data_source stringclasses 10
values | prompt listlengths 2 2 | ability stringclasses 2
values | reward_model dict | extra_info dict |
|---|---|---|---|---|
orca_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Tommy is looking at his change collection. He has some dimes and pennies. He has twice as many nickels as dimes. He has 4 quarters. He has 10 times as many pennies as quarters. H... | math | {
"ground_truth": "10",
"style": "rule"
} | {
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synthetic_amc | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A point $R$ is located outside of circle $\\omega$ with center $O$ and radius $10$ units. Find the locus of the midpoint $M$ of the segment from $R$ to a point $S$ as $S$ varies ... | math | {
"ground_truth": "\\text{B}",
"style": "rule"
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"index": 1,
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orca_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Diego can carry a certain amount of fruit home in his bookbag. He buys a pound of watermelon, a pound of grapes, a pound of oranges, and 17 pounds of apples. What is the total we... | math | {
"ground_truth": "20",
"style": "rule"
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"index": 2,
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cn_k12 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $$f(x)= \\begin{cases} a^{x}, x<0 \\\\ ( \\frac {1}{4}-a)x+2a, x\\geq0\\end{cases}$$ such that for any $x\\_1 \\neq x\\_2$, the inequality $$\\frac {f(x_{1})-f... | math | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
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"index": 3,
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cn_k12 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
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{
"content": "For a cubic function $f(x)=ax^3+bx^2+cx+d\\ (a\\neq 0)$, define: if the equation $f''(x)=0$ has a real solution $x_0$, then the point $(x_0, f(x_0))$ is called an \"inflection po... | math | {
"ground_truth": "2012",
"style": "rule"
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olympiads | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
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"content": "Write an \\( n \\)-digit number using the digits 1 and 2, such that no two consecutive digits are both 1. Denote the number of such \\( n \\)-digit numbers as \\( f(n) \\). Find ... | math | {
"ground_truth": "144",
"style": "rule"
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"index": 5,
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cn_k12 | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
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"content": "Let $f(x)$ be a function defined on $R$. For any $x_{1}$, $x_{2} \\in R$, it holds that $f(x_{1}+x_{2})=f(x_{1})+f(x_{2})+1$. Also, when $x > 0$, $f(x) > f(0)$ always holds. Whic... | math | {
"ground_truth": "ACD",
"style": "rule"
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"index": 6,
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olympiads | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
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"content": "Points \\( E \\) and \\( F \\) are chosen on the sides \\( BC \\) and \\( CD \\) of the square \\( ABCD \\) in such a way that the angle \\( EAF \\) is \\( 45^\\circ \\). The sid... | math | {
"ground_truth": "2",
"style": "rule"
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"index": 7,
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synthetic_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Billy and Bobbi each selected a positive integer less than 150. Billy's number is a multiple of 15, and Bobbi's number is a multiple of 20. What is the probability that they sele... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"index": 8,
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cn_k12 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given \\\\(m,n\\\\) represent two different lines, and \\\\(\\alpha\\\\) represents a plane, which of the following statements is correct? \\\\((\\quad)\\)\nA: If \\\\(m\\paralle... | math | {
"ground_truth": "\\text{B}",
"style": "rule"
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"index": 9,
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cn_k12 | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
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{
"content": "There are five different books, of which two are Chinese language books, two are math books, and one is a physics book. If they are randomly placed side by side on the same shelf... | math | {
"ground_truth": "\\frac{1}{5}",
"style": "rule"
} | {
"index": 10,
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orca_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Heather is going to sew some aprons for a kiddie crew program. She already was able to sew 13 aprons, and today, she sewed three times as many aprons. Heather needs to sew 49 apr... | math | {
"ground_truth": "150",
"style": "rule"
} | {
"index": 11,
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orca_math | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A group of men decided to do a work in 50 days. Some of them became absent, and the rest of the group did the work in 60 days. The original number of men was 60. How many men bec... | math | {
"ground_truth": "10",
"style": "rule"
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"index": 12,
