index int64 0 999 | prompt stringclasses 100
values | status stringclasses 2
values | output stringlengths 0 431 | error stringclasses 2
values | metrics dict | trace_tree dict | problem_index int64 0 99 | generation_index int64 0 9 | level_num int64 1 1 | type stringclasses 7
values | ground_truth stringclasses 73
values | original_problem stringclasses 100
values |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | If $x$ satisfies $\frac{1}{2}-\frac{1}{3}=\frac{3}{x}$, then what is the value of $x$ ?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{18}
Insight: When solving simple rational equations, clearing denominators by multiplying by the least common multiple is an efficient method. | null | {
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"fragment": "",
"main_problem": "If $x$ satisfies $\\frac{1}{2}-\\frac{1}{3}=\\frac{3}{x}$, then what is the value of $x$ ?\n\nPlease provide... | 0 | 0 | 1 | Algebra | 18 | If $x$ satisfies $\frac{1}{2}-\frac{1}{3}=\frac{3}{x}$, then what is the value of $x$ ?
Please provide your final answer in the format \boxed{answer}. |
1 | If $x$ satisfies $\frac{1}{2}-\frac{1}{3}=\frac{3}{x}$, then what is the value of $x$ ?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{18}
Insight: Simple fraction subtraction and cross-multiplication are key steps in solving such rational equations. | null | {
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"prompt": "If $x$ satisfies $\\frac{1}{2}-\\frac{1}{3}=\\frac{3}{x}$, then what is the value of $x$ ?\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "If $x$ satisfies $\\frac{1}{2}-\\frac{1}{3}=\\frac{3}{x}$, then what is the value of $x$ ?\n\nPlease provide... | 0 | 1 | 1 | Algebra | 18 | If $x$ satisfies $\frac{1}{2}-\frac{1}{3}=\frac{3}{x}$, then what is the value of $x$ ?
Please provide your final answer in the format \boxed{answer}. |
2 | If $x$ satisfies $\frac{1}{2}-\frac{1}{3}=\frac{3}{x}$, then what is the value of $x$ ?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{\frac{18}{5}}
Insight: When solving rational equations, simplifying one side first can streamline the process by reducing the number of fractions to manipulate. | null | {
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"prompt": "If $x$ satisfies $\\frac{1}{2}-\\frac{1}{3}=\\frac{3}{x}$, then what is the value of $x$ ?\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "If $x$ satisfies $\\frac{1}{2}-\\frac{1}{3}=\\frac{3}{x}$, then what is the value of $x$ ?\n\nPlease provide... | 0 | 2 | 1 | Algebra | 18 | If $x$ satisfies $\frac{1}{2}-\frac{1}{3}=\frac{3}{x}$, then what is the value of $x$ ?
Please provide your final answer in the format \boxed{answer}. |
3 | If $x$ satisfies $\frac{1}{2}-\frac{1}{3}=\frac{3}{x}$, then what is the value of $x$ ?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{18} | null | {
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"prompt": "If $x$ satisfies $\\frac{1}{2}-\\frac{1}{3}=\\frac{3}{x}$, then what is the value of $x$ ?\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "\n\nTo find \\( x \\) satisfying the equation \\( \\frac{1}{2} - \\frac{1}{3} = \\frac{3}{x} \\), I first compute the left-hand si... | 0 | 3 | 1 | Algebra | 18 | If $x$ satisfies $\frac{1}{2}-\frac{1}{3}=\frac{3}{x}$, then what is the value of $x$ ?
Please provide your final answer in the format \boxed{answer}. |
4 | If $x$ satisfies $\frac{1}{2}-\frac{1}{3}=\frac{3}{x}$, then what is the value of $x$ ?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{18} | null | {
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"prompt": "If $x$ satisfies $\\frac{1}{2}-\\frac{1}{3}=\\frac{3}{x}$, then what is the value of $x$ ?\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "If $x$ satisfies $\\frac{1}{2}-\\frac{1}{3}=\\frac{3}{x}$, then what is the value of $x$ ?\n\nPlease provide... | 0 | 4 | 1 | Algebra | 18 | If $x$ satisfies $\frac{1}{2}-\frac{1}{3}=\frac{3}{x}$, then what is the value of $x$ ?
Please provide your final answer in the format \boxed{answer}. |
5 | If $x$ satisfies $\frac{1}{2}-\frac{1}{3}=\frac{3}{x}$, then what is the value of $x$ ?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{18} | null | {
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"prompt": "If $x$ satisfies $\\frac{1}{2}-\\frac{1}{3}=\\frac{3}{x}$, then what is the value of $x$ ?\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "\n\nI need to solve the equation \\(\\frac{1}{2}-\\frac{1}{3}=\\frac{3}{x}\\) for \\(x\\). The left side is a difference of two fr... | 0 | 5 | 1 | Algebra | 18 | If $x$ satisfies $\frac{1}{2}-\frac{1}{3}=\frac{3}{x}$, then what is the value of $x$ ?
Please provide your final answer in the format \boxed{answer}. |
6 | If $x$ satisfies $\frac{1}{2}-\frac{1}{3}=\frac{3}{x}$, then what is the value of $x$ ?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{18}
Insight: The equation reduces to a straightforward computation, emphasizing the need to handle fractions carefully and perform cross-multiplication correctly. | null | {
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"prompt": "If $x$ satisfies $\\frac{1}{2}-\\frac{1}{3}=\\frac{3}{x}$, then what is the value of $x$ ?\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "If $x$ satisfies $\\frac{1}{2}-\\frac{1}{3}=\\frac{3}{x}$, then what is the value of $x$ ?\n\nPlease provide... | 0 | 6 | 1 | Algebra | 18 | If $x$ satisfies $\frac{1}{2}-\frac{1}{3}=\frac{3}{x}$, then what is the value of $x$ ?
