Split (2)

train · 214k rows

Subsets and Splits

No community queries yet

The top public SQL queries from the community will appear here once available.

prompt listlengths 1 1	chosen listlengths 1 1	rejected listlengths 1 1	dataset stringclasses 4 values
[ { "content": "In a rectangular coordinate system, if a line passes through the points (-13,-18), (17,22) and (x,2) then what is the value of x?", "role": "user" } ]	[ { "content": "Let's think step by step.\nStep 1: First, we need to find the slope of the line. The slope of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $\\frac{y_2-y_1}{x_2-x_1}$.\n\nUsing the points (-13,-18) and (17,22), the slope of the line is\n\\[\\frac{22-(-18)}{17-(-13)}=\\...	[ { "content": "Let's think step by step.\nStep 1: First, we need to find the slope of the line. The slope of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $\\frac{y_2-y_1}{x_2-x_1}$.\n\nUsing the points (-13,-18) and (17,22), the slope of the line is\n\\[\\frac{22-(-18)}{17-(-13)}=\\...	xinlai/Math-Step-DPO-10K
[ { "content": "Average weight of 10 people increased by 1.5 kg when one person of 45 kg is replaced by a new man. Then weight of the new man is", "role": "user" } ]	[ { "content": "Let's think step by step.\nStep 1: Let's say the total weight of the original 10 people is $W$ kg.\n\nStep 2: If one person of 45 kg is replaced by a new man, the total weight of the 10 people becomes $W - 45 + x$, where $x$ is the weight of the new man.\n\nStep 3:\n The problem states that the a...	[ { "content": "Let's think step by step.\nStep 1: Let's say the total weight of the original 10 people is $W$ kg.\n\nStep 2: If one person of 45 kg is replaced by a new man, the total weight of the 10 people becomes $W - 45 + x$, where $x$ is the weight of the new man.\n\nStep 3:\n We are told that this new tot...	xinlai/Math-Step-DPO-10K
[ { "content": "Each week, Harry is paid x dollars per hour for the first 30 hours and 1.5x dollars for each additional hour worked that week. Each week, Annie is paid x dollars per hour for the first 40 hours and 2x dollars for each additional hour worked that week. Last week Annie worked a total of 56 hours. If...	[ { "content": "Let's think step by step.\nStep 1: Calculate how much Annie was paid last week.\n\nAnnie worked a total of 56 hours, and for the first 40 hours, she was paid $x per hour. So for the first 40 hours, she earned $40x$.\n\nFor the remaining hours, which is $56 - 40 = 16$ hours, she was paid $2x$ per ...	[ { "content": "Let's think step by step.\nStep 1: Calculate how much Annie was paid last week.\n\nAnnie worked a total of 56 hours, and for the first 40 hours, she was paid $x per hour. So for the first 40 hours, she earned $40x$.\n\nFor the remaining hours, which is $56 - 40 = 16$ hours, she was paid $2x$ per ...	xinlai/Math-Step-DPO-10K
[ { "content": "A batsman makes a score of 85 runs in the 17th inning and thus increases his averages by 3.Find his average after 17th inning?", "role": "user" } ]	[ { "content": "Let's think step by step.\nStep 1: The batsman's total runs before the 17th inning can be found by using the formula for the average. The average is calculated by dividing the total runs by the number of innings. So if the average before the 17th inning is $A$ and the total runs before the 17th i...	[ { "content": "Let's think step by step.\nStep 1: The batsman's total runs before the 17th inning can be found by using the formula for the average. The average is calculated by dividing the total runs by the number of innings. So if the average before the 17th inning is $A$ and the total runs before the 17th i...	xinlai/Math-Step-DPO-10K
[ { "content": "What least value must be assigned to * so that th number 197*5462 is divisible by 9?", "role": "user" } ]	[ { "content": "Let's think step by step.\nStep 1: To check if a number is divisible by 9, we need to check if the sum of its digits is divisible by 9.\n\nStep 2:\n The number is 197*5462. Let's add up the digits we know: $1 + 9 + 7 + 5 + 4 + 6 + 2 = 34$.\n\nStep 3: Now, let's call the digit we don't know yet $x...	[ { "content": "Let's think step by step.\nStep 1: To check if a number is divisible by 9, we need to check if the sum of its digits is divisible by 9.\n\nStep 2:\n The sum of the digits of the number 1975462 is $1 + 9 + 7 + + 5 + 4 + 6 + 2 = 33 + $.\n\nStep 3: We want to find the smallest value of such th...	xinlai/Math-Step-DPO-10K