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synthetic_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the greatest value of $x$ such that \\[\\frac{x^2 - x - 90}{x-9} = \\frac{2}{x+7}.\\]",
"role": "user"
}
] | math | {
"ground_truth": "-4",
"style": "rule"
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"index": 13,
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cn_k12 | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the complex number $z$ satisfies $(z-3i)(2+i)=5i$ (where $i$ is the imaginary unit), find the conjugate of $z$.\n\nA: $(-2-2i)$\nB: $(-2+2i)$\nC: $(2-2i)$\nD: $(2+2i)$... | math | {
"ground_truth": "2-5i",
"style": "rule"
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synthetic_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many even natural-number factors does \\( n = 2^3 \\cdot 5^1 \\cdot 11^2 \\) have?",
"role": "user"
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] | math | {
"ground_truth": "18",
"style": "rule"
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"index": 15,
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orca_math | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "When Erick went to the market to sell his fruits, he realized that the price of lemons had risen by $4 for each lemon. The price of grapes had also increased by half the price th... | math | {
"ground_truth": "\\$2220",
"style": "rule"
} | {
"index": 16,
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orca_math | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
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{
"content": "You need to subtract 46 from a certain number, but mistakenly subtracted 64, and got 122. Find the result of the correct calculation.",
"role": "user"
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] | math | {
"ground_truth": "140",
"style": "rule"
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"index": 17,
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synthetic_amc | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the difference between a 7.5% sales tax and a 6.25% sales tax on an item priced at $50 before tax.\nA) $0.50\nB) $0.625\nC) $0.75\nD) $1.00\nE) $1.25",
"role": "use... | math | {
"ground_truth": "B",
"style": "rule"
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"index": 18,
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orca_math | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A retailer buys a radio for Rs 225. His overhead expenses are Rs 30. He sells the radio for some amount. The profit percent of the retailer is 17.64705882352942%. What is the sel... | math | {
"ground_truth": "300",
"style": "rule"
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"index": 19,
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cn_k12 | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the polar coordinate system, the distance from the center of the circle $\\rho = 4 \\cos \\theta \\left( \\,\\rho \\in R \\, \\right)$ to the line $\\theta = \\frac{\\pi}{3}$ ... | math | {
"ground_truth": "\\sqrt{3}",
"style": "rule"
} | {
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synthetic_math | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the base ten equivalent of $45321_{7}$?",
"role": "user"
}
] | math | {
"ground_truth": "11481",
"style": "rule"
} | {
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olympiads | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
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{
"content": "Try to fill a $4 \\times 4$ grid with 16 non-zero numbers so that the sum of the numbers in each row, each column, and each diagonal (including all 14 diagonals that pass through... | math | {
"ground_truth": "\\text{A possible solution is:}",
"style": "rule"
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orca_math | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
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{
"content": "A trader bought a car at a 20% discount on its original price, with an additional 5% depreciation per year for 2 years. He also paid 3% of the purchase price in taxes and 2% of t... | math | {
"ground_truth": "33.96\\%",
"style": "rule"
} | {
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orca_math | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
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{
"content": "Greg's mom made some cookies for the family and cut them in half. Greg ate some halves, his brother, Brad, had 6 halves, and there were 18 halves left. Greg's mom made 14 whole c... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"index": 24,
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orca_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "When positive integer x is divided by positive integer y, the remainder is some number. If x / y = 6.12, and the value of y is 49.99999999999996, what is the remainder when x is ... | math | {
"ground_truth": "0",
"style": "rule"
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orca_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A number, when divided by 125, gives a remainder of 40. When the same number is divided by another value, the remainder is 11. What is the value that the number is divided by to ... | math | {
"ground_truth": "29",
"style": "rule"
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orca_math | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Rachel strolled to Nicholas's house. It is 10 miles from Rachel's house to Nicholas's house. Rachel went at a speed of 2 miles per hour. How long did it take Rachel to get there?... | math | {