Please provide your final answer in the format \boxed{answer}. |
7 | If $x$ satisfies $\frac{1}{2}-\frac{1}{3}=\frac{3}{x}$, then what is the value of $x$ ?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{18} | null | {
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} | {
"prompt": "If $x$ satisfies $\\frac{1}{2}-\\frac{1}{3}=\\frac{3}{x}$, then what is the value of $x$ ?\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "If $x$ satisfies $\\frac{1}{2}-\\frac{1}{3}=\\frac{3}{x}$, then what is the value of $x$ ?\n\nPlease provide... | 0 | 7 | 1 | Algebra | 18 | If $x$ satisfies $\frac{1}{2}-\frac{1}{3}=\frac{3}{x}$, then what is the value of $x$ ?
Please provide your final answer in the format \boxed{answer}. |
8 | If $x$ satisfies $\frac{1}{2}-\frac{1}{3}=\frac{3}{x}$, then what is the value of $x$ ?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{18}
Insight: When solving rational equations, simplifying one side first often reduces to a straightforward algebraic manipulation like cross-multiplication. | null | {
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} | {
"prompt": "If $x$ satisfies $\\frac{1}{2}-\\frac{1}{3}=\\frac{3}{x}$, then what is the value of $x$ ?\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "\n\nI need to solve the equation \\(\\frac{1}{2}-\\frac{1}{3}=\\frac{3}{x}\\) for \\(x\\). This involves basic arithmetic and alge... | 0 | 8 | 1 | Algebra | 18 | If $x$ satisfies $\frac{1}{2}-\frac{1}{3}=\frac{3}{x}$, then what is the value of $x$ ?
Please provide your final answer in the format \boxed{answer}. |
9 | If $x$ satisfies $\frac{1}{2}-\frac{1}{3}=\frac{3}{x}$, then what is the value of $x$ ?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{18}
Insight: Simple algebraic manipulation—computing the difference of fractions and cross-multiplying—yields the solution efficiently. | null | {
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"prompt": "If $x$ satisfies $\\frac{1}{2}-\\frac{1}{3}=\\frac{3}{x}$, then what is the value of $x$ ?\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "If $x$ satisfies $\\frac{1}{2}-\\frac{1}{3}=\\frac{3}{x}$, then what is the value of $x$ ?\n\nPlease provide... | 0 | 9 | 1 | Algebra | 18 | If $x$ satisfies $\frac{1}{2}-\frac{1}{3}=\frac{3}{x}$, then what is the value of $x$ ?
Please provide your final answer in the format \boxed{answer}. |
10 | Compute $54 \times 46$ in your head.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{2484}
Insight: For numbers symmetric around a multiple of 10, the difference of squares formula provides a quick mental calculation method. | null | {
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"prompt": "Compute $54 \\times 46$ in your head.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Compute $54 \\times 46$ in your head.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "I need to com... | 1 | 0 | 1 | Algebra | 2484 | Compute $54 \times 46$ in your head.
Please provide your final answer in the format \boxed{answer}. |
11 | Compute $54 \times 46$ in your head.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{2484} | null | {
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"prompt": "Compute $54 \\times 46$ in your head.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Compute $54 \\times 46$ in your head.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "I need to com... | 1 | 1 | 1 | Algebra | 2484 | Compute $54 \times 46$ in your head.
Please provide your final answer in the format \boxed{answer}. |
12 | Compute $54 \times 46$ in your head.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{2484}
Insight: For numbers symmetric around a round number, using the difference of squares can simplify mental multiplication. | null | {
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} | {
"prompt": "Compute $54 \\times 46$ in your head.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Compute $54 \\times 46$ in your head.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "I need to com... | 1 | 2 | 1 | Algebra | 2484 | Compute $54 \times 46$ in your head.
Please provide your final answer in the format \boxed{answer}. |
13 | Compute $54 \times 46$ in your head.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{2484} | null | {
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"prompt": "Compute $54 \\times 46$ in your head.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Compute $54 \\times 46$ in your head.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "I notice that... | 1 | 3 | 1 | Algebra | 2484 | Compute $54 \times 46$ in your head.
Please provide your final answer in the format \boxed{answer}. |
14 | Compute $54 \times 46$ in your head.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{2484}
Insight: For numbers symmetric around a multiple of 10, using the difference of squares identity simplifies mental multiplication. | null | {
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"total_llm_calls": 1,
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} | {
"prompt": "Compute $54 \\times 46$ in your head.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Compute $54 \\times 46$ in your head.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "I need to com... | 1 | 4 | 1 | Algebra | 2484 | Compute $54 \times 46$ in your head.
Please provide your final answer in the format \boxed{answer}. |
15 | Compute $54 \times 46$ in your head.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{2484}
Insight: Using the difference of squares pattern (a+b)(a-b) = a² - b² simplifies mental multiplication when the numbers are equidistant from a round number. | null | {
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"prompt": "Compute $54 \\times 46$ in your head.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Compute $54 \\times 46$ in your head.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "I notice that... | 1 | 5 | 1 | Algebra | 2484 | Compute $54 \times 46$ in your head.
