prompt string | prompt_id string | chosen list | rejected list | messages list | id string | task string | dataset string | n_turns int64 | reward_score_chosen float64 | reward_score_rejected float64 | reward_margin float64 | score_chosen float64 | score_rejected float64 | is_difficult int64 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
Our school's girls volleyball team has 14 players, including a set of 3 triplets: Alicia, Amanda, and Anna. In how many ways can we choose 6 starters if exactly one of the triplets... | 7cf940f14ef4c2f25b1ef72786f416cfc1217f38c8faca5d523b499cc3007a84 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nOur school's girls volleyball team has 14 players, including a set of 3 triplets: Alicia, Amanda, and Anna. In how many ways can we choose 6 starters if ex... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nOur school's girls volleyball team has 14 players, including a set of 3 triplets: Alicia, Amanda, and Anna. In how many ways can we choose 6 starters if ex... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nOur school's girls volleyball team has 14 players, including a set of 3 triplets: Alicia, Amanda, and Anna. In how many ways can we choose 6 starters if ex... | 7cf940f14ef4c2f25b1ef72786f416cfc1217f38c8faca5d523b499cc3007a84_5_4 | Math_CoT | MATH | 7 | 23.625 | -32.25 | 55.875 | 23.625 | -32.25 | 0 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
Cathy and Chris got summer jobs at the cake shop and were supposed to work 20 hours per week each for 2 months. During that time, Chris got sick for one week and Cathy took her shif... | 2f55044dc7018c1739c78c11114b00d0e51847d28d98d5618e5b3ee77500c7b6 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nCathy and Chris got summer jobs at the cake shop and were supposed to work 20 hours per week each for 2 months. During that time, Chris got sick for one wee... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nCathy and Chris got summer jobs at the cake shop and were supposed to work 20 hours per week each for 2 months. During that time, Chris got sick for one wee... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nCathy and Chris got summer jobs at the cake shop and were supposed to work 20 hours per week each for 2 months. During that time, Chris got sick for one wee... | 2f55044dc7018c1739c78c11114b00d0e51847d28d98d5618e5b3ee77500c7b6_2_2 | Math_CoT | gsm8k | 3 | 25.625 | -25.375 | 51 | 25.625 | -25.375 | 0 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
There are 13 animals in a farm. Out of the 13 animals, 4 are chickens and remaining are buffalos. How many animal legs are there in the farm? | ac4c1c81f54928f4d82deaa34078de891e1d3faf55f944093cc8da33c5582421 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThere are 13 animals in a farm. Out of the 13 animals, 4 are chickens and remaining are buffalos. How many animal legs are there in the farm?",
"role": ... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThere are 13 animals in a farm. Out of the 13 animals, 4 are chickens and remaining are buffalos. How many animal legs are there in the farm?",
"role": ... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThere are 13 animals in a farm. Out of the 13 animals, 4 are chickens and remaining are buffalos. How many animal legs are there in the farm?",
"role": ... | ac4c1c81f54928f4d82deaa34078de891e1d3faf55f944093cc8da33c5582421_1_1 | Math_CoT | numglue | 1 | 21 | -25.625 | 46.625 | 21 | -25.625 | 0 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
Let $F(x)$ be a polynomial such that $F(6) = 15$ and\[\frac{F(3x)}{F(x+3)} = 9-\frac{48x+54}{x^2+5x+6}\]for $x \in \mathbb{R}$ such that both sides are defined. Find $F(12)$. | b0c6f65f23b1bd207f0d583d1a63499f5a76ab2f02882892e65c9ee1f220ea4b | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nLet $F(x)$ be a polynomial such that $F(6) = 15$ and\\[\\frac{F(3x)}{F(x+3)} = 9-\\frac{48x+54}{x^2+5x+6}\\]for $x \\in \\mathbb{R}$ such that both sides ar... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nLet $F(x)$ be a polynomial such that $F(6) = 15$ and\\[\\frac{F(3x)}{F(x+3)} = 9-\\frac{48x+54}{x^2+5x+6}\\]for $x \\in \\mathbb{R}$ such that both sides ar... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nLet $F(x)$ be a polynomial such that $F(6) = 15$ and\\[\\frac{F(3x)}{F(x+3)} = 9-\\frac{48x+54}{x^2+5x+6}\\]for $x \\in \\mathbb{R}$ such that both sides ar... | 179039f9f3fe76d239c864a993975421cc94a7063b898418cd99e641817051f0_1_1 | Math_CoT | MATH | 1 | 24.125 | -20.75 | 44.875 | 24.125 | -20.75 | 0 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