"ground_truth": "5",
"style": "rule"
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"index": 27,
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orca_math | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "An order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth. What would be the cost of a carpet whose length and breadth are 42.7% ... | math | {
"ground_truth": "4371.78",
"style": "rule"
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synthetic_math | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
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{
"content": "In triangle $PQR$, $PQ = 21$, $PR = 28$, $QR = 35$, and $PS$ is an angle bisector. Find the ratio of the area of triangle $PQS$ to the area of triangle $PRS$. (Express your answe... | math | {
"ground_truth": "\\frac{3}{4}",
"style": "rule"
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olympiads | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Schoolchildren were given 7 sheets of paper and asked to cut some of them into 7 pieces. The resulting pieces of paper were mixed and they were again asked to cut some of them in... | math | {
"ground_truth": "54",
"style": "rule"
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"index": 30,
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gsm8k | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "John wants to lose weight. He eats 1800 calories a day and burns 2300 a day. If he needs to burn 4000 calories to lose 1 pound how many days will it take to lose 10 pounds?",
... | math | {
"ground_truth": "80",
"style": "rule"
} | {
"index": 31,
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orca_math | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "One-fourth of a number is greater than one-fifth of the number succeeding it by 1. Find the number.",
"role": "user"
}
] | math | {
"ground_truth": "24",
"style": "rule"
} | {
"index": 32,
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orca_math | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A theater has 80 seats. On opening night, they sold out, selling adult tickets for 12 dollars each and child tickets for 5 dollars each. They sold 63 child tickets. How much mone... | math | {
"ground_truth": "\\$519",
"style": "rule"
} | {
"index": 33,
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cn_k12 | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the random variable $X$ follows a binomial distribution with $P(X=0)=0.8$ and $P(X=1)=0.2$, and let $Y=3X-2$, then $P(Y=-2)=$ \\_\\_\\_\\_\\_\\_.",
"role": "user"
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] | math | {
"ground_truth": "0.8",
"style": "rule"
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synthetic_math | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the smallest positive real number $x$ such that\n\\[\\lfloor x^2 \\rfloor - x \\lfloor x \\rfloor = 4.\\]",
"role": "user"
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] | math | {
"ground_truth": "\\frac{29}{5}",
"style": "rule"
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"index": 35,
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synthetic_math | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For real numbers \\(t \\neq 0,\\) the point\n\\[\n(x, y) = \\left( \\frac{2t + 1}{t}, \\frac{t - 2}{t} \\right)\n\\]\nis plotted. All the plotted points lie on what kind of curve... | math | {
"ground_truth": "\\text{(E)}",
"style": "rule"
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olympiads | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\(T_{0}=1, T_{1}=x, T_{k+1}=2 x T_{k}-T_{k-1}\\) for \\(k \\in \\mathbb{N}\\). Express \\(T_{5}\\) and \\(T_{0}+T_{1}+T_{2}+T_{3}\\) in standard form.",
"role": "user"
... | math | {
"ground_truth": "T_5 = 16x^5 - 20x^3 + 5x, \\quad T_0 + T_1 + T_2 + T_3 = 4x^3 + 2x^2 - 2x",
"style": "rule"
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synthetic_amc | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the number of revolutions of a wheel, with a fixed center and an outside diameter of $10$ feet, required for a point on the rim to travel half a mile.\nA) $\\frac{132}{... | math | {
"ground_truth": "C",
"style": "rule"
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cn_k12 | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $f(x)$ be a function defined on $\\mathbb{R}$ that is never zero, and for any $x, y \\in \\mathbb{R}$, it satisfies $f(x) \\bullet f(y) = f(x + y)$. If ${a_1} = \\frac{1}{2},... | math | {
"ground_truth": "[\\frac{1}{2}, 1)",
"style": "rule"
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cn_k12 | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $f(x)=2\\sqrt{3}\\sin{x}\\cos{x}+2\\cos^2{x}-1$ where $x\\in\\mathbb{R}$. \n$(1)$ Find the intervals where the function $f(x)$ is decreasing, and determine it... | math | {
"ground_truth": "\\cos{2x_0} = \\frac{3 - 4\\sqrt{3}}{10}",
"style": "rule"
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"index": 40,
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synthetic_math | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If four people are selected at random from a group of nine men and six women, what is the probability that at least one woman is selected? Express your answer as a common fractio... | math | {
"ground_truth": "\\frac{137}{151}",
"style": "rule"