[ { "content": "X and Y are two towns. Ganesh covers the distance from X to Y at an average speed of 60 Km/hr. However, he covers the distance from Y to X at an average speed of 30 Km/hr. His average speed during the whole journey in km/hr. is :", "role": "user" } ]	[ { "content": "Let's think step by step.\nStep 1: Let's say the distance between X and Y is $d$ km. \n\nStep 2: The time it takes for Ganesh to travel from X to Y at a speed of 60 km/hr is $\\frac{d}{60}$ hours.\n\nStep 3: The time it takes for him to travel from Y to X at a speed of 30 km/hr is $\\frac{d}{30...	[ { "content": "Let's think step by step.\nStep 1: Let's say the distance between X and Y is $d$ km. \n\nStep 2: The time it takes for Ganesh to travel from X to Y at a speed of 60 km/hr is $\\frac{d}{60}$ hours.\n\nStep 3: The time it takes for him to travel from Y to X at a speed of 30 km/hr is $\\frac{d}{30...	xinlai/Math-Step-DPO-10K
[ { "content": "Find the number of ways in which 5 identical balls can be distributed among 10 identical boxes, if not more than one ball can go into a box?", "role": "user" } ]	[ { "content": "Let's think step by step.\nStep 1: We have 5 identical balls and 10 identical boxes. We want to distribute these balls among the boxes such that no more than one ball goes into a box.\n\nStep 2:\n This problem can be thought of as finding the number of ways to choose 5 boxes out of the 10 availab...	[ { "content": "Let's think step by step.\nStep 1: We have 5 identical balls and 10 identical boxes. We want to distribute these balls among the boxes such that no more than one ball goes into a box.\n\nStep 2:\n This is a problem of combinations with repetition. The formula for combinations with repetition is $...	xinlai/Math-Step-DPO-10K
[ { "content": "17 men take 21 days of 8 hours each to do a piece of work. How many days of 6 hours each would 21 women take to do the same. If 3 women do as much work as 2 men?", "role": "user" } ]	[ { "content": "Let's think step by step.\nStep 1: First, we need to find out how much work is done by 17 men in 21 days of 8 hours each. The total work done is the product of the number of men, the number of days, and the number of hours per day. So the total work done is $17 \\times 21 \\times 8 = 2856$ man-da...	[ { "content": "Let's think step by step.\nStep 1: First, we need to find out how much work is done by 17 men in 21 days of 8 hours each. The total work done is the product of the number of men, the number of days, and the number of hours per day. So the total work done is $17 \\times 21 \\times 8 = 2856$ man-da...	xinlai/Math-Step-DPO-10K
[ { "content": "If in a certain code \"RANGE\" is coded as 12345 and \"RANDOM\" is coded as 123678. Then the code for the word\n\"RAM\" would be", "role": "user" } ]	[ { "content": "Let's think step by step.\nStep 1: We can see that the word \"RANGE\" is coded as 12345. This means that each letter in \"RANGE\" corresponds to a unique number from 1 to 5.\n\nStep 2:\n Similarly, the word \"RANDOM\" is coded as 123678. This means that each letter in \"RANDOM\" corresponds to a...	[ { "content": "Let's think step by step.\nStep 1: We can see that the word \"RANGE\" is coded as 12345. This means that each letter in \"RANGE\" corresponds to a unique number from 1 to 5.\n\nStep 2:\n The word \"RANDOM\" is coded as 123678. This means that each letter in \"RANDOM\" corresponds to a unique numb...	xinlai/Math-Step-DPO-10K
[ { "content": "In three coloured boxes - Red, Green and Blue, 108 balls are placed. There are twice as many balls in the green and red boxes combined as there are in the blue box and twice as many in the blue box as there are in the red box. How many balls are there in the green box ?", "role": "user" } ]	[ { "content": "Let's think step by step.\nStep 1: Let's say the number of balls in the red box is $x$. According to the problem, there are twice as many balls in the blue box as there are in the red box, so the number of balls in the blue box is $2x$.\n\nStep 2: Also, the problem states that there are twice as...	[ { "content": "Let's think step by step.\nStep 1: Let's say the number of balls in the red box is $x$. According to the problem, there are twice as many balls in the blue box as there are in the red box, so the number of balls in the blue box is $2x$.\n\nStep 2: Also, the problem states that there are twice as...	xinlai/Math-Step-DPO-10K
