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. He has 100 nickels. How many more dimes does he have than pennies?",
"role": "user"
}
] |
math
|
{
"ground_truth": "10",
"style": "rule"
}
|
{
"index": 0,
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"reward": 0.1,
"split": "train"
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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 over circle $\\omega$, where the segment $RS$ is scaled by $\\frac{1}{3}$ towards $S$.\nA) Circle with center at $\\left(\\frac{R_x + 2O_x}{3}, \\frac{R_y + 2O_y}{3}\\right)$ and radius $10$ units.\nB) Circle with center at $\\left(\\frac{2R_x + O_x}{3}, \\frac{2R_y + O_y}{3}\\right)$ and radius $\\frac{10}{3}$ units.\nC) Circle with center at $(R_x, R_y)$ and radius $5$ units.\nD) Circle with radius $\\frac{20}{3}$ units and arbitrary center.",
"role": "user"
}
] |
math
|
{
"ground_truth": "\\text{B}",
"style": "rule"
}
|
{
"index": 1,
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"reward": 0.1,
"split": "train"
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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 weight of fruit Diego can carry in his bookbag?",
"role": "user"
}
] |
math
|
{
"ground_truth": "20",
"style": "rule"
}
|
{
"index": 2,
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"reward": 0.1,
"split": "train"
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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 $$\\frac {f(x_{1})-f(x_{2})}{x_{1}-x_{2}}<0$$ holds true. Determine the range of values for the real number $a$.",
"role": "user"
}
] |
math
|
{
"ground_truth": "\\frac{1}{2}",
"style": "rule"
}
|
{
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"reward": 0.1,
"split": "train"
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|
cn_k12
|
[
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"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 point\" of the function $y=f(x)$. A student found that \"any cubic function has an 'inflection point'; any cubic function has a center of symmetry; and the 'inflection point' is the center of symmetry.\" Given this discovery, for the function $f(x)=x^3- \\frac{3}{2}x^2+3x-\\frac{1}{4}$, determine its center of symmetry and calculate the sum $f(\\frac{1}{2013})+f(\\frac{2}{2013})+f(\\frac{3}{2013})+\\ldots+f(\\frac{2012}{2013})$.",
"role": "user"
}
] |
math
|
{
"ground_truth": "2012",
"style": "rule"
}
|
{
"index": 4,
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"reward": 0.1,
"split": "train"
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|
olympiads
|
[
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"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 \\( f(10) \\).",
"role": "user"
}
] |
math
|
{
"ground_truth": "144",
"style": "rule"
}
|
{
"index": 5,
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"reward": 0.1,
"split": "train"
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|
cn_k12
|
[
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"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. Which of the following statements is correct?\n\nA: $f(0)=-1$\n\nB: The monotonic increasing interval of the function $f(x)$ is $(0,+\\infty)$\n\nC: The function $g(x)=f(x)+1$ is an odd function\n\nD: The function $f(x)$ is an increasing function on $R$",
"role": "user"
}
] |
math
|
{
"ground_truth": "ACD",
"style": "rule"
}
|
{
"index": 6,
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"reward": 0.1,
"split": "train"
}
|
olympiads
|
[
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"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 side length of the square is 1. Find the perimeter of the triangle \\( CEF \\). Justify your solution.",
"role": "user"
}
] |
math
|
{
"ground_truth": "2",
"style": "rule"
}
|
{
"index": 7,
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"reward": 0.1,
"split": "train"
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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 selected the same number, given that at least one of their numbers is a square? Express your answer as a common fraction.",
"role": "user"
}
] |
math
|
{
"ground_truth": "0",
"style": "rule"
}
|
{
"index": 8,
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"reward": 0.1,
"split": "train"
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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\\parallel\\alpha\\\\) and \\\\(n\\parallel\\alpha\\\\), then \\\\(m\\parallel n\\\\)\nB: If \\\\(m\\perp \\alpha\\\\) and \\\\(n\\subset \\alpha\\\\), then \\\\(m\\perp n\\\\)\nC: If \\\\(m\\perp \\alpha\\\\) and \\\\(m\\perp n\\\\), then \\\\(n\\parallel\\alpha\\\\)\nD: If \\\\(m\\parallel\\alpha\\\\) and \\\\(m\\perp n\\\\), then \\\\(n\\perp \\alpha\\\\)",
"role": "user"
}
] |
math
|
{
"ground_truth": "\\text{B}",
"style": "rule"
}
|
{
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"reward": 0.1,
"split": "train"
}
|
cn_k12
|
[
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"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, the probability that the books of the same subject are adjacent to each other is ( ).\n\nA: $$\\frac {1}{5}$$\nB: $$\\frac {2}{5}$$\nC: $$\\frac {1}{4}$$\nD: $$\\frac {1}{6}$$",