Please provide your final answer in the format \boxed{answer}. |
16 | Compute $54 \times 46$ in your head.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{2484} | null | {
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} | {
"prompt": "Compute $54 \\times 46$ in your head.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Compute $54 \\times 46$ in your head.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "I need to com... | 1 | 6 | 1 | Algebra | 2484 | Compute $54 \times 46$ in your head.
Please provide your final answer in the format \boxed{answer}. |
17 | Compute $54 \times 46$ in your head.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{2484}
Insight: Recognizing patterns like difference of squares can simplify mental multiplication for numbers symmetric around a base. | null | {
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"prompt": "Compute $54 \\times 46$ in your head.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Compute $54 \\times 46$ in your head.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "I need to com... | 1 | 7 | 1 | Algebra | 2484 | Compute $54 \times 46$ in your head.
Please provide your final answer in the format \boxed{answer}. |
18 | Compute $54 \times 46$ in your head.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{2436}
Insight: Recognizing numbers as symmetric around a central value allows quick mental multiplication using the difference of squares identity. | null | {
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"total_llm_calls": 1,
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"prompt": "Compute $54 \\times 46$ in your head.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Compute $54 \\times 46$ in your head.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "I notice that... | 1 | 8 | 1 | Algebra | 2484 | Compute $54 \times 46$ in your head.
Please provide your final answer in the format \boxed{answer}. |
19 | Compute $54 \times 46$ in your head.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{2484}
Insight: When multiplying two numbers that are equidistant from a common center, the difference of squares trick provides a quick mental calculation. | null | {
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"prompt": "Compute $54 \\times 46$ in your head.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Compute $54 \\times 46$ in your head.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "I need to com... | 1 | 9 | 1 | Algebra | 2484 | Compute $54 \times 46$ in your head.
Please provide your final answer in the format \boxed{answer}. |
20 | A box with a volume of 16 $\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\text{cm}^3$ hold?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{150} | null | {
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"max_subproblems": 0,
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"prompt": "A box with a volume of 16 $\\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\\text{cm}^3$ hold?\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "A box with a volume of 16 $\\text{cm}^3$ can hold 50 papercli... | 2 | 0 | 1 | Algebra | 150 | A box with a volume of 16 $\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\text{cm}^3$ hold?
Please provide your final answer in the format \boxed{answer}. |
21 | A box with a volume of 16 $\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\text{cm}^3$ hold?
Please provide your final answer in the format \boxed{answer}. | FAILED | Tree generation failed. Reason: Maximum recursion depth (5) reached. | {
"actual_latency_seconds": 28.409852266311646,
"total_llm_calls": 5,
"max_tree_depth": 0,
"max_subproblems": 0,
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} | {
"prompt": "A box with a volume of 16 $\\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\\text{cm}^3$ hold?\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "\nWe are given that a box with volume 16 cm³ holds 50 paperclips. We want to find h... | 2 | 1 | 1 | Algebra | 150 | A box with a volume of 16 $\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\text{cm}^3$ hold?
Please provide your final answer in the format \boxed{answer}. | |
22 | A box with a volume of 16 $\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\text{cm}^3$ hold?
Please provide your final answer in the format \boxed{answer}. | FAILED | Tree generation failed. Reason: Maximum recursion depth (5) reached. | {
"actual_latency_seconds": 34.36162734031677,
"total_llm_calls": 5,
"max_tree_depth": 0,
"max_subproblems": 0,
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} | {
"prompt": "A box with a volume of 16 $\\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\\text{cm}^3$ hold?\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "\nWe can determine the number of paperclips by recognizing that the number of paper... | 2 | 2 | 1 | Algebra | 150 | A box with a volume of 16 $\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\text{cm}^3$ hold?
Please provide your final answer in the format \boxed{answer}. | |
23 | A box with a volume of 16 $\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\text{cm}^3$ hold?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{150}
Insight: For directly proportional quantities, scaling one by a factor scales the other by the same factor. | null | {
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"total_llm_calls": 1,
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} | {
"prompt": "A box with a volume of 16 $\\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\\text{cm}^3$ hold?\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "A box with a volume of 16 $\\text{cm}^3$ can hold 50 papercli... | 2 | 3 | 1 | Algebra | 150 | A box with a volume of 16 $\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\text{cm}^3$ hold?
Please provide your final answer in the format \boxed{answer}. |
24 | A box with a volume of 16 $\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\text{cm}^3$ hold?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{150} | null | {
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"prompt": "A box with a volume of 16 $\\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\\text{cm}^3$ hold?\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "A box with a volume of 16 $\\text{cm}^3$ can hold 50 papercli... | 2 | 4 | 1 | Algebra | 150 | A box with a volume of 16 $\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\text{cm}^3$ hold?
Please provide your final answer in the format \boxed{answer}. |
25 | A box with a volume of 16 $\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\text{cm}^3$ hold?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{150} | null | {
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"prompt": "A box with a volume of 16 $\\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\\text{cm}^3$ hold?\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "A box with a volume of 16 $\\text{cm}^3$ can hold 50 papercli... | 2 | 5 | 1 | Algebra | 150 | A box with a volume of 16 $\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\text{cm}^3$ hold?