[ { "content": "Jake, Lena, Fred, and Inna need to drive home from a corporate reception in an SUV that can seat 7 people. If only Inna or Jake can drive, how many seat allocations are possible?", "role": "user" } ]	[ { "content": "Let's think step by step.\nStep 1: Choose the driver. There are 2 people who can drive, Jake or Inna. So there are 2 ways to choose the driver.\n\nStep 2:\n Choose the remaining 3 people to sit in the 6 remaining seats. The number of ways to arrange 3 people in 6 seats is $6P3 = \\frac{6!}{(6-3)...	[ { "content": "Let's think step by step.\nStep 1: Choose the driver. There are 2 people who can drive, Jake or Inna. So there are 2 ways to choose the driver.\n\nStep 2:\n Choose the remaining 3 people to ride in the SUV. There are 3 people left, and we need to choose 3 out of them. The number of ways to do thi...	xinlai/Math-Step-DPO-10K
[ { "content": "A 3-digit number 4a3 is added to another 3-digit number 984 to give a 4-digit number 13b7, which is divisible by 11. Then, (a + b) = ?", "role": "user" } ]	[ { "content": "Let's think step by step.\nStep 1: 4a3 + 984 = 13b7. This means that $400 + 10a + 3 + 984 = 1300 + 10b + 7$.\nSimplifying the left side gives $400 + 10a + 3 + 984 = 1387 + 10a$. Simplifying the right side gives $1300 + 10b + 7 = 1307 + 10b$.\nSo we have $1387 + 10a = 1307 + 10b$.\n\nStep 2:\n Subt...	[ { "content": "Let's think step by step.\nStep 1: 4a3 + 984 = 13b7. This means that $400 + 10a + 3 + 984 = 1300 + 10b + 7$.\nSimplifying the left side gives $400 + 10a + 3 + 984 = 1387 + 10a$. Simplifying the right side gives $1300 + 10b + 7 = 1307 + 10b$.\nSo we have $1387 + 10a = 1307 + 10b$.\n\nStep 2:\n Subt...	xinlai/Math-Step-DPO-10K
[ { "content": "What is the 4 digit number in which the 1st digit is 1/3 of the second, the 3rd is the sum of the 1st and 2nd, and the last is three times the 2nd?", "role": "user" } ]	[ { "content": "Let's think step by step.\nStep 1: Let's call the second digit $x$. According to the problem, the first digit is $\\frac{1}{3}$ of the second digit, so the first digit is $\\frac{x}{3}$.\n\nStep 2: The third digit is the sum of the first and second digit, so it is $\\frac{x}{3} + x = \\frac{4x}{...	[ { "content": "Let's think step by step.\nStep 1: Let's call the second digit $x$. According to the problem, the first digit is $\\frac{1}{3}$ of the second digit, so the first digit is $\\frac{x}{3}$.\n\nStep 2: The third digit is the sum of the first and second digit, so it is $\\frac{x}{3} + x = \\frac{4x}{...	xinlai/Math-Step-DPO-10K
[ { "content": "Molly can do a task in 15 days while Sandy can do the task in 10 days. How many days will it take to complete the task if both work together?", "role": "user" } ]	[ { "content": "Let's think step by step.\nStep 1: First, we need to find out how much work Molly and Sandy can do in one day.\n\nMolly can do a task in 15 days, so in one day, she can do $1/15$ of the task.\nSimilarly, Sandy can do a task in 10 days, so in one day, she can do $1/10$ of the task.\n\nStep 2:\n No...	[ { "content": "Let's think step by step.\nStep 1: First, we need to find out how much work Molly and Sandy can do in one day.\n\nMolly can do a task in 15 days, so in one day, she can do $1/15$ of the task.\nSimilarly, Sandy can do a task in 10 days, so in one day, she can do $1/10$ of the task.\n\nStep 2:\n No...	xinlai/Math-Step-DPO-10K