"role": "user"
}
] |
math
|
{
"ground_truth": "\\frac{1}{5}",
"style": "rule"
}
|
{
"index": 10,
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"reward": 0.1,
"split": "train"
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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 aprons tomorrow if she wants to sew half of the remaining number of aprons needed. How many aprons does Heather need to sew in total for the kiddie crew program?",
"role": "user"
}
] |
math
|
{
"ground_truth": "150",
"style": "rule"
}
|
{
"index": 11,
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"reward": 0.1,
"split": "train"
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|
orca_math
|
[
{
"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 became absent?",
"role": "user"
}
] |
math
|
{
"ground_truth": "10",
"style": "rule"
}
|
{
"index": 12,
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"reward": 0.1,
"split": "train"
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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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"reward": 0.1,
"split": "train"
}
|
cn_k12
|
[
{
"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: $(2+2i)$",
"role": "user"
}
] |
math
|
{
"ground_truth": "2-5i",
"style": "rule"
}
|
{
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"reward": 0.1,
"split": "train"
}
|
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"
}
] |
math
|
{
"ground_truth": "18",
"style": "rule"
}
|
{
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"reward": 0.1,
"split": "train"
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|
orca_math
|
[
{
"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 that the price of lemon increased by per grape. He had planned to sell the lemons at $8 and the grapes at $7, and he had 80 lemons and 140 grapes in his basket. How much money did he collect from selling the fruits at the new prices?",
"role": "user"
}
] |
math
|
{
"ground_truth": "\\$2220",
"style": "rule"
}
|
{
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"reward": 0.1,
"split": "train"
}
|
orca_math
|
[
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"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"
}
] |
math
|
{
"ground_truth": "140",
"style": "rule"
}
|
{
"index": 17,
"knowledge_emb": [
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"reward": 0.1,
"split": "train"
}
|
synthetic_amc
|
[
{
"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": "user"
}
] |
math
|
{
"ground_truth": "B",
"style": "rule"
}
|
{
"index": 18,
"knowledge_emb": [
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"reward": 0.1,
"split": "train"
}
|
orca_math
|
[
{
"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 selling price of the radio?",
"role": "user"
}
] |
math
|
{
"ground_truth": "300",
"style": "rule"
}
|
{
"index": 19,
"knowledge_emb": [
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],
"reward": 0.1,
"split": "train"
}
|
cn_k12
|
[
{
"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 $\\theta = \\frac{\\pi}{3}$ is\nA: $\\sqrt{3}$\nB: $2\\sqrt{3}$\nC: $1$\nD: $2$",
"role": "user"
}
] |
math
|
{
"ground_truth": "\\sqrt{3}",
"style": "rule"
}
|
{
"index": 20,
"knowledge_emb": [
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"reward": 0.1,
"split": "train"
}
|
synthetic_math
|
[
{
"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"
}
|
{
"index": 21,
"knowledge_emb": [
0,
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],
"reward": 0.1,
"split": "train"
}
|
olympiads
|
[
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"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 1, 2, or 3 cells) equals zero.",
"role": "user"
}
] |
math
|
{
"ground_truth": "\\text{A possible solution is:}",
"style": "rule"
}
|
{
"index": 22,
"knowledge_emb": [
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],
"reward": 0.1,
"split": "train"
}
|
orca_math
|
[
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"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 the purchase price in insurance fees for each year. Furthermore, he spent 1% of the original price on maintenance. After that, he sold it at a 70% increase on the price he bought it (including depreciation, taxes, insurance, and maintenance costs). What percent of profit or loss did he make on the original price?",
"role": "user"
}
] |
math
|
{
"ground_truth": "33.96\\%",
"style": "rule"
}
|
{
"index": 23,
"knowledge_emb": [
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],
"reward": 0.1,
"split": "train"
}
|
orca_math
|
[
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"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 cookies. How many halves did Greg eat?",
"role": "user"
}
] |
math
|
{
"ground_truth": "4",
"style": "rule"
}
|
{
"index": 24,
"knowledge_emb": [
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],
"reward": 0.1,
"split": "train"
}
|
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 divided by y?",
"role": "user"
}
] |
math
|
{
"ground_truth": "0",
"style": "rule"
}
|
{
"index": 25,
"knowledge_emb": [
