Kitchen Sync
Collection
23 items
•
Updated
instruction
stringlengths 23
1.11k
| samples
sequencelengths 10k
10k
| unit_tests
listlengths 18
20
| unit_test_model
stringclasses 1
value | level
stringclasses 5
values | type
stringclasses 7
values | problem
stringlengths 23
1.11k
| solution
stringlengths 57
2.74k
| example_id
int64 0
127
| unit_test_results
sequencelengths 1k
1k
| evaluation_model
stringclasses 1
value | response_pass_rates
sequencelengths 1k
1k
| unit_test_pass_rates
sequencelengths 18
20
| overall_pass_rate
float64 0.13
1
|
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
"At her track meet, Alice ran at a speed of $9\\ \\text{m/s}$ for $12$ seconds. How many meters did (...TRUNCATED) | [" Alice ran at a speed of $9\\ \\text{m/s}$ for $12$ seconds, so she ran a total of $9\\cdot12=\\bo(...TRUNCATED) | [{"justification":"This test verifies that the solution correctly interprets the given speed and tim(...TRUNCATED) | meta-llama/Meta-Llama-3.1-405B-Instruct-Turbo | Level 1 | Algebra | "At her track meet, Alice ran at a speed of $9\\ \\text{m/s}$ for $12$ seconds. How many meters did (...TRUNCATED) | "Letting $v$ denote speed, $x$ denote distance, and $t$ denote time, we have $v=\\frac{x}{t}$. In ou(...TRUNCATED) | 8 | [["[Passed]","[Passed]","[Passed]","[Passed]","[Passed]","[Passed]","[Unknown]","[Unknown]","[Passed(...TRUNCATED) | gpt-4o | [0.75,0.8,0.8,0.8,1.0,1.0,0.8,0.8,1.0,0.75,0.75,0.8,1.0,0.8,0.8,0.8,0.75,0.8,0.8,1.0,0.8,0.8,0.7,0.8(...TRUNCATED) | [
1,
1,
1,
1,
1,
1,
0.09,
0.081,
1,
1,
0.996,
0.999,
0.999,
1,
0.985,
0.854,
0.755,
0.15,
0.073,
1
] | 0.7991 |
Evaluate $\left\lceil\sqrt{27}\right\rceil - \left\lfloor\sqrt{26}\right\rfloor$. | [" We have that $\\sqrt{27} = 3\\sqrt{3} \\approx 5.196$, so $\\left\\lceil\\sqrt{27}\\right\\rceil (...TRUNCATED) | [{"justification":"Verifies that the solution correctly interprets the mathematical expression given(...TRUNCATED) | meta-llama/Meta-Llama-3.1-405B-Instruct-Turbo | Level 2 | Algebra | Evaluate $\left\lceil\sqrt{27}\right\rceil - \left\lfloor\sqrt{26}\right\rfloor$. | "Because $\\sqrt{25}<\\sqrt{26}<\\sqrt{27}<\\sqrt{36}$, we have $\\left\\lceil\\sqrt{27}\\right\\rce(...TRUNCATED) | 4 | [["[Passed]","[Passed]","[Passed]","[Failed]","[Passed]","[Passed]","[Passed]","[Passed]","[Passed]"(...TRUNCATED) | gpt-4o | [0.9,1.0,0.95,1.0,0.8,0.8,0.65,0.95,0.85,1.0,0.65,0.25,0.75,1.0,0.95,1.0,0.75,0.85,0.9,1.0,1.0,1.0,0(...TRUNCATED) | [0.998,0.583,0.59,0.849,0.924,0.906,0.95,0.929,0.877,0.826,0.893,0.878,0.804,0.878,0.831,0.691,0.926(...TRUNCATED) | 0.84875 |