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orca_math | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Nicholas starts with 8 bottle caps. He gets some more from Catherine and ends up with 93 bottle caps. How many bottle caps did Catherine give to Nicholas?",
"role": "user"
... | math | {
"ground_truth": "85",
"style": "rule"
} | {
"index": 42,
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cn_k12 | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $\\{a_n\\}$ be an arithmetic sequence with a non-zero common difference, satisfying $a_4^2 + a_5^2 = a_6^2 + a_7^2$. Determine the sum of the first 10 terms of this sequence ... | math | {
"ground_truth": "0",
"style": "rule"
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"index": 43,
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synthetic_amc | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
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"content": "Points $C$ and $D$ are $7$ units apart. How many lines in a given plane containing $C$ and $D$ are $3$ units from $C$ and $4$ units from $D$?\n$\\text{(A) } 0\\quad \\text{(B) } ... | math | {
"ground_truth": "\\text{(D) } 3",
"style": "rule"
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cn_k12 | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $0 < x < 1$, then the maximum value of $f(x) = x(1-x)$ is \\_\\_\\_\\_\\_\\_.",
"role": "user"
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] | math | {
"ground_truth": "\\frac {1}{4}",
"style": "rule"
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"index": 45,
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orca_math | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "There are 840 male and female participants in a meeting. Half the female participants and some proportion of the male participants are democrats. One-third of all the participant... | math | {
"ground_truth": "1:4",
"style": "rule"
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olympiads | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The number of 2007-digit decimal numbers $\\overline{2 a_{1} a_{2} a_{3} \\cdots a_{2006}}$ in which the digits $a_{1}, a_{2}, a_{3}, \\cdots, a_{2006}$ contain an odd number of ... | math | {
"ground_truth": "\\text{B}",
"style": "rule"
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cn_k12 | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given events $A$, $B$, $P(B)=\\frac{1}{3}$, $P(\\overline{B}|A)=\\frac{3}{4}$, $P(\\overline{B}|\\overline{A})=\\frac{1}{2}$, then $P\\left(A\\right)=\\left(\\ \\ \\right)$\n\nA:... | math | {
"ground_truth": "C",
"style": "rule"
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synthetic_math | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For all integers $n$ greater than 1, define $a_n = \\dfrac{1}{\\log_n 3003}$. Let $d = a_3 + a_4 + a_5 + a_6$ and $e = a_{15} + a_{16} + a_{17} + a_{18} + a_{19}$. Find $d - e$."... | math | {
"ground_truth": "\\log_{3003} \\frac{1}{323}",
"style": "rule"
} | {
"index": 49,
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aops_forum | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
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"content": "In the plane, two intersecting lines $a$ and $b$ are given, along with a circle $\\omega$ that has no common points with these lines. For any line $\\ell||b$ , define $A=... | math | {
"ground_truth": "\\frac{r^2}{ka}",
"style": "rule"
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synthetic_math | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
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{
"content": "Following the directions of the arrows, how many different paths are there from $A$ to $D$?\n\n[asy]\npair A,B,C,D;\nA=(0,0);\nB=(3,0);\nC=(6,0);\nD=(9,0);\ndot(A);\ndot(B);\ndot... | math | {
"ground_truth": "12",
"style": "rule"
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
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"content": "**p1.** Point $P$ has coordinate value $(3,2)$ , and point $Q$ has coordinate value $(6, x)$ . For what value of $x$ does Line $PQ$ have a slope of $6$ ?**p2.** I have... | math | {
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cn_k12 | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
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"content": "Given the ellipse $\\frac{x^{2}}{9}+ \\frac{y^{2}}{m^{2}}=1$ (where $0<m<3$), the length of its major axis is twice that of its minor axis. Find the value of $m$.\nA: $\\frac{3}{... | math | {
"ground_truth": "\\frac{3}{2}",
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cn_k12 | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
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"content": "Given the polar equation of curve C is $\\rho=2\\cos\\theta$, with the pole as the origin of the Cartesian coordinate system and the polar axis as the positive half-axis of the x... | math | {
"ground_truth": "1, 1+ \\sqrt {2}, 1- \\sqrt {2}",
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synthetic_math | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
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{
"content": "Mr. Fast eats a pizza slice in 5 minutes, Mr. Slow eats a pizza slice in 10 minutes, and Mr. Steady eats a pizza slice in 8 minutes. How long does it take for them to eat 24 pizz... | math | {
"ground_truth": "56",
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synthetic_math | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