Please provide your final answer in the format \boxed{answer}. |
26 | A box with a volume of 16 $\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\text{cm}^3$ hold?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{150}
Insight: Direct proportionality allows scaling by a factor of the volume ratio. | null | {
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"prompt": "A box with a volume of 16 $\\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\\text{cm}^3$ hold?\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "A box with a volume of 16 $\\text{cm}^3$ can hold 50 papercli... | 2 | 6 | 1 | Algebra | 150 | A box with a volume of 16 $\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\text{cm}^3$ hold?
Please provide your final answer in the format \boxed{answer}. |
27 | A box with a volume of 16 $\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\text{cm}^3$ hold?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{150} | null | {
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"prompt": "A box with a volume of 16 $\\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\\text{cm}^3$ hold?\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "\nThe problem involves a direct proportionality between volume and the number of pa... | 2 | 7 | 1 | Algebra | 150 | A box with a volume of 16 $\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\text{cm}^3$ hold?
Please provide your final answer in the format \boxed{answer}. |
28 | A box with a volume of 16 $\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\text{cm}^3$ hold?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{150}
Insight: For problems involving direct proportionality, scaling by the ratio of quantities is a quick and reliable method, especially when the relationship is linear and constant density is assumed. | null | {
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"prompt": "A box with a volume of 16 $\\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\\text{cm}^3$ hold?\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "\nThe problem involves a proportional relationship between box volume and paperclip... | 2 | 8 | 1 | Algebra | 150 | A box with a volume of 16 $\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\text{cm}^3$ hold?
Please provide your final answer in the format \boxed{answer}. |
29 | A box with a volume of 16 $\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\text{cm}^3$ hold?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{150} | null | {
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"prompt": "A box with a volume of 16 $\\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\\text{cm}^3$ hold?\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "A box with a volume of 16 $\\text{cm}^3$ can hold 50 papercli... | 2 | 9 | 1 | Algebra | 150 | A box with a volume of 16 $\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\text{cm}^3$ hold?
Please provide your final answer in the format \boxed{answer}. |
30 | Jeremiah is riding in a car that is traveling 60 miles per hour. At this rate, how many minutes will it take him to travel 20 miles?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{20} | null | {
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"fragment": "",
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Please provide your final answer in the format \boxed{answer}. |
31 | Jeremiah is riding in a car that is traveling 60 miles per hour. At this rate, how many minutes will it take him to travel 20 miles?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{20} | null | {
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"fragment": "",
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Please provide your final answer in the format \boxed{answer}. |
32 | Jeremiah is riding in a car that is traveling 60 miles per hour. At this rate, how many minutes will it take him to travel 20 miles?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{20} | null | {
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"prompt": "Jeremiah is riding in a car that is traveling 60 miles per hour. At this rate, how many minutes will it take him to travel 20 miles?\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
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Please provide your final answer in the format \boxed{answer}. |
33 | Jeremiah is riding in a car that is traveling 60 miles per hour. At this rate, how many minutes will it take him to travel 20 miles?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{20} | null | {
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"prompt": "Jeremiah is riding in a car that is traveling 60 miles per hour. At this rate, how many minutes will it take him to travel 20 miles?\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Jeremiah is riding in a car that is traveling 60 miles per hour. A... | 3 | 3 | 1 | Algebra | 20 | Jeremiah is riding in a car that is traveling 60 miles per hour. At this rate, how many minutes will it take him to travel 20 miles?
Please provide your final answer in the format \boxed{answer}. |
34 | Jeremiah is riding in a car that is traveling 60 miles per hour. At this rate, how many minutes will it take him to travel 20 miles?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{20} | null | {
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} | {
"prompt": "Jeremiah is riding in a car that is traveling 60 miles per hour. At this rate, how many minutes will it take him to travel 20 miles?\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Jeremiah is riding in a car that is traveling 60 miles per hour. A... | 3 | 4 | 1 | Algebra | 20 | Jeremiah is riding in a car that is traveling 60 miles per hour. At this rate, how many minutes will it take him to travel 20 miles?
Please provide your final answer in the format \boxed{answer}. |
35 | Jeremiah is riding in a car that is traveling 60 miles per hour. At this rate, how many minutes will it take him to travel 20 miles?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{20}
Insight: This problem demonstrates the basic relationship between distance, rate, and time: time = distance / rate. When rate is constant, the calculation is straightforward. | null | {
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"prompt": "Jeremiah is riding in a car that is traveling 60 miles per hour. At this rate, how many minutes will it take him to travel 20 miles?\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Jeremiah is riding in a car that is traveling 60 miles per hour. A... | 3 | 5 | 1 | Algebra | 20 | Jeremiah is riding in a car that is traveling 60 miles per hour. At this rate, how many minutes will it take him to travel 20 miles?
Please provide your final answer in the format \boxed{answer}. |
36 | Jeremiah is riding in a car that is traveling 60 miles per hour. At this rate, how many minutes will it take him to travel 20 miles?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{20}
Insight: When speed is 60 mph, the time in minutes equals the distance in miles, a useful shortcut for similar problems. | null | {
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"prompt": "Jeremiah is riding in a car that is traveling 60 miles per hour. At this rate, how many minutes will it take him to travel 20 miles?\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Jeremiah is riding in a car that is traveling 60 miles per hour. A... | 3 | 6 | 1 | Algebra | 20 | Jeremiah is riding in a car that is traveling 60 miles per hour. At this rate, how many minutes will it take him to travel 20 miles?