Johnny has been playing guitar for a while now. He practices the same amount each day. As of 20 days ago he had half as much practice as he has currently. How many days will pass ... | b74a67accd33ee6b6320512ac108d105750f807acbefa7eb80fa62d8a7d5d5d7 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nJohnny has been playing guitar for a while now. He practices the same amount each day. As of 20 days ago he had half as much practice as he has currently. ... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nJohnny has been playing guitar for a while now. He practices the same amount each day. As of 20 days ago he had half as much practice as he has currently. ... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nJohnny has been playing guitar for a while now. He practices the same amount each day. As of 20 days ago he had half as much practice as he has currently. ... | b74a67accd33ee6b6320512ac108d105750f807acbefa7eb80fa62d8a7d5d5d7_5_5 | Math_CoT | gsm8k | 9 | 14.5 | -29 | 43.5 | 14.5 | -29 | 0 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
In a right-angled triangle, the sum of the squares of the three side lengths is 1800. What is the length of the hypotenuse of this triangle? | 1c65b1fe50eaed2ad6233b5ea7a69c842765130baa54e2ec9ac2b2af6ada2d65 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nIn a right-angled triangle, the sum of the squares of the three side lengths is 1800. What is the length of the hypotenuse of this triangle?",
"role": ... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nIn a right-angled triangle, the sum of the squares of the three side lengths is 1800. What is the length of the hypotenuse of this triangle?",
"role": ... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nIn a right-angled triangle, the sum of the squares of the three side lengths is 1800. What is the length of the hypotenuse of this triangle?",
"role": ... | 1c65b1fe50eaed2ad6233b5ea7a69c842765130baa54e2ec9ac2b2af6ada2d65_5_4 | Math_CoT | MATH | 7 | 27.875 | -15.5625 | 43.4375 | 27.875 | -15.5625 | 0 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
Miranda wants to buy a pair of heels she saw online. She saved money for 3 months. Her sister heard that she was sad and gave her $50 for her to buy the heels. If she paid $260 in t... | c0253a6cb013ac8fa4ab3acf087967cc71e8017d44a7f72922ee42f1c8373433 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nMiranda wants to buy a pair of heels she saw online. She saved money for 3 months. Her sister heard that she was sad and gave her $50 for her to buy the hee... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nMiranda wants to buy a pair of heels she saw online. She saved money for 3 months. Her sister heard that she was sad and gave her $50 for her to buy the hee... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nMiranda wants to buy a pair of heels she saw online. She saved money for 3 months. Her sister heard that she was sad and gave her $50 for her to buy the hee... | c0253a6cb013ac8fa4ab3acf087967cc71e8017d44a7f72922ee42f1c8373433_3_3 | Math_CoT | gsm8k | 5 | 25 | -17.5 | 42.5 | 25 | -17.5 | 0 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
$ABCDEFGH$ shown below is a cube with volume 1. Find the volume of pyramid $ABCH$.
[asy]
import three;
triple A,B,C,D,EE,F,G,H;
A = (0,0,0);
B = (1,0,0);
C = (1,1,0);
D= (0,1,0);
... | 85302d63b9bd502fcf1abe1549d6d4396dae18535831e22aabc370456f0ba635 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\n$ABCDEFGH$ shown below is a cube with volume 1. Find the volume of pyramid $ABCH$.\n\n[asy]\nimport three;\ntriple A,B,C,D,EE,F,G,H;\nA = (0,0,0);\nB = (1,... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\n$ABCDEFGH$ shown below is a cube with volume 1. Find the volume of pyramid $ABCH$.\n\n[asy]\nimport three;\ntriple A,B,C,D,EE,F,G,H;\nA = (0,0,0);\nB = (1,... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\n$ABCDEFGH$ shown below is a cube with volume 1. Find the volume of pyramid $ABCH$.\n\n[asy]\nimport three;\ntriple A,B,C,D,EE,F,G,H;\nA = (0,0,0);\nB = (1,... | c74a284cb9ef426be17ad18a6976b11146716cd372f5de4cf7237aa5082768f4_1_1 | Math_CoT | MATH | 1 | 23.625 | -18.875 | 42.5 | 23.625 | -18.875 | 0 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
The volume of a cylinder is $54\pi$ $\text{cm}^3$. How many cubic centimeters are in the volume of a cone with the same radius and height as the cylinder? Express your answer in ter... | 7bfbf1c2156aa751a58b4b3e8845597fb656691c2951b47f6e0727e9b37a857d | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe volume of a cylinder is $54\\pi$ $\\text{cm}^3$. How many cubic centimeters are in the volume of a cone with the same radius and height as the cylinder?... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe volume of a cylinder is $54\\pi$ $\\text{cm}^3$. How many cubic centimeters are in the volume of a cone with the same radius and height as the cylinder?... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe volume of a cylinder is $54\\pi$ $\\text{cm}^3$. How many cubic centimeters are in the volume of a cone with the same radius and height as the cylinder?... | 6fae99e7b660f95daef959e3fcfa4eca870bc7e31b24bb07b0f56a9099c98f7c_1_1 | Math_CoT | MATH | 1 | 30.5 | -11.6875 | 42.1875 | 30.5 | -11.6875 | 0 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
A square is divided into five congruent rectangles, as shown. If the perimeter of each of these five rectangles is 36 inches, what is the perimeter of the square, in inches?