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"content": "Let \\( a, b, \\) and \\( c \\) be the roots of the equation \\( x^3 - 18x^2 + 20x - 8 = 0 \\). Find the value of \\( (2+a)(2+b)(2+c) \\).",
"role": "user"
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] | math | {
"ground_truth": "128",
"style": "rule"
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cn_k12 | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
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"content": "The function $f(x)=x^{3}+ax^{2}+(a+6)x+1$ has extreme values on $R$. Determine the range of values for the real number $a$.\nA: $-3\\leqslant a\\leqslant 6$\nB: $a\\geqslant 6$ o... | math | {
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cn_k12 | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
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"content": "In \\\\(\\triangle ABC\\\\), the sides opposite to angles \\\\(A\\\\), \\\\(B\\\\), and \\\\(C\\\\) are denoted as \\\\(a\\\\), \\\\(b\\\\), and \\\\(c\\\\) respectively. Given t... | math | {
"ground_truth": "A = 135^{\\circ}, a = \\sqrt{29}",
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orca_math | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
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"content": "a farmer has an apple orchard consisting of fuji and gala apple trees . due to high winds this year 10 % of his trees cross pollinated . the number of his trees that are pure fuj... | math | {
"ground_truth": "27",
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orca_math | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
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"content": "A trader marked the selling price of an article at 50% above the cost price. At the time of selling, he allows a certain discount and suffers a loss of 1%. What is the percentage... | math | {
"ground_truth": "34\\%",
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orca_math | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
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"content": "A multinational company has a yearly subscription to three categories of professional magazines: Category A, Category B, and Category C. The subscription costs for these categori... | math | {
"ground_truth": "€561.1615",
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cn_k12 | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
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"content": "(5 points) (2015 Zaozhuang School-Level Mock) The negation of the proposition \"There exists an $x \\in \\mathbb{R}$ such that $x^3 - 2x + 1 = 0$\" is ( ).\n\nA. There exists an ... | math | {
"ground_truth": "\\forall x \\in \\mathbb{R}, x^3 - 2x + 1 \\neq 0",
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cn_k12 | [
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"content": "Given the curve $y= \\frac {1}{3}x^{3}+ \\frac {4}{3}$,\n(1) Find the equation of the tangent line at point P(2,4);\n(2) Find the equation of the tangent line passing through poi... | math | {
"ground_truth": "4x-y-4=0",
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orca_math | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
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"content": "Every bedtime, Juwella reads a book. Three nights ago, she read 15 pages. She read some ratio of pages two nights ago compared to three nights ago, while last night she read 5 pa... | math | {
"ground_truth": "2:1",
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synthetic_math | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
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"content": "Find all angles $\\theta,$ $0 \\le \\theta \\le 2\\pi,$ with the following property: For all real numbers $x,$ $0 \\le x \\le 1,$\n\\[\nx^3 \\cos \\theta + x(1 - x) - (1 - x)^3 \... | math | {
"ground_truth": "\\left(\\frac{\\pi}{2}, \\pi\\right)",
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synthetic_math | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
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"content": "A triangle has side lengths of 10, 24, and 26 units. What is the area of this triangle, in square units?",
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"ground_truth": "120 \\text{ square units}",
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orca_math | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
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"content": "Let x be the original number, and y be an additional number such that y = x^2 + 5x - 12. Find the number x which, when multiplied by 15, is increased by 280, while also satisfyin... | math | {
"ground_truth": "x^2",
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synthetic_math | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
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"content": "Let $\\theta$ be the angle between the line\n\\[\\frac{x - 2}{4} = \\frac{y + 3}{5} = \\frac{z + 1}{7}\\]\nand the plane $5x - 3y + 4z = 6.$ Find $\\sin \\theta.$",
"role": ... | math | {
"ground_truth": "\\frac{\\sqrt{3411}}{67}",
"style": "rule"
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synthetic_math | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many positive 3-digit numbers are divisible by 13?",
"role": "user"
}
] | math | {
"ground_truth": "69",
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cn_k12 | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
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{