[ { "content": "If Rs. 782 is divided into three parts, proportional to\n1/2:2/3:3/4 find the first part.", "role": "user" } ]	[ { "content": "Let's think step by step.\nStep 1: We need to find the least common denominator (LCD) of the fractions 1/2, 2/3, and 3/4. The LCD of 2, 3, and 4 is 12. So we can rewrite the fractions with denominator 12:\n\\[ \\frac{1}{2} = \\frac{6}{12}, \\quad \\frac{2}{3} = \\frac{8}{12}, \\quad \\text{and} \...	[ { "content": "Let's think step by step.\nStep 1: We need to find the least common denominator (LCD) of the fractions 1/2, 2/3, and 3/4. The LCD of 2, 3, and 4 is 12. So we can rewrite the fractions with denominator 12:\n\\[ \\frac{1}{2} = \\frac{6}{12}, \\quad \\frac{2}{3} = \\frac{8}{12}, \\quad \\text{and} \...	xinlai/Math-Step-DPO-10K
[ { "content": "Simplify: 1398 x 1398", "role": "user" } ]	[ { "content": "Let's think step by step.\nStep 1: 1398 x 1398 can be written as $(1400 - 2)^2$.\n\nStep 2: Now we can expand this using the formula $(a - b)^2 = a^2 - 2ab + b^2$.\n\nSo, $(1400 - 2)^2 = 1400^2 - 2 x 1400 x 2 + 2^2$.\n\nStep 3: Let's calculate each part:\n\n$1400^2 = 1960000$,\n\n$2 x 1400 x 2 = 5...	[ { "content": "Let's think step by step.\nStep 1: 1398 x 1398 can be written as $(1400 - 2)^2$.\n\nStep 2: Now we can expand this using the formula $(a - b)^2 = a^2 - 2ab + b^2$.\n\nSo, $(1400 - 2)^2 = 1400^2 - 2 x 1400 x 2 + 2^2$.\n\nStep 3: Let's calculate each part:\n\n$1400^2 = 1960000$,\n\n$2 x 1400 x 2 = 5...	xinlai/Math-Step-DPO-10K
[ { "content": "A company that ships boxes to a total of 13 distribution centers uses color coding to identify each center. If either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors, what is the mini...	[ { "content": "Let's think step by step.\nStep 1: 13 distribution centers need to be represented using either a single color or a pair of two different colors.\n\nStep 2:\n The number of ways to choose one color from n colors is simply n. The number of ways to choose two different colors from n colors is $\\bino...	[ { "content": "Let's think step by step.\nStep 1: 13 distribution centers need to be represented using either a single color or a pair of two different colors.\n\nStep 2:\n Let's start with the minimum number of colors needed. If we use only one color for each center, we would need 13 different colors. But we wa...	xinlai/Math-Step-DPO-10K
[ { "content": "The difference between C.I. and S.I. on an amount of Rs. 15,000 for 2 years is Rs. 54. What is the rate of interest per annum?", "role": "user" } ]	[ { "content": "Let's think step by step.\nStep 1: Let's denote the rate of interest per annum as $r$.\n\nStep 2: The formula for simple interest (S.I.) is given by $S.I. = PRT$, where $P$ is the principal amount, $R$ is the rate of interest, and $T$ is the time in years. So, the S.I. for the given problem is $S...	[ { "content": "Let's think step by step.\nStep 1: Let's denote the rate of interest per annum as $r$.\n\nStep 2: The formula for simple interest (S.I.) is given by $S.I. = PRT$, where $P$ is the principal amount, $R$ is the rate of interest, and $T$ is the time in years. So, the S.I. for the given problem is $S...	xinlai/Math-Step-DPO-10K
[ { "content": "The average expenditure of a labourer for 6 months was 75 and he fell into debt. In the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30. His monthly income i", "role": "user" } ]	[ { "content": "Let's think step by step.\nStep 1: The average expenditure of a labourer for 6 months was 75. This means his total expenditure for 6 months was 756 = 450.\n\nStep 2:\n In the next 4 months, he reduced his monthly expenses to 60. So, his total expenditure for these 4 months was 604 = 240.\n\nSte...	[ { "content": "Let's think step by step.\nStep 1: The average expenditure of a labourer for 6 months was 75. This means his total expenditure for 6 months was 75*6 = 450.\n\nStep 2:\n He fell into debt. Let's say the amount of his debt was D.\n\nStep 3: In the next 4 months, he reduced his monthly expenses to 6...	xinlai/Math-Step-DPO-10K
[ { "content": "What is the sum of all the odd numbers between 24 and 50, inclusive?", "role": "user" } ]	[ { "content": "Let's think step by step.\nStep 1: First, we need to list all the odd numbers between 24 and 50. They are 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, and 49.\n\nStep 2:\n Now, we need to add up all these numbers. We can use the formula for the sum of an arithmetic series to do this. The formu...	[ { "content": "Let's think step by step.\nStep 1: First, we need to list all the odd numbers between 24 and 50. They are 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, and 49.\n\nStep 2:\n To find the sum of these numbers, we just add them up. So the sum is $25+27+29+31+33+35+37+39+41+43+45+47+49$.\n\nStep 3: ...	xinlai/Math-Step-DPO-10K
