data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
DeepScaleR | [
{
"role": "user",
"content": "Brothers Lyosha and Sasha decided to get from home to the skate park. They left at the same time, but Lyosha walked with the skateboard in his hands, while Sasha rode the skateboard. It is known that Sasha rides the skateboard 3 times faster than Lyosha walks with the skateboar... | math | {
"style": "rule",
"ground_truth": "1100"
} | {
"index": 5500,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Brown lives on a street with more than 20 but fewer than 500 houses (all houses are numbered sequentially: $1, 2, 3$, etc.). Brown discovered that the sum of all the numbers from the first house to his own house (inclusive) equals half the sum of all the numbers from the first ... | math | {
"style": "rule",
"ground_truth": "84"
} | {
"index": 5501,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Bryan has some 3 cent stamps and some 4 cent stamps. What is the least number of stamps he can combine so the value of the stamps is 33 cents?"
}
] | math | {
"style": "rule",
"ground_truth": "9"
} | {
"index": 5502,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Bryan has some stamps of 3 cents, 4 cents, and 6 cents. What is the least number of stamps he can combine so the value of the stamps is 50 cents?"
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"index": 5503,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Bully Dima constructed a rectangle from 38 wooden toothpicks in the shape of a $3 \\times 5$ grid. Then he simultaneously ignited two adjacent corners of the rectangle, as marked on the diagram.\n\nIt is known that one toothpick burns in 10 seconds. How many seconds will it tak... | math | {
"style": "rule",
"ground_truth": "65"
} | {
"index": 5504,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Bully Vasya loves to run on the escalator in the subway, and he runs down twice as fast as up. If the escalator is not working, it takes Vasya 6 minutes to run up and down. If the escalator is moving down, it takes Vasya 13.5 minutes to run up and down. How many seconds will it... | math | {
"style": "rule",
"ground_truth": "324"
} | {
"index": 5505,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Burattino got on a train. After travelling half of the total distance, he fell asleep and slept until there was only half of the distance he slept left to travel. What fraction of the total journey did Burattino travel awake?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{2}{3}"
} | {
"index": 5506,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Bus stop \\(B\\) is located on a straight highway between stops \\(A\\) and \\(C\\). After some time driving from \\(A\\), the bus finds itself at a point on the highway where the distance to one of the three stops is equal to the sum of the distances to the other two stops. Af... | math | {
"style": "rule",
"ground_truth": "180"
} | {
"index": 5507,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Buses from Dallas to Houston leave every hour on the hour. Buses from Houston to Dallas leave every hour on the half hour. The trip from one city to the other takes $5$ hours. Assuming the buses travel on the same highway, how many Dallas-bound buses does a Houston-bound bus pa... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"index": 5508,
"solution": "1. **Understanding the Problem**: A Houston-bound bus leaves at 12:30 PM and takes 5 hours to reach Houston, i.e., it arrives at 5:30 PM. Dallas-bound buses leave every hour on the hour and also take 5 hours. We need to determine how many Dallas-bound buses the Houston-bound bus passes... |
DeepScaleR | [
{
"role": "user",
"content": "Buses leave Moscow for Voronezh every hour, at 00 minutes. Buses leave Voronezh for Moscow every hour, at 30 minutes. The trip between cities takes 8 hours. How many buses from Voronezh will a bus leaving Moscow meet on its way?"