"content": "Calligraphy is a cultural treasure of the Chinese nation, a precious wealth of human civilization, and an important part of basic education in our country. A certain school is pr... | math | {
"ground_truth": "\\text{The school can purchase at most 50 brushes.}",
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cn_k12 | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
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"content": "Given $x=\\sqrt{6}-\\sqrt{2}$, the value of the algebraic expression $2x^2+4\\sqrt{2}x$ is ______.",
"role": "user"
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] | math | {
"ground_truth": "8",
"style": "rule"
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cn_k12 | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
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"content": "Given the line $x+y=1$ and the circle $x^{2}+y^{2}=a$ intersect at points $A$ and $B$. $O$ is the origin, and $C$ is a point on the circle. If $\\overrightarrow{OA} + \\overright... | math | {
"ground_truth": "2",
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synthetic_amc | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
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{
"content": "Consider a 10-sided polygon $ABCDEFGHIJ$, where each side has alternating lengths of 5 and 3 units, and each two consecutive sides form a right angle. Suppose that $\\overline{AE... | math | {
"ground_truth": "B",
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cn_k12 | [
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"content": "The general term formula of the sequence $\\{a_n\\}$ is $a_n=2n-49$. When $S_n$ is minimized, $n$ equals \\_\\_\\_\\_\\_\\_.",
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"ground_truth": "24",
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olympiads | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
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{
"content": "Person A and person B play a game to fill in the coefficients of a polynomial of degree at least 4:\n\\[ x^{2n} + \\square x^{2n-1} + \\square x^{2n-2} + \\cdots + \\square x + 1... | math | {
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orca_math | [
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{
"content": "Logan recorded the snowfall every day during a snowstorm . He recorded 0.33 centimeter on Wednesday , 0.33 centimeter on Thursday , and 0.22 centimeter on Friday. Logan recorded ... | math | {
"ground_truth": "0.88",
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cn_k12 | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
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"content": "The sum of the first $n$ terms of an arithmetic sequence $\\{a_n\\}$ is $S_n$. If $a_1=2$ and $S=12$, then $a_6$ equals ( )\nA: $8$\nB: $12$\nC: $10$\nD: $14$",
"role": "u... | math | {
"ground_truth": "B",
"style": "rule"
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aops_forum | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the coordinates of the point in the plane at which the sum of the distances from it to the three points $(0, 0)$ , $(2, 0)$ , $(0, \\sqrt{3})$ is minimal.",
"role": ... | math | {
"ground_truth": "\\left(1, \\frac{5.5\\sqrt{3} - 3}{13}\\right)",
"style": "rule"
} | {
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olympiads | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "On the base \\(AD\\) of trapezoid \\(ABCD\\), a point \\(K\\) is given. Find a point \\(M\\) on the base \\(BC\\) for which the area of the common part of triangles \\(AMD\\) and... | math | {
"ground_truth": "\\frac{BM}{MC} = \\frac{AK}{KD}",
"style": "rule"
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orca_math | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Hadassah takes six hours to paint 12 small paintings and eight hours to paint 6 large paintings. If she plans to paint 15 more small paintings, 10 more large paintings, and takes... | math | {
"ground_truth": "24.8",
"style": "rule"
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olympiads | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "As shown in the figure, a rectangular prism with length, width, and height of $15, 5, 4$ respectively has a smaller rectangular prism with length, width, and height of $y, 5, x$ ... | math | {
"ground_truth": "3, 12",
"style": "rule"
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olympiads | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The numbers \\(1, 2, \\ldots, 20\\) are put into a hat. Claire draws two numbers from the hat uniformly at random, \\(a < b\\), and then puts them back into the hat. Then, Willia... | math | {
"ground_truth": "\\frac{181}{361}",
"style": "rule"
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synthetic_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A circle with a radius of 6 cm is tangent to the two shorter sides and one of the longer sides of a rectangle. The area of the rectangle is three times the area of the circle. Ca... | math | {
"ground_truth": "12",
"style": "rule"
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"index": 83,
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olympiads | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the acute triangle \\( \\triangle ABC \\), \\(\\angle A = 45^\\circ\\). Points \\( O \\) and \\( H \\) are the circumcenter and orthocenter, respectively. \\(BD\\) is the alti... | math | {
"ground_truth": "DX = DO",