[ { "content": "Tim and Jim enter into a partnership by investing $700 and $300 respectively. At the end of one year, they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the inve...	[ { "content": "Let's think step by step.\nStep 1: Let's say the total profit made by their business in that year is $P$. \n\nStep 2:\n A third of the profit is divided equally for the efforts they have put into the business. This means that $\\frac{P}{3}$ is divided equally between Tim and Jim. Since they divid...	[ { "content": "Let's think step by step.\nStep 1: Let's say the total profit made by their business in that year is $P$. \n\nStep 2:\n A third of the profit is divided equally for the efforts they have put into the business. This means each of them gets $P/3$.\n\nStep 3: The remaining amount of profit is divide...	xinlai/Math-Step-DPO-10K
[ { "content": "The speed of a train including stoppages is 90 kmph and excluding stoppages is 120 kmph. Of how many minutes does the train stop per hour?", "role": "user" } ]	[ { "content": "Let's think step by step.\nStep 1: Let's denote the time spent on stoppages as $x$ (in hours).\n\nStep 2:\n The speed of the train including stoppages is 90 kmph, which means that in one hour (or 60 minutes), the train travels 90 km. This can be written as $90 = \\frac{120 \\cdot (1-x)}{1}$.\n\nS...	[ { "content": "Let's think step by step.\nStep 1: Let's denote the time spent on stoppages as $x$ (in hours).\n\nStep 2:\n The speed of the train including stoppages is 90 kmph. This means that in 1 hour (or 60 minutes), the train travels 90 km. But this 1 hour includes the time spent on stoppages. So, the actu...	xinlai/Math-Step-DPO-10K
[ { "content": "P and Q can do a work in 30 days. Q and R can do the same work in 24 days and R and P in 20 days. They started the work together, but Q and R left after 10 days. How many days more will P take to finish the work?", "role": "user" } ]	[ { "content": "Let's think step by step.\nStep 1: Let's find out the work rate of each person.\n\nWhen P and Q work together, they can finish the work in 30 days. So their combined work rate is 1/30 of the work per day. Similarly, Q and R can finish the work in 24 days, so their combined work rate is 1/24 of th...	[ { "content": "Let's think step by step.\nStep 1: Let's find out the work rate of each person.\n\nWhen P and Q work together, they can finish the work in 30 days. So their combined work rate is 1/30 of the work per day. Similarly, Q and R can finish the work in 24 days, so their combined work rate is 1/24 of th...	xinlai/Math-Step-DPO-10K
[ { "content": "Three numbers are in the ratio 3:4:5 and their L.C.M. is 600. Their H.C.F is?", "role": "user" } ]	[ { "content": "Let's think step by step.\nStep 1: 3 numbers are in the ratio 3:4:5. Let's assume that the three numbers are 3x, 4x, and 5x for some positive integer x.\n\nStep 2:\n The L.C.M. of the three numbers is given as 600. The L.C.M. of 3x, 4x, and 5x is 60x (since the L.C.M. of 3, 4, and 5 is 60). So we ...	[ { "content": "Let's think step by step.\nStep 1: 3 numbers are in the ratio 3:4:5. Let's assume that the three numbers are 3x, 4x, and 5x for some positive integer x.\n\nStep 2:\n The L.C.M. (Least Common Multiple) of the three numbers is given as 600. We know that the L.C.M. of the three numbers is also equal ...	xinlai/Math-Step-DPO-10K
[ { "content": "At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.40000?", "role": "user" } ]	[ { "content": "Let's think step by step.\nStep 1: We need to calculate the compound interest for 3 years at a rate of 10% per annum. The formula for compound interest is $A = P(1 + r/n)^{nt}$, where:\n- $A$ is the amount of money accumulated after n years, including interest.\n- $P$ is the principal amount (the...	[ { "content": "Let's think step by step.\nStep 1: We need to calculate the compound interest for 3 years at a rate of 10% per annum. The formula for compound interest is $A = P(1 + r/n)^{nt}$, where:\n- $A$ is the amount of money accumulated after n years, including interest.\n- $P$ is the principal amount (the...	xinlai/Math-Step-DPO-10K