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],
"reward": 0.1,
"split": "train"
}
|
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 get a remainder of 11?",
"role": "user"
}
] |
math
|
{
"ground_truth": "29",
"style": "rule"
}
|
{
"index": 26,
"knowledge_emb": [
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],
"reward": 0.1,
"split": "train"
}
|
orca_math
|
[
{
"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?",
"role": "user"
}
] |
math
|
{
"ground_truth": "5",
"style": "rule"
}
|
{
"index": 27,
"knowledge_emb": [
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],
"reward": 0.1,
"split": "train"
}
|
orca_math
|
[
{
"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% more and 27.5% more respectively than the first carpet? Given that the cost of the carpet is RS. 46.35 per sq. m.",
"role": "user"
}
] |
math
|
{
"ground_truth": "4371.78",
"style": "rule"
}
|
{
"index": 28,
"knowledge_emb": [
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0,
1
],
"reward": 0.1,
"split": "train"
}
|
synthetic_math
|
[
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"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 answer as a fraction in lowest terms.)",
"role": "user"
}
] |
math
|
{
"ground_truth": "\\frac{3}{4}",
"style": "rule"
}
|
{
"index": 29,
"knowledge_emb": [
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0
],
"reward": 0.1,
"split": "train"
}
|
olympiads
|
[
{
"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 into 7 pieces. This process was repeated several times. How many pieces of paper need to be cut in order to end up with 331 pieces?",
"role": "user"
}
] |
math
|
{
"ground_truth": "54",
"style": "rule"
}
|
{
"index": 30,
"knowledge_emb": [
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1,
0
],
"reward": 0.1,
"split": "train"
}
|
gsm8k
|
[
{
"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?",
"role": "user"
}
] |
math
|
{
"ground_truth": "80",
"style": "rule"
}
|
{
"index": 31,
"knowledge_emb": [
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0,
0,
1,
0,
0,
0,
0,
0,
1,
1
],
"reward": 0.1,
"split": "train"
}
|
orca_math
|
[
{
"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,
"knowledge_emb": [
0,
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1,
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0
],
"reward": 0.1,
"split": "train"
}
|
orca_math
|
[
{
"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 money did they make in total?",
"role": "user"
}
] |
math
|
{
"ground_truth": "\\$519",
"style": "rule"
}
|
{
"index": 33,
"knowledge_emb": [
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],
"reward": 0.1,
"split": "train"
}
|
cn_k12
|
[
{
"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"
}
] |
math
|
{
"ground_truth": "0.8",
"style": "rule"
}
|
{
"index": 34,
"knowledge_emb": [
0,
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0
],
"reward": 0.1,
"split": "train"
}
|
synthetic_math
|
[
{
"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"
}
] |
math
|
{
"ground_truth": "\\frac{29}{5}",
"style": "rule"
}
|
{
"index": 35,
"knowledge_emb": [
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"reward": 0.1,
"split": "train"
}
|
synthetic_math
|
[
{
"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?\n\n(A) Line\n(B) Circle\n(C) Parabola\n(D) Ellipse\n(E) Hyperbola\n\nEnter the letter of the correct option.",
"role": "user"
}
] |
math
|
{
"ground_truth": "\\text{(E)}",
"style": "rule"
}
|
{
"index": 36,
"knowledge_emb": [
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],
"reward": 0.1,
"split": "train"
}
|
olympiads
|
[
{
"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"
}
|
{
"index": 37,
"knowledge_emb": [
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"reward": 0.1,
"split": "train"
}
|
synthetic_amc
|
[
{
"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) $\\frac{132}{\\pi}$\nB) $264$\nC) $\\frac{264}{\\pi}$\nD) $132\\pi$\nE) $\\text{none of these}$",
"role": "user"
}
] |
math
|
{
"ground_truth": "C",
"style": "rule"
}
|
{
"index": 38,
"knowledge_emb": [
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1
],
"reward": 0.1,
"split": "train"
}
|
cn_k12
|
[
{
"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 ${a_1} = \\frac{1}{2}, {a_n} = f(n), (n \\in \\mathbb{N}^+)$, then the range of the sum of the first $n$ terms of the sequence ${{a_n}}$ denoted by ${S_n}$ is $\\underline{\\underline{\\qquad\\qquad}}$.\n\nA: $(1, 2)$\nB: $[\\frac{1}{2}, 1)$\nC: $[\\frac{2}{3}, 1)$\nD: $(1, \\frac{3}{2}]$",
"role": "user"
}
] |
math
|
{
"ground_truth": "[\\frac{1}{2}, 1)",
"style": "rule"
}
|
{
"index": 39,
"knowledge_emb": [
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],
"reward": 0.1,
"split": "train"
}
|
cn_k12
|
[
{
"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 its maximum and minimum values on the interval $[0,\\frac{\\pi}{2}]$. \n$(2)$ If $f(x_0)=\\frac{6}{5}$ and $x_0\\in[\\frac{\\pi}{4},\\frac{\\pi}{2}]$, find the value of $\\cos{2x_{0}}$.",
"role": "user"
}
] |
math
|
{
"ground_truth": "\\cos{2x_0} = \\frac{3 - 4\\sqrt{3}}{10}",
"style": "rule"
}
|
{
"index": 40,
"knowledge_emb": [
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],
"reward": 0.1,