"Josh and Mike live 13 miles apart. Yesterday Josh started to ride his bicycle toward Mike's house. (...TRUNCATED) | [" If Mike rode for $t$ hours, then Josh rode for $2t$ hours. If Mike's rate was $r$ miles per hour(...TRUNCATED) | [{"justification":"Verifies the initial understanding of the distance between Josh and Mike.","quest(...TRUNCATED) | meta-llama/Meta-Llama-3.1-405B-Instruct-Turbo | Level 4 | Algebra | "Josh and Mike live 13 miles apart. Yesterday Josh started to ride his bicycle toward Mike's house. (...TRUNCATED) | "Because $\\text{(rate)(time)} = \\text{(distance)}$, the distance Josh rode was $(4/5)(2) = 8/5$ of(...TRUNCATED) | 7 | [["[Passed]","[Passed]","[Passed]","[Passed]","[Passed]","[Passed]","[Passed]","[Passed]","[Passed]"(...TRUNCATED) | gpt-4o | [0.8947368421052632,0.8421052631578947,0.8421052631578947,0.8947368421052632,0.9473684210526315,0.68(...TRUNCATED) | [0.977,0.968,0.993,0.907,0.914,0.811,0.67,0.852,0.866,0.204,0.903,0.94,0.849,0.831,0.781,0.837,0.501(...TRUNCATED) | 0.812105 |
"If $j$ and $k$ are inversely proportional and $j = 42$ when $k = 56$, what is the value of $j$ when(...TRUNCATED) | [" We have that $j = \\frac{c}{k}$ for some constant $c$. When $j = 42$ and $k = 56$, we have\n\n$$(...TRUNCATED) | [{"justification":"Verifying correct interpretation of the problem's given information and relations(...TRUNCATED) | meta-llama/Meta-Llama-3.1-405B-Instruct-Turbo | Level 3 | Algebra | "If $j$ and $k$ are inversely proportional and $j = 42$ when $k = 56$, what is the value of $j$ when(...TRUNCATED) | "By the definition of inverse proportion, the product $jk$ is always equal to some constant $C$. Su(...TRUNCATED) | 3 | [["[Passed]","[Failed]","[Passed]","[Passed]","[Passed]","[Passed]","[Passed]","[Passed]","[Failed]"(...TRUNCATED) | gpt-4o | [0.7368421052631579,0.7894736842105263,0.7368421052631579,0.7368421052631579,0.7368421052631579,0.78(...TRUNCATED) | [1.0,0.906,0.919,0.999,0.998,0.995,0.995,0.993,0.003,0.02,0.996,0.001,0.421,0.993,0.995,0.969,0.994,(...TRUNCATED) | 0.797579 |
"A ball travels on a parabolic path in which the height (in feet) is given by the expression $-25t^2(...TRUNCATED) | [" The vertex of the parabola is at $t = -\\frac{b}{2a} = -\\frac{75}{2(-25)} = \\boxed{1.5}.$\nFina(...TRUNCATED) | [{"justification":"Understanding the problem statement is crucial, this confirms the solution acknow(...TRUNCATED) | meta-llama/Meta-Llama-3.1-405B-Instruct-Turbo | Level 5 | Algebra | "A ball travels on a parabolic path in which the height (in feet) is given by the expression $-25t^2(...TRUNCATED) | "First, we find the maximum height of the ball by maximizing the expression $-25t^2+75t+24$. We will(...TRUNCATED) | 2 | [["[Passed]","[Passed]","[Failed]","[Passed]","[Passed]","[Passed]","[Passed]","[Passed]","[Passed]"(...TRUNCATED) | gpt-4o | [0.7,0.4,0.6,0.6,0.65,0.65,0.45,0.7,0.7,0.5,0.7,0.75,0.7,0.75,0.45,0.45,0.6,0.75,0.7,0.5,0.8,0.8,0.6(...TRUNCATED) | [0.997,0.771,0.135,0.972,0.653,0.773,0.757,0.801,0.819,0.558,0.05,0.984,0.278,0.943,0.928,0.762,0.86(...TRUNCATED) | 0.63125 |