[ { "content": "A can do a piece of work n 7 days of 9 hours each and B alone can do it in 6 days of 7 hours each. How long will they take to do it working together 8 2/5 hours a day?", "role": "user" } ]	[ { "content": "Let's think step by step.\nStep 1: First, we need to find out how much work A and B can do in one day.\n\nFor A, he can do a piece of work in 7 days of 9 hours each, so in one day, he can do $\\frac{1}{7 \\times 9} = \\frac{1}{63}$ of the work.\n\nFor B, he can do a piece of work in 6 days of 7 h...	[ { "content": "Let's think step by step.\nStep 1: First, we need to find out how much work A and B can do in one day.\n\nFor A, he can do a piece of work in 7 days of 9 hours each, so in one day, he can do $\\frac{1}{7 \\times 9} = \\frac{1}{63}$ of the work.\n\nFor B, he can do a piece of work in 6 days of 7 h...	xinlai/Math-Step-DPO-10K
[ { "content": "Two machines, Y and Z, work at constant rates producing identical items. Machine Y produces 30 items in the same time Machine Z produces 24 items. If machine Y takes 36 minutes to produce a batch of items, how many minutes does it take for machine Z to produce the same number of items?", "role...	[ { "content": "Let's think step by step.\nStep 1: We know that Machine Y produces 30 items in the same time Machine Z produces 24 items. This means the ratio of the production rates of Y and Z is $30:24$ or $5:4$. This means that for every 5 items produced by Y, Z produces 4 items.\n\nStep 2: We know that Machi...	[ { "content": "Let's think step by step.\nStep 1: We know that Machine Y produces 30 items in the same time Machine Z produces 24 items. This means the ratio of the production rates of Y and Z is $30:24$ or $5:4$. This means that for every 5 items produced by Y, Z produces 4 items.\n\nStep 2: We know that Machi...	xinlai/Math-Step-DPO-10K
[ { "content": "Calculate the different number of ways 5 boys and 3 girls can sit on a bench?", "role": "user" } ]	[ { "content": "Let's think step by step.\nStep 1: First, we need to find the total number of ways to arrange 8 people (5 boys and 3 girls) on a bench. This is a simple permutation problem because the order of the people matters.\n\nThe number of ways to arrange $n$ objects is given by $n!$ (n factorial), which ...	[ { "content": "Let's think step by step.\nStep 1: First, we need to find the total number of ways to arrange 8 people (5 boys and 3 girls) on a bench. This is a simple permutation problem because the order of the people matters.\n\nThe number of ways to arrange $n$ objects is given by $n!$ (n factorial), which ...	xinlai/Math-Step-DPO-10K
[ { "content": "A grocery shop has a sale of Rs. 6535, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?", "role": "user" } ]	[ { "content": "Let's think step by step.\nStep 1:\n First, we need to find the total sale for the first five months. We do this by adding up the sale for each month:\nRs. 6535 + Rs. 6927 + Rs. 6855 + Rs. 7230 + Rs. 6562 = Rs. 34109.\n\nStep 2: The problem states that the grocery shop wants to have an average sal...	[ { "content": "Let's think step by step.\nStep 1:\n First, we need to find the total of the sales for the first five months. We do this by adding up all the sales:\n\\[6535 + 6927 + 6855 + 7230 + 6562 = 34609.\\]\n\nStep 2: The grocery shop wants an average sale of Rs. 6500 over six months. The total sale for s...	xinlai/Math-Step-DPO-10K
[ { "content": "How many numbers between 200 and 400 begin or end with 2?", "role": "user" } ]	[ { "content": "Let's think step by step.\nStep 1: Count the number of numbers between 200 and 400 that begin with 2.\nThe numbers between 200 and 400 that begin with 2 are 200, 201, 202, ..., 299. This is an arithmetic sequence with first term $a_1 = 200$, last term $a_n = 299$, and common difference $d = 1$. T...	[ { "content": "Let's think step by step.\nStep 1: Count the number of numbers between 200 and 400 that begin with 2.\nThe numbers between 200 and 400 that begin with 2 are 200, 201, 202, ..., 299. This is an arithmetic sequence with first term $a_1 = 200$, last term $a_n = 299$, and common difference $d = 1$. T...	xinlai/Math-Step-DPO-10K