"split": "train"
}
|
synthetic_math
|
[
{
"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 fraction.",
"role": "user"
}
] |
math
|
{
"ground_truth": "\\frac{137}{151}",
"style": "rule"
}
|
{
"index": 41,
"knowledge_emb": [
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],
"reward": 0.1,
"split": "train"
}
|
orca_math
|
[
{
"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,
"knowledge_emb": [
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],
"reward": 0.1,
"split": "train"
}
|
cn_k12
|
[
{
"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 ($S_{10} = \\underline{\\quad}$).\nA: $0$\nB: $-5$\nC: $-10$\nD: $5$",
"role": "user"
}
] |
math
|
{
"ground_truth": "0",
"style": "rule"
}
|
{
"index": 43,
"knowledge_emb": [
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0,
0,
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0,
0,
0,
0
],
"reward": 0.1,
"split": "train"
}
|
synthetic_amc
|
[
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"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$\\text{(A) } 0\\quad \\text{(B) } 1\\quad \\text{(C) } 2\\quad \\text{(D) } 3\\quad \\text{(E) more than }3$",
"role": "user"
}
] |
math
|
{
"ground_truth": "\\text{(D) } 3",
"style": "rule"
}
|
{
"index": 44,
"knowledge_emb": [
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],
"reward": 0.1,
"split": "train"
}
|
cn_k12
|
[
{
"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"
}
] |
math
|
{
"ground_truth": "\\frac {1}{4}",
"style": "rule"
}
|
{
"index": 45,
"knowledge_emb": [
0,
0,
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],
"reward": 0.1,
"split": "train"
}
|
orca_math
|
[
{
"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 participants are democrats. There are 140 female democrats. What is the ratio of male democrats to the total number of male participants?",
"role": "user"
}
] |
math
|
{
"ground_truth": "1:4",
"style": "rule"
}
|
{
"index": 46,
"knowledge_emb": [
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],
"reward": 0.1,
"split": "train"
}
|
olympiads
|
[
{
"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 9's is\nA. $\\frac{1}{2}\\left(10^{2006}+8^{2006}\\right)$\nB. $\\frac{1}{2}\\left(10^{2006}-8^{2006}\\right)$\nC. $10^{2006}+8^{2006}$\nD. $10^{2006}-8^{2006}$",
"role": "user"
}
] |
math
|
{
"ground_truth": "\\text{B}",
"style": "rule"
}
|
{
"index": 47,
"knowledge_emb": [
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],
"reward": 0.1,
"split": "train"
}
|
cn_k12
|
[
{
"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: $\\frac{1}{4}$\n\nB: $\\frac{1}{3}$\n\nC: $\\frac{2}{3}$\n\nD: $\\frac{1}{2}$",
"role": "user"
}
] |
math
|
{
"ground_truth": "C",
"style": "rule"
}
|
{
"index": 48,
"knowledge_emb": [
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],
"reward": 0.1,
"split": "train"
}
|
synthetic_math
|
[
{
"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 $d - e$.",
"role": "user"
}
] |
math
|
{
"ground_truth": "\\log_{3003} \\frac{1}{323}",
"style": "rule"
}
|
{
"index": 49,
"knowledge_emb": [
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0,
1,
1,
0,
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0,
1,
1,
0
],
"reward": 0.1,
"split": "train"
}
|
aops_forum
|
[
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"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 $A=\\ell\\cap a$ , and $\\{B,C\\}=\\ell\\cap \\omega$ such that $B$ is on segment $AC$ . Construct the line $\\ell$ such that the ratio $\\frac{|BC|}{|AB|}$ is maximal.",
"role": "user"
}
] |
math
|
{
"ground_truth": "\\frac{r^2}{ka}",
"style": "rule"
}
|
{
"index": 50,
"knowledge_emb": [
0,
0,
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1,
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],
"reward": 0.1,
"split": "train"
}
|
synthetic_math
|
[
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"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(C);\ndot(D);\nlabel(\"$A$\",A,S);\nlabel(\"$B$\",B,S);\nlabel(\"$C$\",C,S);\nlabel(\"$D$\",D,S);\ndraw((0,0)--(1.5,1)--(3,0),Arrow);\ndraw((0,0)--(1.5,-1)--(3,0),Arrow);\ndraw(B--(4.5,1)--C,Arrow);\ndraw(B--(4.5,-1)--C,Arrow);\ndraw(C--(7.5,1)--D,Arrow);\ndraw(C--(7.5,-1)--D,Arrow);\ndraw(A--(4.5,3)--C,Arrow);\ndraw(B--(7.5,3)--D,Arrow);\n[/asy]",
"role": "user"
}
] |
math
|
{
"ground_truth": "12",
"style": "rule"
}
|
{
"index": 51,
"knowledge_emb": [
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"reward": 0.1,
"split": "train"
}
|
aops_forum
|
[