Please provide your final answer in the format \boxed{answer}. |
37 | Jeremiah is riding in a car that is traveling 60 miles per hour. At this rate, how many minutes will it take him to travel 20 miles?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
20 minutes
Insight: When speed is constant, time is proportional to distance. This simple proportion can be used for similar distance-rate-time problems. | null | {
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"fragment": "",
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Please provide your final answer in the format \boxed{answer}. |
38 | Jeremiah is riding in a car that is traveling 60 miles per hour. At this rate, how many minutes will it take him to travel 20 miles?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{20} | null | {
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Please provide your final answer in the format \boxed{answer}. |
39 | Jeremiah is riding in a car that is traveling 60 miles per hour. At this rate, how many minutes will it take him to travel 20 miles?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{20} | null | {
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Please provide your final answer in the format \boxed{answer}. |
40 | Evaluate: $(723)(723)-(722)(724)$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{1} | null | {
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"main_problem": "Evaluate: $(723)(723)-(722)(724)$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "I notice that the e... | 4 | 0 | 1 | Algebra | 1 | Evaluate: $(723)(723)-(722)(724)$.
Please provide your final answer in the format \boxed{answer}. |
41 | Evaluate: $(723)(723)-(722)(724)$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{1} | null | {
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"prompt": "Evaluate: $(723)(723)-(722)(724)$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
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"main_problem": "Evaluate: $(723)(723)-(722)(724)$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "We need to compute ... | 4 | 1 | 1 | Algebra | 1 | Evaluate: $(723)(723)-(722)(724)$.
Please provide your final answer in the format \boxed{answer}. |
42 | Evaluate: $(723)(723)-(722)(724)$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{1} | null | {
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"prompt": "Evaluate: $(723)(723)-(722)(724)$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "\n\nI need to compute (723)(723) - (722)(724). This is a difference of products. I can compute each product separately, then subtract. But maybe there's a simpler algebraic way: note tha... | 4 | 2 | 1 | Algebra | 1 | Evaluate: $(723)(723)-(722)(724)$.
Please provide your final answer in the format \boxed{answer}. |
43 | Evaluate: $(723)(723)-(722)(724)$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{1} | null | {
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"prompt": "Evaluate: $(723)(723)-(722)(724)$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Evaluate: $(723)(723)-(722)(724)$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "Observe that this e... | 4 | 3 | 1 | Algebra | 1 | Evaluate: $(723)(723)-(722)(724)$.
Please provide your final answer in the format \boxed{answer}. |
44 | Evaluate: $(723)(723)-(722)(724)$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{1}
Insight: Algebraic substitution can simplify evaluation of numerical expressions, revealing elegant patterns. | null | {
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"prompt": "Evaluate: $(723)(723)-(722)(724)$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Evaluate: $(723)(723)-(722)(724)$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "I recognize this ex... | 4 | 4 | 1 | Algebra | 1 | Evaluate: $(723)(723)-(722)(724)$.
Please provide your final answer in the format \boxed{answer}. |
45 | Evaluate: $(723)(723)-(722)(724)$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{1} | null | {
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"prompt": "Evaluate: $(723)(723)-(722)(724)$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Evaluate: $(723)(723)-(722)(724)$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "I notice that (723)... | 4 | 5 | 1 | Algebra | 1 | Evaluate: $(723)(723)-(722)(724)$.
Please provide your final answer in the format \boxed{answer}. |
46 | Evaluate: $(723)(723)-(722)(724)$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{1} | null | {
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"prompt": "Evaluate: $(723)(723)-(722)(724)$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Evaluate: $(723)(723)-(722)(724)$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "The expression is o... | 4 | 6 | 1 | Algebra | 1 | Evaluate: $(723)(723)-(722)(724)$.
Please provide your final answer in the format \boxed{answer}. |
47 | Evaluate: $(723)(723)-(722)(724)$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{1}
Insight: For any number a, (a-1)(a+1) = a^2 - 1, so a^2 - (a-1)(a+1) = 1. This pattern simplifies many such expressions. | null | {
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"prompt": "Evaluate: $(723)(723)-(722)(724)$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
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"main_problem": "Evaluate: $(723)(723)-(722)(724)$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "I need to compute t... | 4 | 7 | 1 | Algebra | 1 | Evaluate: $(723)(723)-(722)(724)$.
Please provide your final answer in the format \boxed{answer}. |
48 | Evaluate: $(723)(723)-(722)(724)$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
1
Insight: Recognizing patterns like \(a^2 - (a-1)(a+1)\) allows quick simplification to 1 without direct multiplication. | null | {
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"prompt": "Evaluate: $(723)(723)-(722)(724)$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Evaluate: $(723)(723)-(722)(724)$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "I notice this expre... | 4 | 8 | 1 | Algebra | 1 | Evaluate: $(723)(723)-(722)(724)$.
Please provide your final answer in the format \boxed{answer}. |
49 | Evaluate: $(723)(723)-(722)(724)$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{1}
Insight: Recognizing patterns like $(n-1)(n+1)=n^2-1$ can simplify expressions involving products of numbers close to a common value. | null | {
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"prompt": "Evaluate: $(723)(723)-(722)(724)$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "\n\nI need to evaluate the expression $(723)(723)-(722)(724)$. I can think of two different approaches: one is to compute each product directly and then subtract, and the other is to use... | 4 | 9 | 1 | Algebra | 1 | Evaluate: $(723)(723)-(722)(724)$.