}
] | math | {
"style": "rule",
"ground_truth": "16"
} | {
"index": 5509,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Buses travel along a country road, at equal intervals in both directions and at equal speeds. A cyclist, traveling at $16 \\, \\mathrm{km/h}$, begins counting buses from the moment when two buses meet beside him. He counts the 31st bus approaching from the front and the 15th bu... | math | {
"style": "rule",
"ground_truth": "46"
} | {
"index": 5510,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Buses. At the stop near Absent-Minded Scientist's house, buses of two routes stop: No. 152 and No. 251. Both go to the metro station. The interval between buses No. 152 is exactly 5 minutes, and the interval between buses No. 251 is exactly 7 minutes. The intervals are strictly... | math | {
"style": "rule",
"ground_truth": "5/14"
} | {
"index": 5511,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Business is a little slow at Lou's Fine Shoes, so Lou decides to have a sale. On Friday, Lou increases all of Thursday's prices by $10$ percent. Over the weekend, Lou advertises the sale: \"Ten percent off the listed price. Sale starts Monday.\" How much does a pair of shoes co... | math | {
"style": "rule",
"ground_truth": "39.60"
} | {
"index": 5512,
"solution": "1. **Calculate the price increase on Friday:**\n The price of the shoes on Thursday is $40$ dollars. On Friday, Lou increases the prices by $10\\%$. Therefore, the price on Friday can be calculated as follows:\n \\[\n \\text{Price on Friday} = \\text{Price on Thursday} \\times (1... |
DeepScaleR | [
{
"role": "user",
"content": "Businessmen Ivanov, Petrov, and Sidorov decided to create a car company. Ivanov bought 70 identical cars for the company, Petrov bought 40 identical cars, and Sidorov contributed 44 million rubles to the company. It is known that Ivanov and Petrov can share the money among them... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"index": 5513,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Butch and Sundance need to get out of Dodge. To travel as quickly as possible, each alternates walking and riding their only horse, Sparky, as follows. Butch begins by walking while Sundance rides. When Sundance reaches the first of the hitching posts that are conveniently loca... | math | {
"style": "rule",
"ground_truth": "279"
} | {
"index": 5514,
"solution": "When they meet at the milepost, Sparky has been ridden for $n$ miles total. Assume Butch rides Sparky for $a$ miles, and Sundance rides for $n-a$ miles. Thus, we can set up an equation, given that Sparky takes $\\frac{1}{6}$ hours per mile, Butch takes $\\frac{1}{4}$ hours per mile, an... |
DeepScaleR | [
{
"role": "user",
"content": "By a proper divisor of a natural number we mean a positive integral divisor other than 1 and the number itself. A natural number greater than 1 will be called nice if it is equal to the product of its distinct proper divisors. What is the sum of the first ten nice numbers?"
}... | math | {
"style": "rule",
"ground_truth": "182"
} | {
"index": 5515,
"solution": "Let $p(n)$ denote the product of the distinct proper divisors of $n$. A number $n$ is nice in one of two instances:\nIt has exactly two distinct prime divisors.\n If we let $n = pq$, where $p,q$ are the prime factors, then its proper divisors are $p$ and $q$, and $p(n) = p \\cdot q = n... |
DeepScaleR | [
{
"role": "user",
"content": "By definition, a polygon is regular if all its angles and sides are equal. Points \\( A, B, C, D \\) are consecutive vertices of a regular polygon (in that order). It is known that the angle \\( ABD = 135^\\circ \\). How many vertices does this polygon have?"
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"index": 5516,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "By expanding the expression \\((1+\\sqrt{11})^{214}\\) using the binomial theorem, we obtain terms of the form \\(C_{214}^{k}(\\sqrt{11})^{k}\\). Find the value of \\( k \\) for which this term has the greatest value."
}
] | math | {
"style": "rule",
"ground_truth": "165"
} | {
"index": 5517,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "By how many zeros does the number 2012! end?"
}
] | math | {
"style": "rule",
"ground_truth": "501"
} | {
"index": 5518,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "By how much did the dollar exchange rate change over the course of 2014 (from January 1, 2014, to December 31, 2014)? Provide the answer in rubles, rounded to the nearest whole number (answer - whole number)."
}
] | math | {
"style": "rule",
"ground_truth": "24"
} | {
"index": 5519,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "By joining four identical trapezoids, each with equal non-parallel sides and bases measuring 50 cm and 30 cm, we form a square with an area of 2500 cm² that has a square hole in the middle. What is the area, in cm², of each of the four trapezoids?"
