p-bench
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stringclasses 5
values | answer
stringclasses 5
values | url
stringclasses 5
values | _index
stringclasses 5
values | question
stringclasses 5
values | solution
stringclasses 2
values | dataset
stringclasses 2
values | aggregated_pass_rate
float64 0.5
0.93
| accessor_pass@k
dict |
|---|---|---|---|---|---|---|---|---|
amc23_52 | 4.0 | https://artofproblemsolving.com/wiki/index.php/2023_AMC_12A_Problems/Problem_2 | 52 | The weight of $\frac{1}{3}$ of a large pizza together with $3 \frac{1}{2}$ cups of orange slices is the same as the weight of $\frac{3}{4}$ of a large pizza together with $\frac{1}{2}$ cup of orange slices. A cup of orange slices weighs $\frac{1}{4}$ of a pound. What is the weight, in pounds, of a large pizza? The answer can be written in the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. What is $m-n$? | amc23 | 0.784375 | {
"Llama-3.1-8B-Instruct": {
"K": 64,
"pass@K": 0.34375000000000006
},
"Llama-3.3-70B-Instruct": {
"K": 64,
"pass@K": 1
},
"QwQ-32B": {
"K": 64,
"pass@K": 1
},
"Qwen2.5-7B-Instruct": {
"K": 64,
"pass@K": 0.953125
},
"Qwen2.5-Math-7B": {
"K": 64,
"pass@K": 0.625
}
} |
|
aime24_60 | 204 | https://artofproblemsolving.com/wiki/index.php/2024_AIME_I_Problems/Problem_1 | 60 | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, including $t$ minutes spent in the coffee shop. Suppose Aya walks at $s+\frac{1}{2}$ kilometers per hour. Find the number of minutes the walk takes her, including the $t$ minutes spent in the coffee shop. | $\frac{9}{s} + t = 4$ in hours and $\frac{9}{s+2} + t = 2.4$ in hours.
Subtracting the second equation from the first, we get,
$\frac{9}{s} - \frac{9}{s+2} = 1.6$
Multiplying by $(s)(s+2)$, we get
$9s+18-9s=18=1.6s^{2} + 3.2s$
Multiplying by 5/2 on both sides, we get
$0 = 4s^{2} + 8s - 45$
Factoring gives us
$(2s-5)(2s+9) = 0$, of which the solution we want is $s=2.5$.
Substituting this back to the first equation, we can find that $t = 0.4$ hours.
Lastly, $s + \frac{1}{2} = 3$ kilometers per hour, so
$\frac{9}{3} + 0.4 = 3.4$ hours, or $\framebox{204}$ minutes
-Failure.net
The amount of hours spent while walking on the first travel is $\frac{240-t}{6}$. Thus, we have the equation $(240-t)(s) = 540$, and by the same logic, the second equation yields $(144-t)(s+2) = 540$. We have $240s-st = 540$, and $288+144s-2t-st = 540$. We subtract the two equations to get $96s+2t-288 = 0$, so we have $48s+t = 144$, so $t = 144-48s$, and now we have $(96+48s)(s) = 540$. The numerator of $s$ must evenly divide 540, however, $s$ must be less than 3. We can guess that $s = 2.5$. Now, $2.5+0.5 = 3$. Taking $\frac{9}{3} = 3$, we find that it will take three hours for the 9 kilometers to be traveled. The t minutes spent at the coffeeshop can be written as $144-48(2.5)$, so t = 24. $180 + 24 = 204$. -sepehr2010 | aime24 | 0.503125 | {
"Llama-3.1-8B-Instruct": {
"K": 64,
"pass@K": 0.078125
},
"Llama-3.3-70B-Instruct": {
"K": 64,
"pass@K": 0.796875
},
"QwQ-32B": {
"K": 64,
"pass@K": 1
},
"Qwen2.5-7B-Instruct": {
"K": 64,
"pass@K": 0.53125
},
"Qwen2.5-Math-7B": {
"K": 64,
"pass@K": 0.109375
}
} |
amc23_69 | 13.0 | https://artofproblemsolving.com/wiki/index.php/2023_AMC_12B_Problems/Problem_13 | 69 | A rectangular box $P$ has distinct edge lengths $a$, $b$, and $c$. The sum of the lengths of all $12$ edges of $P$ is $13$, the areas of all $6$ faces of $P$ is $\frac{11}{2}$, and the volume of $P$ is $\frac{1}{2}$. Find the length of the longest interior diagonal connecting two vertices of $P$. The final answer can be written in the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. What is $m+n$? | amc23 | 0.509375 | {
"Llama-3.1-8B-Instruct": {
"K": 64,
"pass@K": 0.296875
},
"Llama-3.3-70B-Instruct": {
"K": 64,
"pass@K": 0.296875
},
"QwQ-32B": {
"K": 64,
"pass@K": 1
},
"Qwen2.5-7B-Instruct": {
"K": 64,
"pass@K": 0.4375
},
"Qwen2.5-Math-7B": {
"K": 64,
"pass@K": 0.515625
}
} |
|
amc23_73 | 50.0 | https://artofproblemsolving.com/wiki/index.php/2023_AMC_12B_Problems/Problem_2 | 73 | Carlos went to a sports store to buy running shoes. Running shoes were on sale, with prices reduced by $20\%$ on every pair of shoes. Carlos also knew that he had to pay a $7.5\%$ sales tax on the discounted price. He had $$43$ dollars. What is the original (before discount) price of the most expensive shoes he could afford to buy? | amc23 | 0.8875 | {
"Llama-3.1-8B-Instruct": {
"K": 64,
"pass@K": 0.65625
},
"Llama-3.3-70B-Instruct": {
"K": 64,
"pass@K": 1
},
"QwQ-32B": {
"K": 64,
"pass@K": 1
},
"Qwen2.5-7B-Instruct": {
"K": 64,
"pass@K": 1
},
"Qwen2.5-Math-7B": {
"K": 64,
"pass@K": 0.7812500000000001
}
} |
|
amc23_45 | 45.0 | https://artofproblemsolving.com/wiki/index.php/2023_AMC_12A_Problems/Problem_11 | 45 | What is the degree measure of the acute angle formed by lines with slopes $2$ and $\frac{1}{3}$? | amc23 | 0.93125 | {
"Llama-3.1-8B-Instruct": {
"K": 64,
"pass@K": 0.8125
},
"Llama-3.3-70B-Instruct": {
"K": 64,
"pass@K": 1
},
"QwQ-32B": {
"K": 64,
"pass@K": 1
},
"Qwen2.5-7B-Instruct": {
"K": 64,
"pass@K": 1
},
"Qwen2.5-Math-7B": {
"K": 64,
"pass@K": 0.8437500000000001
}
} |
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