Please provide your final answer in the format \boxed{answer}. |
50 | Evaluate $\log_327$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{3}
Insight: This is a direct application of the definition of logarithm when the argument is a power of the base, a basic pattern in evaluating logarithms. | null | {
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"prompt": "Evaluate $\\log_327$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
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"main_problem": "Evaluate $\\log_327$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "I need to compute the logarithm base 3 of 27.... | 5 | 0 | 1 | Algebra | 3 | Evaluate $\log_327$.
Please provide your final answer in the format \boxed{answer}. |
51 | Evaluate $\log_327$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{3} | null | {
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"prompt": "Evaluate $\\log_327$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Evaluate $\\log_327$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "I need to evaluate \\(\\log_3 27\\). Recogniz... | 5 | 1 | 1 | Algebra | 3 | Evaluate $\log_327$.
Please provide your final answer in the format \boxed{answer}. |
52 | Evaluate $\log_327$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{3}
Insight: When evaluating logarithms of the form log_b(a), check if a can be expressed as a power of b; if a = b^k, then log_b(a) = k. | null | {
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"prompt": "Evaluate $\\log_327$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Evaluate $\\log_327$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "I need to evaluate log base 3 of 27. Since 27... | 5 | 2 | 1 | Algebra | 3 | Evaluate $\log_327$.
Please provide your final answer in the format \boxed{answer}. |
53 | Evaluate $\log_327$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{3} | null | {
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"prompt": "Evaluate $\\log_327$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Evaluate $\\log_327$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "I need to evaluate \\(\\log_3 27\\). Recogniz... | 5 | 3 | 1 | Algebra | 3 | Evaluate $\log_327$.
Please provide your final answer in the format \boxed{answer}. |
54 | Evaluate $\log_327$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{3} | null | {
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} | {
"prompt": "Evaluate $\\log_327$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Evaluate $\\log_327$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "I need to evaluate log base 3 of 27. I know t... | 5 | 4 | 1 | Algebra | 3 | Evaluate $\log_327$.
Please provide your final answer in the format \boxed{answer}. |
55 | Evaluate $\log_327$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{3}
Insight: For evaluating logarithms of powers of the base, use the property log_b(b^x) = x. | null | {
"actual_latency_seconds": 4.122848987579346,
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"prompt": "Evaluate $\\log_327$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Evaluate $\\log_327$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "I need to evaluate log base 3 of 27. This is ... | 5 | 5 | 1 | Algebra | 3 | Evaluate $\log_327$.
Please provide your final answer in the format \boxed{answer}. |
56 | Evaluate $\log_327$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{3}
Insight: This problem demonstrates the basic logarithm definition: $\log_b b^k = k$. | null | {
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"prompt": "Evaluate $\\log_327$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Evaluate $\\log_327$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "To evaluate $\\log_3 27$, I recall that the l... | 5 | 6 | 1 | Algebra | 3 | Evaluate $\log_327$.
Please provide your final answer in the format \boxed{answer}. |
57 | Evaluate $\log_327$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{3} | null | {
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"prompt": "Evaluate $\\log_327$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Evaluate $\\log_327$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "I need to evaluate log base 3 of 27. I recall... | 5 | 7 | 1 | Algebra | 3 | Evaluate $\log_327$.
Please provide your final answer in the format \boxed{answer}. |
58 | Evaluate $\log_327$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{3}
Insight: For evaluating logarithms of the form \(\log_b (b^k)\), the answer is simply \(k\). Here \(b=3\) and \(k=3\). | null | {
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"prompt": "Evaluate $\\log_327$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Evaluate $\\log_327$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "We are asked to evaluate \\(\\log_3 27\\). Th... | 5 | 8 | 1 | Algebra | 3 | Evaluate $\log_327$.
Please provide your final answer in the format \boxed{answer}. |
59 | Evaluate $\log_327$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{3} | null | {
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"prompt": "Evaluate $\\log_327$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Evaluate $\\log_327$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "I need to evaluate \\(\\log_3 27\\). This is ... | 5 | 9 | 1 | Algebra | 3 | Evaluate $\log_327$.
Please provide your final answer in the format \boxed{answer}. |
60 | Evaluate $3x^2+5x-1$ if $x=7$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{181} | null | {
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} | {
"prompt": "Evaluate $3x^2+5x-1$ if $x=7$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Evaluate $3x^2+5x-1$ if $x=7$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "We need to compute the valu... | 6 | 0 | 1 | Algebra | 181 | Evaluate $3x^2+5x-1$ if $x=7$.
Please provide your final answer in the format \boxed{answer}. |
61 | Evaluate $3x^2+5x-1$ if $x=7$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{181} | null | {
"actual_latency_seconds": 20.89598512649536,
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"prompt": "Evaluate $3x^2+5x-1$ if $x=7$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "\n\nWe are asked to evaluate the quadratic expression \\(3x^2+5x-1\\) when \\(x=7\\). This is a straightforward substitution problem. We can compute each term separately: first, \\(x^2 = 7^2... | 6 | 1 | 1 | Algebra | 181 | Evaluate $3x^2+5x-1$ if $x=7$.
Please provide your final answer in the format \boxed{answer}. |
62 | Evaluate $3x^2+5x-1$ if $x=7$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{181} | null | {
"actual_latency_seconds": 6.667558908462524,
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"prompt": "Evaluate $3x^2+5x-1$ if $x=7$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Evaluate $3x^2+5x-1$ if $x=7$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "I need to evaluate the expr... | 6 | 2 | 1 | Algebra | 181 | Evaluate $3x^2+5x-1$ if $x=7$.