}
] | math | {
"style": "rule",
"ground_truth": "400"
} | {
"index": 5520,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "By multiplying a natural number by the number that is one greater than it, the product takes the form $ABCD$, where $A, B, C, D$ are different digits. Starting with the number that is 3 less, the product takes the form $CABD$. Starting with the number that is 30 less, the produ... | math | {
"style": "rule",
"ground_truth": "8372"
} | {
"index": 5521,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "By partial fractions,\n\\[\\frac{1}{x(x + 1)(x + 2)(x + 3)(x + 4)} = \\frac{A}{x} + \\frac{B}{x + 1} + \\frac{C}{x + 2} + \\frac{D}{x + 3} + \\frac{E}{x + 4}\\]for some constants $A,$ $B,$ $C,$ $D,$ and $E.$ Find $A + B + C + D + E.$"
}
] | math | {
"style": "rule",
"ground_truth": "0"
} | {
"index": 5522,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "By permuting the digits of 20130518, how many different eight-digit positive odd numbers can be formed?"
}
] | math | {
"style": "rule",
"ground_truth": "3600"
} | {
"index": 5523,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "By solving the inequality \\(\\sqrt{x^{2}+3 x-54}-\\sqrt{x^{2}+27 x+162}<8 \\sqrt{\\frac{x-6}{x+9}}\\), find the sum of its integer solutions within the interval \\([-25, 25]\\)."
}
] | math | {
"style": "rule",
"ground_truth": "310"
} | {
"index": 5524,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "By using equations, recurring decimals can be converted into fractions. For example, when converting $0.\\overline{3}$ into a fraction, we can let $0.\\overline{3} = x$. From $0.\\overline{3} = 0.333\\ldots$, we know that $10x = 3.333\\ldots$. Therefore, $10x = 3 + 0.\\overline... | math | {
"style": "rule",
"ground_truth": "\\frac{27}{110}"
} | {
"index": 5525,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "By what common fraction does $0.\\overline{06}$ exceed $0.06$?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{1650}"
} | {
"index": 5526,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "By what common fraction does $0.\\overline{81}$ exceed $0.81$?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{9}{1100}"
} | {
"index": 5527,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "C is the complex numbers. \\( f : \\mathbb{C} \\to \\mathbb{R} \\) is defined by \\( f(z) = |z^3 - z + 2| \\). What is the maximum value of \\( f \\) on the unit circle \\( |z| = 1 \\)?"
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{13}"
} | {
"index": 5528,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Cagney can frost a cupcake every 15 seconds and Lacey can frost a cupcake every 45 seconds. Working together, calculate the number of cupcakes they can frost in 10 minutes."
}
] | math | {
"style": "rule",
"ground_truth": "53"
} | {
"index": 5529,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Cagney can frost a cupcake every 15 seconds, Lacey can frost a cupcake every 25 seconds, and Hardy can frost a cupcake every 50 seconds. Calculate the number of cupcakes that Cagney, Lacey, and Hardy can frost together in 6 minutes."
}
] | math | {
"style": "rule",
"ground_truth": "45"
} | {
"index": 5530,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Cagney can frost a cupcake every 15 seconds, while Lacey can frost every 40 seconds. They take a 10-second break after every 10 cupcakes. Calculate the number of cupcakes that they can frost together in 10 minutes."
}
] | math | {
"style": "rule",
"ground_truth": "50"
} | {
"index": 5531,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Cagney can frost a cupcake every 18 seconds and Lacey can frost a cupcake every 40 seconds. Lacey starts working 1 minute after Cagney starts. Calculate the number of cupcakes that they can frost together in 6 minutes."
}
] | math | {
"style": "rule",
"ground_truth": "27"
} | {
"index": 5532,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Cagney can frost a cupcake every 20 seconds and Lacey can frost a cupcake every 30 seconds. Working together, how many cupcakes can they frost in 5 minutes?"