The sum of the two $5$-digit numbers $AMC10$ and $AMC12$ is $123422.$ What is $A + M + C?$ | [" We have that $AMC10 + AMC12 = 123422,$ so $AMC10 + AMC10 + 2 = 123422.$ Therefore, $2AMC10 = 1234(...TRUNCATED) | [{"justification":"Verifying the solution correctly interprets the problem statement is crucial for (...TRUNCATED) | meta-llama/Meta-Llama-3.1-405B-Instruct-Turbo | Level 2 | Algebra | The sum of the two $5$-digit numbers $AMC10$ and $AMC12$ is $123422.$ What is $A + M + C?$ | "Since the last two digits of $AMC10$ and $AMC12$ sum to $22,$ we have \\[\nAMC + AMC = 2(AMC) = 123(...TRUNCATED) | 0 | [["[Passed]","[Failed]","[Passed]","[Failed]","[Failed]","[Failed]","[Failed]","[Passed]","[Failed]"(...TRUNCATED) | gpt-4o | [0.25,0.5,0.25,0.4,0.25,0.3,0.7,0.1,0.3,0.55,0.35,0.5,0.25,0.25,0.1,0.4,0.7,0.2,0.15,0.2,0.3,0.65,0.(...TRUNCATED) | [0.947,0.666,0.716,0.501,0.029,0.202,0.03,0.469,0.045,0.366,0.242,0.22,0.274,0.871,0.788,0.213,0.204(...TRUNCATED) | 0.36585 |
Solve for $a$: $\dfrac{8^{-1}}{4^{-1}}-a^{-1}=1$. | [" We have that\n\n\\begin{align*}\n\\frac{8^{-1}}{4^{-1}}-a^{-1}&=1\\\\\n\\Rightarrow\\qquad \\frac(...TRUNCATED) | [{"justification":"Verifying the initial setup correctly interprets negative exponents as reciprocal(...TRUNCATED) | meta-llama/Meta-Llama-3.1-405B-Instruct-Turbo | Level 2 | Algebra | Solve for $a$: $\dfrac{8^{-1}}{4^{-1}}-a^{-1}=1$. | "First, we simplify the left side, using the exponent rule $x^{-1} = \\frac1x$. We have \\[\n\\fra(...TRUNCATED) | 1 | [["[Passed]","[Passed]","[Passed]","[Passed]","[Failed]","[Passed]","[Failed]","[Passed]","[Passed]"(...TRUNCATED) | gpt-4o | [0.75,0.65,0.15,0.65,0.1,0.05,0.25,0.8,0.25,0.25,0.2,0.35,0.8,0.45,0.45,0.4,0.25,0.3,0.6,0.75,0.15,0(...TRUNCATED) | [0.876,0.895,0.317,0.821,0.121,0.473,0.1,0.963,0.631,0.42,0.515,0.507,0.46,0.384,0.327,0.003,0.117,0(...TRUNCATED) | 0.44495 |
"The sum of three numbers $a, b$ and $c$ is 88. If we decrease $a$ by 5, we get $N$. If we increase (...TRUNCATED) | [" If we decrease $a$ by 5, we get $N$, so $a-5=N$. If we increase $b$ by 5, we get $N$, so $b+5=N$.