Please provide your final answer in the format \boxed{answer}. |
63 | Evaluate $3x^2+5x-1$ if $x=7$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{181} | null | {
"actual_latency_seconds": 7.9514479637146,
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"prompt": "Evaluate $3x^2+5x-1$ if $x=7$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Evaluate $3x^2+5x-1$ if $x=7$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "To evaluate the expression ... | 6 | 3 | 1 | Algebra | 181 | Evaluate $3x^2+5x-1$ if $x=7$.
Please provide your final answer in the format \boxed{answer}. |
64 | Evaluate $3x^2+5x-1$ if $x=7$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{181} | null | {
"actual_latency_seconds": 6.006285667419434,
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} | {
"prompt": "Evaluate $3x^2+5x-1$ if $x=7$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Evaluate $3x^2+5x-1$ if $x=7$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "To evaluate the expression ... | 6 | 4 | 1 | Algebra | 181 | Evaluate $3x^2+5x-1$ if $x=7$.
Please provide your final answer in the format \boxed{answer}. |
65 | Evaluate $3x^2+5x-1$ if $x=7$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{181} | null | {
"actual_latency_seconds": 7.922222375869751,
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"prompt": "Evaluate $3x^2+5x-1$ if $x=7$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Evaluate $3x^2+5x-1$ if $x=7$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "To evaluate the expression ... | 6 | 5 | 1 | Algebra | 181 | Evaluate $3x^2+5x-1$ if $x=7$.
Please provide your final answer in the format \boxed{answer}. |
66 | Evaluate $3x^2+5x-1$ if $x=7$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{181} | null | {
"actual_latency_seconds": 6.987624168395996,
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} | {
"prompt": "Evaluate $3x^2+5x-1$ if $x=7$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Evaluate $3x^2+5x-1$ if $x=7$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "To evaluate the polynomial ... | 6 | 6 | 1 | Algebra | 181 | Evaluate $3x^2+5x-1$ if $x=7$.
Please provide your final answer in the format \boxed{answer}. |
67 | Evaluate $3x^2+5x-1$ if $x=7$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{181}
Insight: Direct substitution and order of operations (PEMDAS/BODMAS) are reliable for evaluating polynomial expressions. | null | {
"actual_latency_seconds": 9.118818521499634,
"total_llm_calls": 1,
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} | {
"prompt": "Evaluate $3x^2+5x-1$ if $x=7$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Evaluate $3x^2+5x-1$ if $x=7$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "To evaluate \\(3x^2 + 5x - ... | 6 | 7 | 1 | Algebra | 181 | Evaluate $3x^2+5x-1$ if $x=7$.
Please provide your final answer in the format \boxed{answer}. |
68 | Evaluate $3x^2+5x-1$ if $x=7$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{181}
Insight: Evaluating a polynomial at a given value can be efficiently broken into independent arithmetic computations, demonstrating the utility of parallel processing for straightforward calculations. | null | {
"actual_latency_seconds": 21.946310997009277,
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"prompt": "Evaluate $3x^2+5x-1$ if $x=7$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "\n\nTo evaluate the quadratic expression \\(3x^2+5x-1\\) at \\(x=7\\), we can break it into three independent arithmetic computations: \\(3 \\times 7^2\\), \\(5 \\times 7\\), and the constan... | 6 | 8 | 1 | Algebra | 181 | Evaluate $3x^2+5x-1$ if $x=7$.
Please provide your final answer in the format \boxed{answer}. |
69 | Evaluate $3x^2+5x-1$ if $x=7$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
181
Insight: Evaluating a polynomial at a specific value can be efficiently done by breaking it into independent term computations, which can be performed in parallel. This decomposition approach is applicable to any polynomial evaluation. | null | {
"actual_latency_seconds": 20.615360975265503,
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} | {
"prompt": "Evaluate $3x^2+5x-1$ if $x=7$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "\n\nWe need to evaluate the quadratic expression at x=7. Since the operations are straightforward and each term can be computed independently, we can decompose into three parallel tasks: com... | 6 | 9 | 1 | Algebra | 181 | Evaluate $3x^2+5x-1$ if $x=7$.
Please provide your final answer in the format \boxed{answer}. |
70 | Compute the value of $252^2 - 248^2$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{2000}
Insight: The difference of squares formula simplifies calculations for expressions like \(x^2 - y^2\) when \(x\) and \(y\) are close integers. | null | {
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"prompt": "Compute the value of $252^2 - 248^2$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Compute the value of $252^2 - 248^2$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "To compute \\... | 7 | 0 | 1 | Algebra | 2000 | Compute the value of $252^2 - 248^2$.
Please provide your final answer in the format \boxed{answer}. |
71 | Compute the value of $252^2 - 248^2$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{2000} | null | {
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"prompt": "Compute the value of $252^2 - 248^2$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Compute the value of $252^2 - 248^2$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "We can comput... | 7 | 1 | 1 | Algebra | 2000 | Compute the value of $252^2 - 248^2$.
Please provide your final answer in the format \boxed{answer}. |
72 | Compute the value of $252^2 - 248^2$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{2000} | null | {
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} | {
"prompt": "Compute the value of $252^2 - 248^2$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Compute the value of $252^2 - 248^2$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "We can comput... | 7 | 2 | 1 | Algebra | 2000 | Compute the value of $252^2 - 248^2$.
