilograms of soybeans."
}
] | math | {
"style": "rule",
"ground_truth": "25"
} | {
"index": 8677,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Every June 1, an ecologist takes a census of the number of wrens in a state park. She noticed that the number is decreasing by $40\\%$ each year. If this trend continues, in what year will the census show that the number of wrens is less than $10\\%$ of what it was on June 1, 2... | math | {
"style": "rule",
"ground_truth": "2009"
} | {
"index": 8678,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Every Sunday, a married couple has breakfast with their mothers. Unfortunately, the relationships each spouse has with the other's mother are quite strained: both know that there is a two-thirds chance of getting into an argument with the mother-in-law. In the event of a confli... | math | {
"style": "rule",
"ground_truth": "4/9"
} | {
"index": 8679,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Every bag of Dummies (a chocolate candy) contains the same number of pieces.\n\nThe Dummies in one bag can't be divided equally among $9$ kids, because after each kid gets the same (whole) number of pieces, $7$ pieces are left over.\n\nIf the Dummies in three bags are divided e... | math | {
"style": "rule",
"ground_truth": "3"
} | {
"index": 8680,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Every card in a deck displays one of three symbols - star, circle, or square, each filled with one of three colors - red, yellow, or blue, and each color is shaded in one of three intensities - light, normal, or dark. The deck contains 27 unique cards, each representing a diffe... | math | {
"style": "rule",
"ground_truth": "702"
} | {
"index": 8681,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Every card in a deck has a picture of one shape - circle, square, or triangle, which is painted in one of the three colors - red, blue, or green. Furthermore, each color is applied in one of three shades - light, medium, or dark. The deck has 27 cards, with every shape-color-sh... | math | {
"style": "rule",
"ground_truth": "117"
} | {
"index": 8682,
"solution": "Treat the sets as ordered. Then for each of the three criterion, there are $3!=6$ choices if the attribute is different and there are $3$ choices is the attribute is the same. Thus all three attributes combine to a total of $(6+3)^3=729$ possibilities. However if all three attributes a... |
DeepScaleR | [
{
"role": "user",
"content": "Every card in a deck has a picture of one shape - circle, square, or triangle, which is painted in one of the three colors - red, blue, or green. Furthermore, each color is applied in one of three shades - light, medium, or dark. The deck has 27 cards, with every shape-color-sh... | math | {
"style": "rule",
"ground_truth": "117"
} | {
"index": 8683,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Every day at noon, a scheduled ship departs from Moscow to Astrakhan and from Astrakhan to Moscow. The ship traveling from Moscow takes exactly four days to reach Astrakhan, then stays there for two days, and at noon two days after its arrival in Astrakhan, it departs back to M... | math | {
"style": "rule",
"ground_truth": "13"
} | {
"index": 8684,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Every day from Monday to Friday, an old man went to the blue sea and cast his net. Each day, the number of fish caught in the net was not greater than the number caught the previous day. Over the five days, the old man caught exactly 100 fish. What is the minimum total number o... | math | {
"style": "rule",
"ground_truth": "50"
} | {
"index": 8685,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Every day, 12 tons of potatoes are delivered to the city using one type of transport from three collective farms. The price per ton is 4 rubles from the first farm, 3 rubles from the second farm, and 1 ruble from the third farm. To ensure timely delivery, the loading process fo... | math | {
"style": "rule",
"ground_truth": "24.6667"
} | {
"index": 8686,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Every day, Xiaoming goes to school along a flat road \\(AB\\), an uphill road \\(BC\\), and a downhill road \\(CD\\) (as shown in the diagram). Given that \\(AB : BC : CD = 1 : 2 : 1\\) and that Xiaoming's speeds on flat, uphill, and downhill roads are in the ratio 3 : 2 : 4, r... | math | {
"style": "rule",
"ground_truth": "19:16"
} | {
"index": 8687,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Every day, from Monday to Friday, an old man went to the blue sea and cast his net into the sea. Each day, he caught no more fish than the previous day. In total, he caught exactly 100 fish over the five days. What is the minimum total number of fish he could have caught on Mon... | math | {
"style": "rule",
"ground_truth": "50"
} | {
"index": 8688,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Every day, from Monday to Friday, an old man went to the blue sea and cast his net into the sea. Each day, the number of fish caught in the net was no greater than the number caught on the previous day. In total, over the five days, the old man caught exactly 100 fish. What is ... | math | {
"style": "rule",
"ground_truth": "50"
} | {
"index": 8689,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Every day, the ram learns the same number of languages. By the evening of his birthday, he knew 1000 languages. On the first day of the same month, he knew 820 languages by evening, and on the last day of that month, he knew 1100 languages. When is the ram's birthday?"