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"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 fewer than one hundred pens. When my pens are grouped into nines, I have one pen left over. When grouped into fives, I have three left over. When grouped into pairs, I have one left over. How many do I have?**p3.** How many unique rearrangements of the word “COMBO” exist?**p4.** A right triangle has sides of length $4x+1$ , $2x-1$ , and $x+9$ , where $x$ is a positive integer, and the side of length $4x+1$ is the hypotenuse. What is the area of the triangle?**p5.** A parabola has vertex $(4,-2)$ and roots $(8,0)$ and $(0,0)$ . What is the coefficient of the linear term when the equation of the parabola is expanded?**p6.** The terms $2x-1$ , $x + 4$ , $4x + 1$ form an arithmetic sequence while the terms $x$ , $x+4$ , $xy^2$ form a geometric sequence. Evaluate $x+y$ .**p7.** A sphere is inscribed inside a cube that is inscribed inside another sphere. The larger sphere has volume $972\\pi$ . Calculate the volume of the space inside the larger sphere but outside the smaller sphere. Express your answer in simplest radical form and in terms of $\\pi$ .**p8.** A computer battery loses $50\\%$ of its remaining power every hour. Assuming the computer begins at full battery, how long will it take for the computer to reach $10\\%$ battery? Express your answer in minutes and round your answer to the nearest hundredth.**p9.** How many two-digit numbers have six factors?**p10.**Thomas is graduating. He decides to attend a college that offers him a sizable scholarship. The number of dollar he receives is an eight digit number using the digits $0$ through $7$ without repetition and follows the following criteria: $\\bullet$ The number is divisible by $5$ . $\\bullet$ The last four digits are prime numbers. $\\bullet$ A three digit number comprised of the last three digits in order is divisible by $11$ . $\\bullet$ A four digit number comprised of the first four digits in order is divisible by $205$ .\nHow much money is Thomas receiving in scholarship?\n\n\nPS. You should use hide for answers. Collected [here](https://artofproblemsolving.com/community/c5h2760506p24143309).",
"role": "user"
}
] |
math
|
{
"ground_truth": "73",
"style": "rule"
}
|
{
"index": 52,
"knowledge_emb": [
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"reward": 0.1,
"split": "train"
}
|
cn_k12
|
[
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"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: $\\frac{3}{2}$\nB: $\\frac{8}{3}$\nC: 1\nD: 2",
"role": "user"
}
] |
math
|
{
"ground_truth": "\\frac{3}{2}",
"style": "rule"
}
|
{
"index": 53,
"knowledge_emb": [
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"reward": 0.1,
"split": "train"
}
|
cn_k12
|
[
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"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-axis, establish a Cartesian coordinate system. The parametric equation of line $l$ is $$\\begin{cases} x= \\frac { \\sqrt {3}}{2}t+m \\\\ y= \\frac {1}{2}t \\end{cases}$$ (t is the parameter).\n(Ⅰ) Find the Cartesian equation of curve C and the general equation of line $l$;\n(Ⅱ) Let point P be $(m,0)$. If line $l$ intersects curve C at points A and B, and $|PA|\\cdot|PB|=1$, find the value of the real number $m$.",
"role": "user"
}
] |
math
|
{
"ground_truth": "1, 1+ \\sqrt {2}, 1- \\sqrt {2}",
"style": "rule"
}
|
{
"index": 54,
"knowledge_emb": [
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"reward": 0.1,
"split": "train"
}
|
synthetic_math
|
[
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"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 pizza slices together? Express your answer in minutes.",
"role": "user"
}
] |
math
|
{
"ground_truth": "56",
"style": "rule"
}
|
{
"index": 55,
"knowledge_emb": [
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"reward": 0.1,
"split": "train"
}
|
synthetic_math
|
[
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"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"
}
] |
math
|
{
"ground_truth": "128",
"style": "rule"
}
|
{
"index": 56,
"knowledge_emb": [
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"reward": 0.1,
"split": "train"
}
|
cn_k12
|
[
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"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: $a\\geqslant 6$ or $a\\leqslant -3$\nC: $-3 < a < 6$\nD: $a > 6$ or $a < -3$",
"role": "user"
}
] |
math
|
{
"ground_truth": "D",
"style": "rule"
}
|
{
"index": 57,
"knowledge_emb": [
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"reward": 0.1,
"split": "train"
}
|
cn_k12
|
[
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In \\\\(\\triangle ABC\\\\), the sides opposite to angles \\\\(A\\\\), \\\\(B\\\\), and \\\\(C\\\\) are denoted as \\\\(a\\\\), \\\\(b\\\\), and \\\\(c\\\\) respectively. Given that \\\\(b=3\\\\), \\\\(\\overrightarrow{AB} \\cdot \\overrightarrow{AC} = -6\\\\), and the area of \\\\(\\triangle ABC\\\\), \\\\(S_{\\triangle ABC} = 3\\\\), find \\\\(A\\\\) and \\\\(a\\\\).",
"role": "user"
}
] |
math
|
{
"ground_truth": "A = 135^{\\circ}, a = \\sqrt{29}",
"style": "rule"
}
|
{
"index": 58,
"knowledge_emb": [
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"reward": 0.1,
"split": "train"
}
|
orca_math
|
[
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"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 fuji plus the cross - pollinated ones totals 153 , while 3 / 4 of all his trees are pure fuji . how many of his trees are pure gala ?",
"role": "user"
}
] |
math
|
{
"ground_truth": "27",
"style": "rule"
}
|
{
"index": 59,
"knowledge_emb": [
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"reward": 0.1,
"split": "train"
}
|
orca_math
|
[
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"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 of the discount he allowed?",
"role": "user"