}
] | math | {
"style": "rule",
"ground_truth": "25"
} | {
"index": 5533,
"solution": "1. **Determine individual rates**: \n - Cagney's rate of frosting cupcakes is 1 cupcake per 20 seconds.\n - Lacey's rate of frosting cupcakes is 1 cupcake per 30 seconds.\n\n2. **Calculate the combined rate**:\n - The combined rate \\( R \\) when two people are working together c... |
DeepScaleR | [
{
"role": "user",
"content": "Cagney can frost a cupcake every 25 seconds and Lacey can frost a cupcake every 35 seconds. If Lacey spends the first minute exclusively preparing frosting and then both work together to frost, determine the number of cupcakes they can frost in 10 minutes."
}
] | math | {
"style": "rule",
"ground_truth": "37"
} | {
"index": 5534,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Cagney can frost a cupcake every 25 seconds and Lacey can frost a cupcake every 35 seconds. They work together for 7 minutes, but there is a 1-minute period where only Cagney is frosting because Lacey takes a break. What is the number of cupcakes they can frost in these 7 minut... | math | {
"style": "rule",
"ground_truth": "26"
} | {
"index": 5535,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate\n\n$$\n\\frac{1 \\times 2 \\times 4+2 \\times 4 \\times 8+3 \\times 6 \\times 12+4 \\times 8 \\times 16}{1 \\times 3 \\times 9+2 \\times 6 \\times 18+3 \\times 9 \\times 27+4 \\times 12 \\times 36}\n$$\n\nOnly a numerical answer is expected here. The answer must be gi... | math | {
"style": "rule",
"ground_truth": "8/27"
} | {
"index": 5536,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate\n\n$$\n\\int_{L}\\left(z^{2}+2z \\bar{z}\\right)d z\n$$\n\nwhere \\( L \\) is the arc of the circle \\( |z|=1 \\) with \\( \\arg z \\in[0, \\pi] \\)."
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{14}{3}"
} | {
"index": 5537,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate\n\n$$\n\\operatorname{tg} \\frac{\\pi}{43} \\cdot \\operatorname{tg} \\frac{2 \\pi}{43}+\\operatorname{tg} \\frac{2 \\pi}{43} \\cdot \\operatorname{tg} \\frac{3 \\pi}{43}+\\ldots+\\operatorname{tg} \\frac{k \\pi}{43} \\cdot \\operatorname{tg} \\frac{(k+1) \\pi}{43}+\\... | math | {
"style": "rule",
"ground_truth": "-2021"
} | {
"index": 5538,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate\n\n$$\n\\operatorname{tg} \\frac{\\pi}{47} \\cdot \\operatorname{tg} \\frac{2 \\pi}{47} + \\operatorname{tg} \\frac{2 \\pi}{47} \\cdot \\operatorname{tg} \\frac{3 \\pi}{47} + \\ldots + \\operatorname{tg} \\frac{k \\pi}{47} \\cdot \\operatorname{tg} \\frac{(k+1) \\pi}{... | math | {
"style": "rule",
"ground_truth": "-2021"
} | {
"index": 5539,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate\n\n(1) Use a simplified method to calculate $2017^{2}-2016 \\times 2018$;\n\n(2) Given $a+b=7$ and $ab=-1$, find the values of $(a+b)^{2}$ and $a^{2}-3ab+b^{2}$."
}
] | math | {
"style": "rule",
"ground_truth": "54"
} | {
"index": 5540,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate\n\\[\\prod_{n = 1}^{13} \\frac{n(n + 2)}{(n + 4)^2}.\\]"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3}{161840}"
} | {
"index": 5541,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate \r\n\r\n\\[T = \\sum \\frac{1}{n_1! \\cdot n_2! \\cdot \\cdots n_{1994}! \\cdot (n_2 + 2 \\cdot n_3 + 3 \\cdot n_4 + \\ldots + 1993 \\cdot n_{1994})!}\\]\r\n\r\nwhere the sum is taken over all 1994-tuples of the numbers $n_1, n_2, \\ldots, n_{1994} \\in \\mathbb{N} \... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{1994!}"
} | {
"index": 5542,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $(-1)^{45} + 2^{(3^2+5^2-4^2)}$."