}
] | math | {
"style": "rule",
"ground_truth": "19"
} | {
"index": 8690,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Every evening, Laura gathers three socks randomly to pack for her gym session next morning. She has 12 black socks, 10 white socks, and 6 striped socks in her drawer. What is the probability that all three socks she picks are of the same type?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{60}{546}"
} | {
"index": 8691,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Every high school in the city of Euclid sent a team of $3$ students to a math contest. Each participant in the contest received a different score. Andrea's score was the median among all students, and hers was the highest score on her team. Andrea's teammates Beth and Carla pla... | math | {
"style": "rule",
"ground_truth": "23"
} | {
"index": 8692,
"solution": "1. **Understanding the problem setup**: Each high school sends 3 students, and each student has a unique score. Andrea's score is the median of all scores, and she has the highest score on her team. Her teammates Beth and Carla placed 37th and 64th, respectively.\n\n2. **Determining An... |
DeepScaleR | [
{
"role": "user",
"content": "Every morning when Tim wakes up, he groggily searches around his sock drawer and picks two socks randomly. If he has 10 gray-bottomed socks and 8 white-bottomed socks in his drawer, what is the probability that he picks a matching pair?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{73}{153}"
} | {
"index": 8693,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Every pair of communities in a county are linked directly by one mode of transportation; bus, train, or airplane. All three methods of transportation are used in the county with no community being serviced by all three modes and no three communities being linked pairwise by the... | math | {
"style": "rule",
"ground_truth": "4"
} | {
"index": 8694,
"solution": "\nLet us consider a set of communities, denoted as vertices in a graph, where each edge between a pair of communities is labeled with one of the following modes of transportation: bus, train, or airplane. The problem imposes the following conditions:\n\n1. All three modes of transporta... |
DeepScaleR | [
{
"role": "user",
"content": "Every positive integer $k$ has a unique factorial base expansion $(f_1,f_2,f_3,\\ldots,f_m)$, meaning that $k=1!\\cdot f_1+2!\\cdot f_2+3!\\cdot f_3+\\cdots+m!\\cdot f_m$, where each $f_i$ is an integer, $0\\le f_i\\le i$, and $0<f_m$. Given that $(f_1,f_2,f_3,\\ldots,f_j)$ is ... | math | {
"style": "rule",
"ground_truth": "495"
} | {
"index": 8695,
"solution": "Note that $1+\\sum_{k=1}^{n-1} {k\\cdot k!} = 1+\\sum_{k=1}^{n-1} {((k+1)\\cdot k!- k!)} = 1+\\sum_{k=1}^{n-1} {((k+1)!- k!)} = n!$\n Thus for all $m\\in\\mathbb{N}$,\n$(32m+16)!-(32m)! = \\left(1+\\sum_{k=1}^{32m+15} {k\\cdot k!}\\right)-\\left(1+\\sum_{k=1}^{32m-1} {k\\cdot k!}\\righ... |
DeepScaleR | [
{
"role": "user",
"content": "Every second, Andrea writes down a random digit uniformly chosen from the set $\\{1,2,3,4\\}$. She stops when the last two numbers she has written sum to a prime number. What is the probability that the last number she writes down is 1?"
}
] | math | {
"style": "rule",
"ground_truth": "15/44"
} | {
"index": 8696,
"solution": "Let $p_{n}$ be the probability that the last number she writes down is 1 when the first number she writes down is $n$. Suppose she starts by writing 2 or 4 . Then she can continue writing either 2 or 4 , but the first time she writes 1 or 3 , she stops. Therefore $p_{2}=p_{4}=\\frac{1}... |
DeepScaleR | [
{
"role": "user",
"content": "Every second, the computer displays a number equal to the sum of the digits of the previous number multiplied by 31. On the first second, the number 2020 was displayed. What number will be displayed on the screen on the 2020th second?"
}
] | math | {
"style": "rule",
"ground_truth": "310"
} | {
"index": 8697,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Every time these two wheels are spun, two numbers are selected by the pointers. What is the probability that the sum of the two selected numbers is even?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"index": 8698,
"solution": "1. **Understanding the Problem**: We need to find the probability that the sum of the numbers selected by spinning two wheels is even. For the sum to be even, both numbers must either be both even or both odd.\n\n2. **Determining the Probabilities**:\n - **Probability of Even Numbers... |
DeepScaleR | [
{
"role": "user",
"content": "Every week Roger pays for a movie ticket and a soda out of his allowance. Last week, Roger's allowance was $A$ dollars. The cost of his movie ticket was $20\\%$ of the difference between $A$ and the cost of his soda, while the cost of his soda was $5\\%$ of the difference betwe... | math | {
"style": "rule",
"ground_truth": "23\\%"
} | {
"index": 8699,
"solution": "1. **Define Variables:**\n Let $m$ represent the cost of the movie ticket and $s$ represent the cost of the soda.\n\n2. **Set Up Equations:**\n According to the problem, we have:\n \\[ m = 0.20(A - s) \\]\n \\[ s = 0.05(A - m) \\]\n\n3. **Convert to Fractional Form:**\n These... |
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