}
] |
math
|
{
"ground_truth": "34\\%",
"style": "rule"
}
|
{
"index": 60,
"knowledge_emb": [
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"reward": 0.1,
"split": "train"
}
|
orca_math
|
[
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"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 categories in USD are $520, $860, and $620, respectively. The company wants to make different percentage cuts in each category's budget: 25% for Category A, 35% for Category B, and 30% for Category C. \n\nThe company needs to convert the subscription costs from USD to EUR using the conversion rate 1 USD = 0.85 EUR. Once the amounts are converted, apply a 7% sales tax on the total subscription costs in EUR.\n\nCalculate how much less the company must spend on these subscriptions in EUR after making the appropriate cuts to each category's budget and including the currency conversion and sales tax.",
"role": "user"
}
] |
math
|
{
"ground_truth": "€561.1615",
"style": "rule"
}
|
{
"index": 61,
"knowledge_emb": [
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"reward": 0.1,
"split": "train"
}
|
cn_k12
|
[
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"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 $x \\in \\mathbb{R}$ such that $x^3 - 2x + 1 \\neq 0$ \nB. There does not exist an $x \\in \\mathbb{R}$ such that $x^3 - 2x + 1 \\neq 0$ \nC. For all $x \\in \\mathbb{R}$, $x^3 - 2x + 1 = 0$ \nD. For all $x \\in \\mathbb{R}$, $x^3 - 2x + 1 \\neq 0$",
"role": "user"
}
] |
math
|
{
"ground_truth": "\\forall x \\in \\mathbb{R}, x^3 - 2x + 1 \\neq 0",
"style": "rule"
}
|
{
"index": 62,
"knowledge_emb": [
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"reward": 0.1,
"split": "train"
}
|
cn_k12
|
[
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"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 point P(2,4).",
"role": "user"
}
] |
math
|
{
"ground_truth": "4x-y-4=0",
"style": "rule"
}
|
{
"index": 63,
"knowledge_emb": [
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],
"reward": 0.1,
"split": "train"
}
|
orca_math
|
[
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"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 pages more than the previous night. She promised to read the remaining pages of the book tonight. If the book has 100 pages, and she will read 20 pages tonight, what is the ratio of the number of pages she read two nights ago to the number of pages she read three nights ago?",
"role": "user"
}
] |
math
|
{
"ground_truth": "2:1",
"style": "rule"
}
|
{
"index": 64,
"knowledge_emb": [
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],
"reward": 0.1,
"split": "train"
}
|
synthetic_math
|
[
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"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 \\sin \\theta < 0.\n\\]",
"role": "user"
}
] |
math
|
{
"ground_truth": "\\left(\\frac{\\pi}{2}, \\pi\\right)",
"style": "rule"
}
|
{
"index": 65,
"knowledge_emb": [
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],
"reward": 0.1,
"split": "train"
}
|
synthetic_math
|
[
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A triangle has side lengths of 10, 24, and 26 units. What is the area of this triangle, in square units?",
"role": "user"
}
] |
math
|
{
"ground_truth": "120 \\text{ square units}",
"style": "rule"
}
|
{
"index": 66,
"knowledge_emb": [
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],
"reward": 0.1,
"split": "train"
}
|
orca_math
|
[
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"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 satisfying the relationship between x and y.",
"role": "user"
}
] |
math
|
{
"ground_truth": "x^2",
"style": "rule"
}
|
{
"index": 67,
"knowledge_emb": [
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"reward": 0.1,
"split": "train"
}
|
synthetic_math
|
[
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"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": "user"
}
] |
math
|
{
"ground_truth": "\\frac{\\sqrt{3411}}{67}",
"style": "rule"
}
|
{
"index": 68,
"knowledge_emb": [
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"reward": 0.1,
"split": "train"
}
|
synthetic_math
|
[
{
"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",
"style": "rule"
}
|
{
"index": 69,
"knowledge_emb": [
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"reward": 0.1,
"split": "train"
}
|
cn_k12
|
[
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"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 preparing to purchase a batch of brushes and rice paper for students' calligraphy classes. It is known that purchasing 40 brushes and 100 sheets of rice paper costs 280 yuan; purchasing 30 brushes and 200 sheets of rice paper costs 260 yuan. \n$(1)$ Find the unit prices of the brushes and rice paper. \n$(2)$ If the school plans to purchase a total of 200 brushes and rice paper with no more than 360 yuan, how many brushes can the school purchase at most?",
"role": "user"
}
] |
math
|
{
"ground_truth": "\\text{The school can purchase at most 50 brushes.}",
"style": "rule"
}
|
{
"index": 70,
"knowledge_emb": [
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],
"reward": 0.1,