(...TRUNCATED) | [{"justification":"Correct interpretation of the initial conditions is crucial for setting up the eq(...TRUNCATED) | meta-llama/Meta-Llama-3.1-405B-Instruct-Turbo | Level 3 | Algebra | "The sum of three numbers $a, b$ and $c$ is 88. If we decrease $a$ by 5, we get $N$. If we increase (...TRUNCATED) | "Translating words into math, we have the equations \\begin{align*}\na+b+c&=88\\\\\na-5&=N\\\\\nb+5&(...TRUNCATED) | 5 | [["[Passed]","[Passed]","[Passed]","[Passed]","[Passed]","[Passed]","[Failed]","[Failed]","[Failed]"(...TRUNCATED) | gpt-4o | [0.8,0.55,0.75,0.6,0.45,0.85,0.85,0.35,0.45,0.8,0.85,0.45,0.55,0.65,0.8,0.75,0.85,0.8,0.8,0.85,0.65,(...TRUNCATED) | [0.95,0.925,0.883,0.854,0.667,0.639,0.012,0.03,0.059,0.635,0.996,0.995,0.778,0.938,0.578,0.606,0.626(...TRUNCATED) | 0.6354 |
"Suppose $\\frac ab = \\frac35$,$\\frac bc=\\frac{15}6$, and $\\frac cd = 6$. What is the value of $(...TRUNCATED) | [" We have that\n\n\\begin{align*}\n\\frac{a}{d}&=\\frac{a}{b}\\cdot\\frac{b}{c}\\cdot\\frac{c}{d}\\(...TRUNCATED) | [{"justification":"Verifies correct interpretation of the given ratios as a starting point for solvi(...TRUNCATED) | meta-llama/Meta-Llama-3.1-405B-Instruct-Turbo | Level 3 | Algebra | "Suppose $\\frac ab = \\frac35$,$\\frac bc=\\frac{15}6$, and $\\frac cd = 6$. What is the value of $(...TRUNCATED) | "Multiply all three equations to find that \\begin{align*}\n\\frac{a}{b}\\cdot\\frac{b}{c}\\cdot\\f(...TRUNCATED) | 6 | [["[Passed]","[Passed]","[Passed]","[Passed]","[Passed]","[Passed]","[Passed]","[Passed]","[Passed]"(...TRUNCATED) | gpt-4o | [1.0,0.85,1.0,1.0,0.8,0.25,1.0,1.0,0.65,0.45,1.0,0.4,1.0,1.0,1.0,1.0,0.95,0.9,1.0,1.0,1.0,0.8,0.95,0(...TRUNCATED) | [0.911,0.933,0.698,0.705,0.705,0.755,0.819,0.871,0.761,0.775,0.815,0.872,0.798,0.757,0.762,0.74,0.75(...TRUNCATED) | 0.79035 |
"The graph of the equation $y=ax^2+bx-6$ is completely below the $x$-axis. If $a^2=49$, what is the (...TRUNCATED) | [" To have the graph of $y = ax^2 + bx - 6$ completely below the $x$-axis, we must have $a > 0$ and (...TRUNCATED) | [{"justification":"To ensure correct problem setup, it's crucial to verify that the parabola opens d(...TRUNCATED) | meta-llama/Meta-Llama-3.1-405B-Instruct-Turbo | Level 5 | Algebra | "The graph of the equation $y=ax^2+bx-6$ is completely below the $x$-axis. If $a^2=49$, what is the (...TRUNCATED) | "Since the parabola is completely below the $x$-axis, it must open downwards (otherwise, it would ha(...TRUNCATED) | 9 | [["[Failed]","[Failed]","[Failed]","[Failed]","[Failed]","[Failed]","[Failed]","[Failed]","[Failed]"(...TRUNCATED) | gpt-4o | [0.1,0.25,0.25,0.15,0.1,0.65,0.15,0.1,0.2,0.3,0.15,0.0,0.2,0.1,0.2,0.1,0.15,0.05,0.55,0.2,0.25,0.4,0(...TRUNCATED) | [0.22,0.011,0.312,0.255,0.031,0.123,0.036,0.2,0.237,0.218,0.793,0.845,0.042,0.571,0.098,0.024,0.124,(...TRUNCATED) | 0.21735 |
End of preview. Expand
in Dataset Viewer.
No dataset card yet
- Downloads last month
- 16
Size of downloaded dataset files:
664 MB
Size of the auto-converted Parquet files:
165 MB
Number of rows:
128