[ { "content": "Marge has Z candies, where Z is an integer such that 20 < Z< 50. If Marge divides the candies equally among 5 children, she will have 2 candies remaining. If she divides the candies among 6 children, she will have 1 candy remaining. How many candies will remain if she divides the candies among 7 c...	[ { "content": "Let's think step by step.\nStep 1: If Marge divides the candies equally among 5 children, she will have 2 candies remaining. This means that the number of candies, $Z$, is 2 more than a multiple of 5. So we can write $Z = 5k + 2$ for some integer $k$.\n\nStep 2: If she divides the candies among 6...	[ { "content": "Let's think step by step.\nStep 1: If Marge divides the candies equally among 5 children, she will have 2 candies remaining. This means that the number of candies, $Z$, is 2 more than a multiple of 5. So we can write $Z = 5k + 2$ for some integer $k$.\n\nStep 2: If she divides the candies among 6...	xinlai/Math-Step-DPO-10K
[ { "content": "Mother,her daughter and her grand child weighs 160 kg. daughter and her daughter(child) weighs 60 kg. child is 1/5th of her grand mother. What is the age of the daughter?", "role": "user" } ]	[ { "content": "Let's think step by step.\nStep 1: Let's say the weight of the child is $x$. According to the problem, the child is 1/5th of her grand mother. This means the weight of the grand mother is $5x$.\n\nStep 2: The daughter and her daughter(child) weighs 60 kg. This means the weight of the daughter is ...	[ { "content": "Let's think step by step.\nStep 1: Let's say the weight of the child is $x$. According to the problem, the child is 1/5th of her grand mother. This means the weight of the grand mother is $5x$.\n\nStep 2: The daughter and her daughter(child) weighs 60 kg. This means the weight of the daughter is ...	xinlai/Math-Step-DPO-10K
[ { "content": "In how many ways can 6 boys and 4 girls sit around a table in such a way that no two girls sit together?", "role": "user" } ]	[ { "content": "Let's think step by step.\nStep 1:\n First, we arrange the boys in a circle. There are 6 boys, so there are $5! = 120$ ways to arrange them in a circle.\n\nStep 2: Now, we need to place the girls in such a way that no two girls sit together. We can think of the boys as creating \"spaces\" for the ...	[ { "content": "Let's think step by step.\nStep 1:\n Arrange the 6 boys in a line. There are $6!$ ways to do this.\nStep 2: Consider the 7 gaps between the boys and the 2 ends. We want to place the 4 girls in these 7 positions in such a way that no two girls sit together. There are $\\binom{7}{4}$ ways to choos...	xinlai/Math-Step-DPO-10K
[ { "content": "Find the average of the series : 120, 148, 420, 150 and 162?", "role": "user" } ]	[ { "content": "Let's think step by step.\nStep 1:\n Add up all the numbers in the series.\n$120 + 148 + 420 + 150 + 162 = 1000$.\n\nStep 2: Count the number of terms in the series. There are 5 terms in this series.\n\nStep 3: To find the average, divide the sum by the number of terms. So, $1000 \\div 5 = 200$.\n...	[ { "content": "Let's think step by step.\nStep 1:\n First, we need to add all the numbers in the series. \n\nThe sum of the series is 120 + 148 + 420 + 150 + 162 = 900.\n\nStep 2: Then, we need to count the number of numbers in the series. There are 5 numbers in the series.\n\nStep 3: To find the average, we di...	xinlai/Math-Step-DPO-10K
[ { "content": "Three number are in the ratio of 3 : 4 : 5 and their L.C.M. is 600. What is their H.C.F.?", "role": "user" } ]	[ { "content": "Let's think step by step.\nStep 1: Let's say the three numbers are $3x$, $4x$, and $5x$.\n\nStep 2:\n The L.C.M. of the three numbers is given as 600. The L.C.M. of $3x$, $4x$, and $5x$ is $60x$. So we have $60x = 600$.\n\nStep 3: Solving the equation $60x = 600$ for $x$, we get $x = \\frac{600...	[ { "content": "Let's think step by step.\nStep 1: Let's say the three numbers are $3x$, $4x$, and $5x$.\n\nStep 2:\n The L.C.M. of $3x$, $4x$, and $5x$ is $20x$.\n\nStep 3: Given that the L.C.M. is 600, so we have $20x = 600$.\n\nStep 4: Solving for $x$, we get $x = \\frac{600}{20} = 30$.\n\nStep 5: So the thre...	xinlai/Math-Step-DPO-10K