[asy]
... | 07250bc7d40d262c7a4ba3e7a1ff54154a76698786919cbad0aa0a7dd989dae4 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nA square is divided into five congruent rectangles, as shown. If the perimeter of each of these five rectangles is 36 inches, what is the perimeter of the s... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nA square is divided into five congruent rectangles, as shown. If the perimeter of each of these five rectangles is 36 inches, what is the perimeter of the s... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nA square is divided into five congruent rectangles, as shown. If the perimeter of each of these five rectangles is 36 inches, what is the perimeter of the s... | b286c7e996799b46a31ce129516b3c46f42275de111b378e39371d526fbbe71f_1_1 | Math_CoT | MATH | 1 | 33 | -9.0625 | 42.0625 | 33 | -9.0625 | 0 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
In a certain city the rate of taxation is the following: $x\%$ tax is collected for an income of $x$ thousand dollars. What income, in dollars, will yield the greatest take home pay... | d605686aa8c30ccca5014c048aede1b4018b075d4c011eaac85ea22f4571b4fa | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nIn a certain city the rate of taxation is the following: $x\\%$ tax is collected for an income of $x$ thousand dollars. What income, in dollars, will yield ... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nIn a certain city the rate of taxation is the following: $x\\%$ tax is collected for an income of $x$ thousand dollars. What income, in dollars, will yield ... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nIn a certain city the rate of taxation is the following: $x\\%$ tax is collected for an income of $x$ thousand dollars. What income, in dollars, will yield ... | d605686aa8c30ccca5014c048aede1b4018b075d4c011eaac85ea22f4571b4fa_3_1 | Math_CoT | MATH | 1 | 27.125 | -14.6875 | 41.8125 | 27.125 | -14.6875 | 0 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
A pen is longer than the rubber by 3 centimeters, and shorter than the pencil by 2 centimeters. Considering the pencil is 12 centimeters long, what is the total length of the rubber... | 8196ca477d835bd9084de2861b8ac262e3cd2cbfde1a1852363e4fd87ddf878d | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nA pen is longer than the rubber by 3 centimeters, and shorter than the pencil by 2 centimeters. Considering the pencil is 12 centimeters long, what is the t... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nA pen is longer than the rubber by 3 centimeters, and shorter than the pencil by 2 centimeters. Considering the pencil is 12 centimeters long, what is the t... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nA pen is longer than the rubber by 3 centimeters, and shorter than the pencil by 2 centimeters. Considering the pencil is 12 centimeters long, what is the t... | 8196ca477d835bd9084de2861b8ac262e3cd2cbfde1a1852363e4fd87ddf878d_3_2 | Math_CoT | gsm8k | 3 | 32.75 | -8.75 | 41.5 | 32.75 | -8.75 | 0 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
For real numbers $t \neq 0,$ the point
\[(x,y) = \left( \frac{t + 1}{t}, \frac{t - 1}{t} \right)\]is plotted. All the plotted points lie on what kind of curve?