}
] | math | {
"style": "rule",
"ground_truth": "262143"
} | {
"index": 5543,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $(-1)^{47} + 2^{(3^3+4^2-6^2)}$."
}
] | math | {
"style": "rule",
"ground_truth": "127"
} | {
"index": 5544,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $(-1)^{53} + 3^{(2^3 + 5^2 - 4!)}$."
}
] | math | {
"style": "rule",
"ground_truth": "19682"
} | {
"index": 5545,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $(-2)^{23} + 2^{(2^4+5^2-7^2)}$."
}
] | math | {
"style": "rule",
"ground_truth": "-8388607.99609375"
} | {
"index": 5546,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $(2.1)(50.5 + 0.15)$ after increasing $50.5$ by $5\\%$. What is the product closest to?"
}
] | math | {
"style": "rule",
"ground_truth": "112"
} | {
"index": 5547,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $(3^5 \\cdot 6^5)^2$."
}
] | math | {
"style": "rule",
"ground_truth": "3570467226624"
} | {
"index": 5548,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $(42 \\div (12 - 10 + 3))^{2} \\cdot 7$."
}
] | math | {
"style": "rule",
"ground_truth": "493.92"
} | {
"index": 5549,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $0.25 \\cdot 0.08$."
}
] | math | {
"style": "rule",
"ground_truth": "0.02"
} | {
"index": 5550,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $0.7$ less than the sum of $34.5$ and $15.2$."
}
] | math | {
"style": "rule",
"ground_truth": "49"
} | {
"index": 5551,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $1,000,000,000,000 - 888,777,888,777$."
}
] | math | {
"style": "rule",
"ground_truth": "111,222,111,223"
} | {
"index": 5552,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $101 \\times 102^{2} - 101 \\times 98^{2}$."
}
] | math | {
"style": "rule",
"ground_truth": "80800"
} | {
"index": 5553,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $1010101_2 + 110011_2$ and express your answer in base $10$."
}
] | math | {
"style": "rule",
"ground_truth": "136"
} | {
"index": 5554,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $1010101_2 + 111000_2$ and write your answer in base $10$."
}
] | math | {
"style": "rule",
"ground_truth": "141"
} | {
"index": 5555,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $180 \\div \\left( 12 + 9 \\times 3 - 4 \\right)$."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{36}{7}"
} | {
"index": 5556,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $3 \\cdot 7^{-1} + 6 \\cdot 13^{-1} \\pmod{60}$.\n\nExpress your answer as an integer from $0$ to $59$, inclusive."
}
] | math | {
"style": "rule",
"ground_truth": "51"
} | {
"index": 5557,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $3 \\cdot 7^{-1} + 9 \\cdot 13^{-1} \\pmod{60}$.\n\nExpress your answer as an integer from $0$ to $59$, inclusive."
}
] | math | {
"style": "rule",
"ground_truth": "42"
} | {
"index": 5558,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $3(72+76+80+84+88+92+96+100+104+108)$."
}
] | math | {
"style": "rule",
"ground_truth": "2700"
} | {
"index": 5559,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $3.5 \\times 0.3 + 1.2 \\times 0.4$."
}
] | math | {
"style": "rule",
"ground_truth": "1.53"
} | {
"index": 5560,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $3.6 \\times 0.25 + 1.5$."
}
] | math | {
"style": "rule",
"ground_truth": "2.4"
} | {
"index": 5561,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $3.6 \\times 0.3$."
}
] | math | {
"style": "rule",
"ground_truth": "1.08"
} | {
"index": 5562,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $45 \\cdot 68 \\cdot 99 \\equiv m \\pmod{25}$, where $0 \\leq m < 25$."
}
] | math | {
"style": "rule",
"ground_truth": "15"
} | {
"index": 5563,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $4535_6 + 23243_6$. Express your answer in base $6$."