"style": "rule"
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"index": 84,
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olympiads | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Compute the indefinite integral:\n\n$$\n\\int \\frac{2 x^{3}+6 x^{2}+5 x+4}{(x-2)(x+1)^{3}} \\, dx\n$$",
"role": "user"
}
] | math | {
"ground_truth": "2 \\ln |x-2| + \\frac{1}{2(x+1)^2} + C",
"style": "rule"
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"index": 85,
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cn_k12 | [
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"role": "system"
},
{
"content": "Given: The lengths of the two sides $AB$ and $AD$ of rectangle $ABCD$ are the two real roots of the equation $x^2-mx+\\frac{m}{2}-\\frac{1}{4}=0$ in terms of $x$. <br/>$(1)$ For ... | math | {
"ground_truth": "\\frac{\\sqrt{17}}{2}",
"style": "rule"
} | {
"index": 86,
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olympiads | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a 3-dimensional space, there are 2016 spheres, none of which coincide. Some of the spheres are red, and the others are green. Each contact point between a red sphere and a gre... | math | {
"ground_truth": "1016064",
"style": "rule"
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cn_k12 | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that \\(f(x)=\\begin{cases} \\ln x, & x > 0 \\\\ a+\\int_{0}^{x}{\\left( 1-\\cos t \\right)dt}, & x\\leqslant 0 \\end{cases}\\) and \\(f(f(1))=2\\), find the value of \\(a\... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"index": 88,
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orca_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Oliver bought eight boxes of candy in the morning. In the afternoon, he bought three times the number of boxes he bought in the morning. Later, he gave away 25% of the total boxe... | math | {
"ground_truth": "24",
"style": "rule"
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synthetic_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\(a\\), \\(b\\), and \\(c\\) be distinct real numbers. Simplify the expression\n\\[\n\\frac{(x + a)^2}{(a - b)(a - c)} + \\frac{(x + b)^2}{(b - a)(b - c)} + \\frac{(x + c)^2... | math | {
"ground_truth": "ax + bx + cx - a - b - c",
"style": "rule"
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orca_math | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A convenience store sold 100 bags of chips in a month. In the first week, some bags of chips were sold. In the second week, thrice as many bags of chips were sold. There was an e... | math | {
"ground_truth": "15",
"style": "rule"
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synthetic_math | [
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"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Solve the congruence $15x + 3 \\equiv 9 \\pmod{21}$ for $x$, and express the solution as $x \\equiv a \\pmod{m}$, where $a < m$ and find $a + m$.",
"role": "user"
}
] | math | {
"ground_truth": "13",
"style": "rule"
} | {
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cn_k12 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Every data point in a set of data is decreased by 80, resulting in a new set of data with an average value of 1.2 and a variance of 4.4. What are the average value and variance o... | math | {
"ground_truth": "81.2, 4.4",
"style": "rule"
} | {
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gsm8k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Jean and her three friends are playing a game of dominoes. There are 28 dominoes in the set, and Jean wants each player to receive the same number of dominoes. How many dominoes ... | math | {
"ground_truth": "7",
"style": "rule"
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orca_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What will be the cost of painting a building with a certain area, if the price per foot of painting is Rs. 15 and the total cost of painting the building is Rs. 840? How large is... | math | {
"ground_truth": "56",
"style": "rule"
} | {
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cn_k12 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given positive numbers $a$ and $b$ satisfying $\\dfrac{1}{a} + \\dfrac{1}{b} = 1$, find the minimum value of $\\dfrac{1}{a-1} + \\dfrac{4}{b-1}$.",
"role": "user"
}
] | math | {
"ground_truth": "4",
"style": "rule"
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orca_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "James took a bike ride for some hours. In the second hour, he traveled 12 miles, which was 20 percent farther than he traveled the first hour. If he traveled 25 percent farther i... | math | {
"ground_truth": "3",
"style": "rule"
} | {
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orca_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The teacher buys 4 black pens and some blue pens for students as awards. The teacher buys 8 pens altogether. How many blue pens does the teacher buy?",
"role": "user"
}
] | math | {
"ground_truth": "4",
"style": "rule"
} | {
"index": 98,
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orca_math | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Martha buys 1 latte for $4.00 every morning for a certain number of days a week. 3 days a week, she buys an iced coffee for $2.00. Her goal for the entire year is to cut her co... | math | {
"ground_truth": "5",
"style": "rule"
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