(A) Line
(B) Circle... | 407c49a905f1fe985b84a64133d02b2c352ef2232fa27c30df091215e0cb070e | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nFor real numbers $t \\neq 0,$ the point\n\\[(x,y) = \\left( \\frac{t + 1}{t}, \\frac{t - 1}{t} \\right)\\]is plotted. All the plotted points lie on what ki... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nFor real numbers $t \\neq 0,$ the point\n\\[(x,y) = \\left( \\frac{t + 1}{t}, \\frac{t - 1}{t} \\right)\\]is plotted. All the plotted points lie on what ki... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nFor real numbers $t \\neq 0,$ the point\n\\[(x,y) = \\left( \\frac{t + 1}{t}, \\frac{t - 1}{t} \\right)\\]is plotted. All the plotted points lie on what ki... | 407c49a905f1fe985b84a64133d02b2c352ef2232fa27c30df091215e0cb070e_4_4 | Math_CoT | MATH | 7 | 25.75 | -15.5 | 41.25 | 25.75 | -15.5 | 0 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
A set of marbles can be divided in equal shares among $2$, $3$, $4$, $5$, or $6$ children with no marbles left over. What is the least number of marbles that the set could have? | 8984b9f9308bdbd8ac4284029d71275862ad5062587278f2506b42d2a9dbb01c | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nA set of marbles can be divided in equal shares among $2$, $3$, $4$, $5$, or $6$ children with no marbles left over. What is the least number of marbles tha... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nA set of marbles can be divided in equal shares among $2$, $3$, $4$, $5$, or $6$ children with no marbles left over. What is the least number of marbles tha... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nA set of marbles can be divided in equal shares among $2$, $3$, $4$, $5$, or $6$ children with no marbles left over. What is the least number of marbles tha... | 8984b9f9308bdbd8ac4284029d71275862ad5062587278f2506b42d2a9dbb01c_2_1 | Math_CoT | MATH | 1 | 28 | -12.9375 | 40.9375 | 28 | -12.9375 | 0 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
Tom attends a party that collects $2000. Half the school attended and the school had 400 people. How much would they have made if 300 people attended? | b6c7af9dcb1307655bc137bdd35668e62d3a73df134a17ec46a4ba794bf6984f | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nTom attends a party that collects $2000. Half the school attended and the school had 400 people. How much would they have made if 300 people attended?",
... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nTom attends a party that collects $2000. Half the school attended and the school had 400 people. How much would they have made if 300 people attended?",
... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nTom attends a party that collects $2000. Half the school attended and the school had 400 people. How much would they have made if 300 people attended?",
... | b6c7af9dcb1307655bc137bdd35668e62d3a73df134a17ec46a4ba794bf6984f_2_2 | Math_CoT | gsm8k | 3 | 28.75 | -11.9375 | 40.6875 | 28.75 | -11.9375 | 0 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
every disk in a bag is either blue , yellow or green . the ratio of blue disks to yellow disks to green disks in this bag is 3 : 7 : 8 . if the total number of disks in the bag is 5... | deaedd28d6e72d3e0b49f7397deee511523ac05fb1ea6855891cb30f637f3c90 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nevery disk in a bag is either blue , yellow or green . the ratio of blue disks to yellow disks to green disks in this bag is 3 : 7 : 8 . if the total number... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nevery disk in a bag is either blue , yellow or green . the ratio of blue disks to yellow disks to green disks in this bag is 3 : 7 : 8 . if the total number... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nevery disk in a bag is either blue , yellow or green . the ratio of blue disks to yellow disks to green disks in this bag is 3 : 7 : 8 . if the total number... | deaedd28d6e72d3e0b49f7397deee511523ac05fb1ea6855891cb30f637f3c90_1_1 | Math_CoT | mathqa | 1 | 34.75 | -5.75 | 40.5 | 34.75 | -5.75 | 0 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
The tallest of 3 trees is 108 feet. The middle sized tree is 6 feet less than half the height of the tallest tree. The smallest tree is 1/4 the height of the middle tree. How tall... | 4e74db38b380da58cba43d1113b43dd9e7447261ca1c0c1c94ad2d789fc98037 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe tallest of 3 trees is 108 feet. The middle sized tree is 6 feet less than half the height of the tallest tree. The smallest tree is 1/4 the height of t... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe tallest of 3 trees is 108 feet. The middle sized tree is 6 feet less than half the height of the tallest tree. The smallest tree is 1/4 the height of t... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe tallest of 3 trees is 108 feet. The middle sized tree is 6 feet less than half the height of the tallest tree. The smallest tree is 1/4 the height of t... | 4e74db38b380da58cba43d1113b43dd9e7447261ca1c0c1c94ad2d789fc98037_1_1 | Math_CoT | gsm8k | 1 | 25.75 | -14.375 | 40.125 | 25.75 | -14.375 | 0 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