"split": "train"
}
|
cn_k12
|
[
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given $x=\\sqrt{6}-\\sqrt{2}$, the value of the algebraic expression $2x^2+4\\sqrt{2}x$ is ______.",
"role": "user"
}
] |
math
|
{
"ground_truth": "8",
"style": "rule"
}
|
{
"index": 71,
"knowledge_emb": [
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],
"reward": 0.1,
"split": "train"
}
|
cn_k12
|
[
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"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 $\\overrightarrow{OA} + \\overrightarrow{OB} = \\overrightarrow{OC}$, find the value of $a$.",
"role": "user"
}
] |
math
|
{
"ground_truth": "2",
"style": "rule"
}
|
{
"index": 72,
"knowledge_emb": [
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"reward": 0.1,
"split": "train"
}
|
synthetic_amc
|
[
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"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 $\\overline{AE}$ and $\\overline{CG}$ meet at point $M$. Find the area of quadrilateral $ABCM$.\nA) $36$\nB) $40$\nC) $44$\nD) $48$\nE) $52$",
"role": "user"
}
] |
math
|
{
"ground_truth": "B",
"style": "rule"
}
|
{
"index": 73,
"knowledge_emb": [
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],
"reward": 0.1,
"split": "train"
}
|
cn_k12
|
[
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The general term formula of the sequence $\\{a_n\\}$ is $a_n=2n-49$. When $S_n$ is minimized, $n$ equals \\_\\_\\_\\_\\_\\_.",
"role": "user"
}
] |
math
|
{
"ground_truth": "24",
"style": "rule"
}
|
{
"index": 74,
"knowledge_emb": [
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"reward": 0.1,
"split": "train"
}
|
olympiads
|
[
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"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 \\]\n\nwhere they take turns to choose one of the blanks and fill it with a real number as the coefficient, until all blanks are filled. If the resulting polynomial has no real roots, person A wins; otherwise, person B wins. If person A goes first, who has a winning strategy? Provide an explanation.",
"role": "user"
}
] |
math
|
{
"ground_truth": "B",
"style": "rule"
}
|
{
"index": 75,
"knowledge_emb": [
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],
"reward": 0.1,
"split": "train"
}
|
orca_math
|
[
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"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 _____ centimeters of snow .",
"role": "user"
}
] |
math
|
{
"ground_truth": "0.88",
"style": "rule"
}
|
{
"index": 76,
"knowledge_emb": [
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],
"reward": 0.1,
"split": "train"
}
|
cn_k12
|
[
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"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": "user"
}
] |
math
|
{
"ground_truth": "B",
"style": "rule"
}
|
{
"index": 77,
"knowledge_emb": [
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],
"reward": 0.1,
"split": "train"
}
|
aops_forum
|
[
{
"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": "user"
}
] |
math
|
{
"ground_truth": "\\left(1, \\frac{5.5\\sqrt{3} - 3}{13}\\right)",
"style": "rule"
}
|
{
"index": 78,
"knowledge_emb": [
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],
"reward": 0.1,
"split": "train"
}
|
olympiads
|
[
{
"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 \\(BKC\\) is maximized.",
"role": "user"
}
] |
math
|
{
"ground_truth": "\\frac{BM}{MC} = \\frac{AK}{KD}",
"style": "rule"
}
|
{
"index": 79,
"knowledge_emb": [
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],
"reward": 0.1,
"split": "train"
}
|
orca_math
|
[
{
"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 a 30-minute break after every third painting, what would be the total time she's taken to finish all the paintings?",
"role": "user"
}
] |
math
|
{
"ground_truth": "24.8",
"style": "rule"
}
|
{
"index": 80,
"knowledge_emb": [
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],
"reward": 0.1,
"split": "train"
}
|
olympiads
|
[
{
"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 $y, 5, x$ (where $x$ and $y$ are integers) cut out from it. The volume of the remaining part is 120. Find $x$ and $y$.",
"role": "user"
}
] |
math
|
{
"ground_truth": "3, 12",
"style": "rule"
}
|
{
"index": 81,
"knowledge_emb": [
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],
"reward": 0.1,
"split": "train"
}
|
olympiads
|
[
{
"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, William draws two numbers from the hat uniformly at random, \\(c < d\\). Let \\(N\\) denote the number of integers \\(n\\) that satisfy exactly one of \\(a \\leq n \\leq b\\) and \\(c \\leq n \\leq d\\). Compute the probability \\(N\\) is even.",
"role": "user"
}
] |
math
|
{
"ground_truth": "\\frac{181}{361}",
"style": "rule"
}
|
{
"index": 82,
"knowledge_emb": [
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],
"reward": 0.1,
"split": "train"
}
|
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. Calculate the length of the shorter side of the rectangle in centimeters, expressing your answer in terms of $\\pi$.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12",
"style": "rule"
}
|
{
"index": 83,
"knowledge_emb": [