}
] | math | {
"style": "rule",
"ground_truth": "32222_6"
} | {
"index": 5564,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $46_8 - 27_8$ and express your answer in base 8."
}
] | math | {
"style": "rule",
"ground_truth": "17_8"
} | {
"index": 5565,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $5.47 + 2.58 + 1.95$ and write the sum as a decimal."
}
] | math | {
"style": "rule",
"ground_truth": "10.00"
} | {
"index": 5566,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $500,000,000,000 - 3 \\times 111,111,111,111$."
}
] | math | {
"style": "rule",
"ground_truth": "166,666,666,667"
} | {
"index": 5567,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $52103_{8} - 1452_{9}$ in base 10."
}
] | math | {
"style": "rule",
"ground_truth": "20471"
} | {
"index": 5568,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $5\\cdot5! + 4\\cdot4!+4!$."
}
] | math | {
"style": "rule",
"ground_truth": "720"
} | {
"index": 5569,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $6 \\cdot 8\\frac{1}{3}$."
}
] | math | {
"style": "rule",
"ground_truth": "50"
} | {
"index": 5570,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $6!-5\\cdot5!-5!$."
}
] | math | {
"style": "rule",
"ground_truth": "0"
} | {
"index": 5571,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $6^6 \\cdot 3^6$."
}
] | math | {
"style": "rule",
"ground_truth": "34012224"
} | {
"index": 5572,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $7 \\cdot 12\\frac{1}{4}$."
}
] | math | {
"style": "rule",
"ground_truth": "85\\frac{3}{4}"
} | {
"index": 5573,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $7 \\cdot 7! + 5 \\cdot 5! + 3 \\cdot 3! + 3!$."
}
] | math | {
"style": "rule",
"ground_truth": "35904"
} | {
"index": 5574,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $7 \\cdot 9\\frac{2}{5}$."
}
] | math | {
"style": "rule",
"ground_truth": "65\\frac{4}{5}"
} | {
"index": 5575,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $7.45 + 2.56$ as a decimal."
}
] | math | {
"style": "rule",
"ground_truth": "10.01"
} | {
"index": 5576,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $8 \\cdot 5\\frac{2}{5} - 3$."
}
] | math | {
"style": "rule",
"ground_truth": "40.2"
} | {
"index": 5577,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $8 \\cdot 9\\frac{2}{5}$."
}
] | math | {
"style": "rule",
"ground_truth": "75\\frac{1}{5}"
} | {
"index": 5578,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $[(12^{12} \\div 12^{11})^2 \\cdot 4^2] \\div 2^4$."
}
] | math | {
"style": "rule",
"ground_truth": "144"
} | {
"index": 5579,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $[(15^{15} \\div 15^{13})^3 \\cdot 3^2] \\div 2^3$."
}
] | math | {
"style": "rule",
"ground_truth": "3^8 \\cdot 5^6 \\cdot 2^{-3}"
} | {
"index": 5580,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $[(6^{6} \\div 6^{5})^3 \\cdot 8^3] \\div 4^3$."
}
] | math | {
"style": "rule",
"ground_truth": "1728"
} | {
"index": 5581,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $[x]$, where $x = -3.7 + 1.5$."
}
] | math | {
"style": "rule",
"ground_truth": "-3"
} | {
"index": 5582,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $\\cos \\frac{\\pi}{9} \\cdot \\cos \\frac{2\\pi}{9} \\cdot \\cos \\frac{4\\pi}{9} = $ ______."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{8}"
} | {
"index": 5583,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $\\displaystyle \\sum_{n=1}^\\infty \\ln \\left(1+\\frac{1}{n}\\right) \\ln\\left( 1+\\frac{1}{2n}\\right)\\ln\\left( 1+\\frac{1}{2n+1}\\right)$."