Bea's mom planted 50 Mahogany and 30 Narra trees on their farm. Due to a typhoon, a total of 5 trees fell. One more Mahogany tree fell than the number of Narra trees that fell. A mo... | 481a7f2d20d5b64567a4cbe098b3ae2dc6969f501964577b274c97a1cf67cfbd | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nBea's mom planted 50 Mahogany and 30 Narra trees on their farm. Due to a typhoon, a total of 5 trees fell. One more Mahogany tree fell than the number of Na... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nBea's mom planted 50 Mahogany and 30 Narra trees on their farm. Due to a typhoon, a total of 5 trees fell. One more Mahogany tree fell than the number of Na... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nBea's mom planted 50 Mahogany and 30 Narra trees on their farm. Due to a typhoon, a total of 5 trees fell. One more Mahogany tree fell than the number of Na... | 481a7f2d20d5b64567a4cbe098b3ae2dc6969f501964577b274c97a1cf67cfbd_4_3 | Math_CoT | gsm8k | 5 | 29.25 | -10.75 | 40 | 29.25 | -10.75 | 0 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
Let $\star (x)$ be the sum of the digits of a positive integer $x$. $\mathcal{S}$ is the set of positive integers such that for all elements $n$ in $\mathcal{S}$, we have that $\sta... | 49731aa0fb5bec86b7cb51c7b8bf10818c7ab58b1083d520f103a891ad0763ba | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nLet $\\star (x)$ be the sum of the digits of a positive integer $x$. $\\mathcal{S}$ is the set of positive integers such that for all elements $n$ in $\\mat... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nLet $\\star (x)$ be the sum of the digits of a positive integer $x$. $\\mathcal{S}$ is the set of positive integers such that for all elements $n$ in $\\mat... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nLet $\\star (x)$ be the sum of the digits of a positive integer $x$. $\\mathcal{S}$ is the set of positive integers such that for all elements $n$ in $\\mat... | 49731aa0fb5bec86b7cb51c7b8bf10818c7ab58b1083d520f103a891ad0763ba_5_1 | Math_CoT | MATH | 1 | 23 | -16.875 | 39.875 | 23 | -16.875 | 0 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
The harmonic mean of two positive integers is the reciprocal of the arithmetic mean of their reciprocals. For how many ordered pairs of positive integers $(x,y)$ with $x<y$ is the h... | 77cb57cc16e3595c415ad229f4a65e566cafba91cb2f880da59a7f1005cf03b2 | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe harmonic mean of two positive integers is the reciprocal of the arithmetic mean of their reciprocals. For how many ordered pairs of positive integers $(... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe harmonic mean of two positive integers is the reciprocal of the arithmetic mean of their reciprocals. For how many ordered pairs of positive integers $(... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe harmonic mean of two positive integers is the reciprocal of the arithmetic mean of their reciprocals. For how many ordered pairs of positive integers $(... | 3d12a6f8be4cf3f25eea620aefc79a5ade6791604141b223b5e93a776b375743_1_1 | Math_CoT | MATH | 1 | 33 | -6.78125 | 39.78125 | 33 | -6.78125 | 0 |
Solve the following math problem step-by-step.
Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}.
Mike buys 6 rose bushes at 75 dollars each, 2 of them are for his friend and the rest are for him. He also buys 2 tiger tooth aloes for 100 dollars each. How much money did he spe... | cb899bcec334d3328c8a0faacaf4756b59a91112bd51dce365a172dcda1ecb6d | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nMike buys 6 rose bushes at 75 dollars each, 2 of them are for his friend and the rest are for him. He also buys 2 tiger tooth aloes for 100 dollars each. ... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nMike buys 6 rose bushes at 75 dollars each, 2 of them are for his friend and the rest are for him. He also buys 2 tiger tooth aloes for 100 dollars each. ... | [
{
"content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nMike buys 6 rose bushes at 75 dollars each, 2 of them are for his friend and the rest are for him. He also buys 2 tiger tooth aloes for 100 dollars each. ... | cb899bcec334d3328c8a0faacaf4756b59a91112bd51dce365a172dcda1ecb6d_2_2 | Math_CoT | gsm8k | 3 | 28.5 | -11.25 | 39.75 | 28.5 | -11.25 | 0 |
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