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],
"reward": 0.1,
"split": "train"
}
|
olympiads
|
[
{
"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 altitude from \\(B\\) to side \\(AC\\) with foot \\(D\\). In the circumcircle of \\( \\triangle ADH \\), let \\( X \\) be the midpoint of arc \\( \\overparen{ADH} \\). Prove that \\( DX = DO \\).",
"role": "user"
}
] |
math
|
{
"ground_truth": "DX = DO",
"style": "rule"
}
|
{
"index": 84,
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],
"reward": 0.1,
"split": "train"
}
|
olympiads
|
[
{
"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"
}
|
{
"index": 85,
"knowledge_emb": [
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"reward": 0.1,
"split": "train"
}
|
cn_k12
|
[
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"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 what value of $m$ is the quadrilateral $ABCD$ a square? Provide a reason for your answer; <br/>$(2)$ If the length of $AB$ is $2$, then the length of the diagonal of rectangle $ABCD$ is ______.",
"role": "user"
}
] |
math
|
{
"ground_truth": "\\frac{\\sqrt{17}}{2}",
"style": "rule"
}
|
{
"index": 86,
"knowledge_emb": [
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],
"reward": 0.1,
"split": "train"
}
|
olympiads
|
[
{
"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 green sphere is painted blue. Find the maximum possible number of blue points.",
"role": "user"
}
] |
math
|
{
"ground_truth": "1016064",
"style": "rule"
}
|
{
"index": 87,
"knowledge_emb": [
0,
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1,
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],
"reward": 0.1,
"split": "train"
}
|
cn_k12
|
[
{
"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\\).",
"role": "user"
}
] |
math
|
{
"ground_truth": "2",
"style": "rule"
}
|
{
"index": 88,
"knowledge_emb": [
0,
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],
"reward": 0.1,
"split": "train"
}
|
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 boxes he had to his friends. How many boxes of candy does Oliver have now?",
"role": "user"
}
] |
math
|
{
"ground_truth": "24",
"style": "rule"
}
|
{
"index": 89,
"knowledge_emb": [
0,
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],
"reward": 0.1,
"split": "train"
}
|
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}{(c - a)(c - b)}.\n\\]",
"role": "user"
}
] |
math
|
{
"ground_truth": "ax + bx + cx - a - b - c",
"style": "rule"
}
|
{
"index": 90,
"knowledge_emb": [
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],
"reward": 0.1,
"split": "train"
}
|
orca_math
|
[
{
"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 equal number of chips sold in the third and fourth week, which was 20 bags each. How many bags of chips were sold in the first week?",
"role": "user"
}
] |
math
|
{
"ground_truth": "15",
"style": "rule"
}
|
{
"index": 91,
"knowledge_emb": [
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],
"reward": 0.1,
"split": "train"
}
|
synthetic_math
|
[
{
"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"
}
|
{
"index": 92,
"knowledge_emb": [
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],
"reward": 0.1,
"split": "train"
}
|
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 of the original data set?",
"role": "user"
}
] |
math
|
{
"ground_truth": "81.2, 4.4",
"style": "rule"
}
|
{
"index": 93,
"knowledge_emb": [
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],
"reward": 0.1,
"split": "train"
}
|
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 will Jean and her friends each receive?",
"role": "user"
}
] |
math
|
{
"ground_truth": "7",
"style": "rule"
}
|
{
"index": 94,
"knowledge_emb": [
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],
"reward": 0.1,
"split": "train"
}
|
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 the area to be painted?",
"role": "user"
}
] |
math
|
{
"ground_truth": "56",
"style": "rule"
}
|
{
"index": 95,
"knowledge_emb": [
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],
"reward": 0.1,
"split": "train"
}
|
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"
}
|
{
"index": 96,
"knowledge_emb": [
0,
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],
"reward": 0.1,
"split": "train"
}
|
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 in the third hour than he did in the second hour, James traveled 37 miles during the entire ride. How many hours did James ride his bike?",
"role": "user"
}
] |
math
|
{
"ground_truth": "3",
"style": "rule"
}
|
{
"index": 97,
"knowledge_emb": [
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],
"reward": 0.1,
"split": "train"
}
|
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,
"knowledge_emb": [
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],
"reward": 0.1,
"split": "train"
}
|
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 coffee spending by 25%. She will save $338. How many days a week does she buy a latte?",
"role": "user"
}
] |
math
|
{
"ground_truth": "5",
"style": "rule"
}
|
{
"index": 99,
"knowledge_emb": [
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],
"reward": 0.1,
"split": "train"
}
|
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