}
] | math | {
"style": "rule",
"ground_truth": "\\[\\frac{\\ln^3(2)}{3}\\]"
} | {
"index": 5584,
"solution": "\nThe problem requires evaluating the infinite series:\n\n\\[\n\\sum_{n=1}^\\infty \\ln \\left(1+\\frac{1}{n}\\right) \\ln\\left( 1+\\frac{1}{2n}\\right)\\ln\\left( 1+\\frac{1}{2n+1}\\right).\n\\]\n\nFirstly, observe the behavior of the logarithmic terms for large \\( n \\). Using the ... |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $\\fbox{2,3,-1}$."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{26}{3}"
} | {
"index": 5585,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $\\frac{1586_{7}}{131_{5}}-3451_{6}+2887_{7}$. Express your answer in base 10."
}
] | math | {
"style": "rule",
"ground_truth": "334"
} | {
"index": 5586,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $\\frac{1}{2} \\cdot \\frac{3}{5} \\cdot \\frac{7}{11}$."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{21}{110}"
} | {
"index": 5587,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $\\frac{1}{4} \\cdot \\frac{2}{5} \\cdot \\frac{3}{6} \\cdot \\frac{4}{7} \\cdots \\frac{49}{52} \\cdot \\frac{50}{53}$. Express your answer as a common fraction."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{23426}"
} | {
"index": 5588,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $\\frac{1}{6} \\cdot \\frac{2}{7} \\cdot \\frac{3}{8} \\cdot \\frac{4}{9} \\cdots \\frac{94}{99} \\cdot \\frac{95}{100}$. Express your answer as a common fraction."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{75287520}"
} | {
"index": 5589,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $\\frac{3 \\cdot 5! + 15\\cdot 4!}{6!}$"
}
] | math | {
"style": "rule",
"ground_truth": "1"
} | {
"index": 5590,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $\\int_{0}^{1} \\frac{\\sin x}{x} \\, dx$ with an accuracy of 0.01."
}
] | math | {
"style": "rule",
"ground_truth": "0.94"
} | {
"index": 5591,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $\\left(\\frac{1}{3}\\right)^{6} \\div \\left(\\frac{2}{5}\\right)^{-4} + \\frac{1}{2}$."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{455657}{911250}"
} | {
"index": 5592,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $\\left(\\sqrt{(\\sqrt{5})^4}\\right)^6$."
}
] | math | {
"style": "rule",
"ground_truth": "15625"
} | {
"index": 5593,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $\\lim _{n \\rightarrow \\infty}\\left(\\sqrt[3^{2}]{3} \\cdot \\sqrt[3^{3}]{3^{2}} \\cdot \\sqrt[3^{4}]{3^{3}} \\ldots \\sqrt[3^{n}]{3^{n-1}}\\right)$."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt[4]{3}"
} | {
"index": 5594,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $\\lim_{n \\to \\infty} \\frac{C_n^2}{n^2+1}$."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"index": 5595,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $\\sin 9^\\circ \\sin 45^\\circ \\sin 69^\\circ \\sin 81^\\circ.$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{0.6293 \\sqrt{2}}{4}"
} | {
"index": 5596,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $\\sqrt[4]{\\sqrt{\\frac{32}{10000}}}$."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt[8]{2}}{\\sqrt{5}}"
} | {
"index": 5597,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $\\sqrt{10p} \\cdot \\sqrt{5p^2} \\cdot \\sqrt{6p^4}$ . Express your answer in simplest radical form in terms of $p$.\n\nNote: When entering a square root with more than one character, you must use parentheses or brackets. For example, you should enter $\\sqrt{14}$ a... | math | {
"style": "rule",
"ground_truth": "10p^3 \\sqrt{3p}"
} | {
"index": 5598,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $\\sqrt{30p} \\cdot \\sqrt{5p} \\cdot \\sqrt{6p}$ . Express your answer in simplest radical form in terms of $p$."
}
] | math | {
"style": "rule",
"ground_truth": "30p \\sqrt{p}"
} | {
"index": 5599,
"solution": ""
} |
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