[ { "content": "In the above number, A and B represent the tens and units digits, respectively. If the above number is divisible by 15, what is the greatest possible value of B x A?", "role": "user" } ]	[ { "content": "Let's think step by step.\nStep 1: A number is divisible by 15 if it is divisible by both 3 and 5.\n\nStep 2: A number is divisible by 5 if its last digit is 0 or 5. So, B can be either 0 or 5.\n\nStep 3: A number is divisible by 3 if the sum of its digits is divisible by 3. So, A + B must be div...	[ { "content": "Let's think step by step.\nStep 1: A number is divisible by 15 if it is divisible by both 3 and 5.\n\nStep 2: A number is divisible by 5 if its last digit is 0 or 5. So, B can be either 0 or 5.\n\nStep 3: A number is divisible by 3 if the sum of its digits is divisible by 3. So, A + B must be div...	xinlai/Math-Step-DPO-10K
[ { "content": "JERRY has 13 ten-dollar bills, 11 five-dollar bills, and 17 one-dollar bills. If JERRY needs to pay exactly $128, what is the least number of bills he will need to use?", "role": "user" } ]	[ { "content": "Let's think step by step.\nStep 1: First, let's calculate how much money Jerry has in total.\nHe has 13 ten-dollar bills, so that's $13 \\times 10 = $130$.\nHe has 11 five-dollar bills, so that's $11 \\times 5 = $55$.\nHe has 17 one-dollar bills, so that's $17 \\times 1 = $17$.\nAdding all these ...	[ { "content": "Let's think step by step.\nStep 1: First, let's calculate how much money Jerry has in total.\nHe has 13 ten-dollar bills, so that's $13 \\times 10 = $130$.\nHe has 11 five-dollar bills, so that's $11 \\times 5 = $55$.\nHe has 17 one-dollar bills, so that's $17 \\times 1 = $17$.\nAdding all these ...	xinlai/Math-Step-DPO-10K
[ { "content": "The C.I. on a certain sum for 2 years at 10% per annum is Rs. 525. The S.I. on the same sum for double the time at half the rate percent per annum is?", "role": "user" } ]	[ { "content": "Let's think step by step.\nStep 1:\n First, let's find out the principal amount. The formula for compound interest (C.I.) is: C.I. = P(1 + r/n)^(nt) - P, where P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the numbe...	[ { "content": "Let's think step by step.\nStep 1:\n Find the principal amount (P) using the formula for compound interest (C.I.).\nThe formula for C.I. is: $A = P(1 + r/n)^{nt}$, where A is the final amount, P is the principal amount, r is the annual interest rate (as a decimal), n is the number of times the in...	xinlai/Math-Step-DPO-10K
[ { "content": "Boy sells a book for Rs. 800 he gets a loss of 20 %, To gain 10%, what should be the SP?", "role": "user" } ]	[ { "content": "Let's think step by step.\nStep 1:\n First, we need to find out the original price of the book. Since the boy sold the book for Rs. 800 and got a loss of 20%, that means the selling price (SP) was 80% of the original price (OP). So we can set up the equation: $800 = 0.8 \\cdot OP$.\n\nStep 2: To s...	[ { "content": "Let's think step by step.\nStep 1:\n 20% loss on Rs. 800 is (20/100) * 800 = Rs. 160. This means that the boy sold the book for Rs. 800 - Rs. 160 = Rs. 640.\n\nStep 2: To gain 10%, the selling price (SP) should be 10% more than the original price (OP). Let's represent the original price as x. So, ...	xinlai/Math-Step-DPO-10K
[ { "content": "Average of 10 matches is 32, How many runs one should should score to increase his average by 3 runs.", "role": "user" } ]	[ { "content": "Let's think step by step.\nStep 1: The total number of runs scored in 10 matches is the average times the number of matches, so it's $32 \\times 10 = 320$.\n\nStep 2: If we want to increase the average by 3 runs, the new average should be $32 + 3 = 35$.\n\nStep 3:\n The total number of runs neede...	[ { "content": "Let's think step by step.\nStep 1: The total number of runs scored in 10 matches is the average times the number of matches, so it's $32 \\times 10 = 320$.\n\nStep 2: If we want to increase the average by 3 runs, the new average should be $32 + 3 = 35$.\n\nStep 3:\n To find out the total number o...	xinlai/Math-Step-DPO-10K