Please provide your final answer in the format \boxed{answer}. |
73 | Compute the value of $252^2 - 248^2$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{2000}
Insight: Recognizing difference of squares simplifies computation, especially when numbers are close. | null | {
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"prompt": "Compute the value of $252^2 - 248^2$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Compute the value of $252^2 - 248^2$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "I can compute... | 7 | 3 | 1 | Algebra | 2000 | Compute the value of $252^2 - 248^2$.
Please provide your final answer in the format \boxed{answer}. |
74 | Compute the value of $252^2 - 248^2$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{2000} | null | {
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"prompt": "Compute the value of $252^2 - 248^2$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Compute the value of $252^2 - 248^2$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "I can compute... | 7 | 4 | 1 | Algebra | 2000 | Compute the value of $252^2 - 248^2$.
Please provide your final answer in the format \boxed{answer}. |
75 | Compute the value of $252^2 - 248^2$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{2000} | null | {
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"prompt": "Compute the value of $252^2 - 248^2$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Compute the value of $252^2 - 248^2$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "I need to com... | 7 | 5 | 1 | Algebra | 2000 | Compute the value of $252^2 - 248^2$.
Please provide your final answer in the format \boxed{answer}. |
76 | Compute the value of $252^2 - 248^2$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{2000} | null | {
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"prompt": "Compute the value of $252^2 - 248^2$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Compute the value of $252^2 - 248^2$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "To find the v... | 7 | 6 | 1 | Algebra | 2000 | Compute the value of $252^2 - 248^2$.
Please provide your final answer in the format \boxed{answer}. |
77 | Compute the value of $252^2 - 248^2$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{2000} | null | {
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"theoretical_parallel_latency": 9.29981255531311
} | {
"prompt": "Compute the value of $252^2 - 248^2$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Compute the value of $252^2 - 248^2$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "I can compute... | 7 | 7 | 1 | Algebra | 2000 | Compute the value of $252^2 - 248^2$.
Please provide your final answer in the format \boxed{answer}. |
78 | Compute the value of $252^2 - 248^2$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{2000}
Insight: Using the difference of squares formula simplifies the computation and reduces the chance of arithmetic errors. | null | {
"actual_latency_seconds": 8.815506219863892,
"total_llm_calls": 1,
"max_tree_depth": 0,
"max_subproblems": 0,
"max_output_chars": 454,
"theoretical_parallel_latency": 8.814608097076416
} | {
"prompt": "Compute the value of $252^2 - 248^2$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Compute the value of $252^2 - 248^2$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "I need to com... | 7 | 8 | 1 | Algebra | 2000 | Compute the value of $252^2 - 248^2$.
Please provide your final answer in the format \boxed{answer}. |
79 | Compute the value of $252^2 - 248^2$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{2000}
Insight: Using the difference of squares formula simplifies the calculation significantly, especially when the numbers are close together. | null | {
"actual_latency_seconds": 6.745598793029785,
"total_llm_calls": 1,
"max_tree_depth": 0,
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"max_output_chars": 345,
"theoretical_parallel_latency": 6.744747638702393
} | {
"prompt": "Compute the value of $252^2 - 248^2$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Compute the value of $252^2 - 248^2$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "I need to com... | 7 | 9 | 1 | Algebra | 2000 | Compute the value of $252^2 - 248^2$.
Please provide your final answer in the format \boxed{answer}. |
80 | Jasmine drank 1.5 pints of water on the first 3 miles of her hike. If she continued at this rate, how many pints of water would she drink in the next 10 miles?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{5}
Insight: The problem demonstrates a direct proportionality between distance and water consumption, where the constant rate can be used to compute consumption for any distance. | null | {
"actual_latency_seconds": 10.208938598632812,
"total_llm_calls": 1,
"max_tree_depth": 0,
"max_subproblems": 0,
"max_output_chars": 687,
"theoretical_parallel_latency": 10.208251476287842
} | {
"prompt": "Jasmine drank 1.5 pints of water on the first 3 miles of her hike. If she continued at this rate, how many pints of water would she drink in the next 10 miles?\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Jasmine drank 1.5 pints of water on the... | 8 | 0 | 1 | Algebra | 5 | Jasmine drank 1.5 pints of water on the first 3 miles of her hike. If she continued at this rate, how many pints of water would she drink in the next 10 miles?
Please provide your final answer in the format \boxed{answer}. |
81 | Jasmine drank 1.5 pints of water on the first 3 miles of her hike. If she continued at this rate, how many pints of water would she drink in the next 10 miles?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{5} | null | {
"actual_latency_seconds": 5.110098361968994,
"total_llm_calls": 1,
"max_tree_depth": 0,
"max_subproblems": 0,
"max_output_chars": 287,
"theoretical_parallel_latency": 5.109076023101807
} | {
"prompt": "Jasmine drank 1.5 pints of water on the first 3 miles of her hike. If she continued at this rate, how many pints of water would she drink in the next 10 miles?\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Jasmine drank 1.5 pints of water on the... | 8 | 1 | 1 | Algebra | 5 | Jasmine drank 1.5 pints of water on the first 3 miles of her hike. If she continued at this rate, how many pints of water would she drink in the next 10 miles?
Please provide your final answer in the format \boxed{answer}. |
82 | Jasmine drank 1.5 pints of water on the first 3 miles of her hike. If she continued at this rate, how many pints of water would she drink in the next 10 miles?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{5} | null | {
"actual_latency_seconds": 4.310041427612305,
"total_llm_calls": 1,
"max_tree_depth": 0,
"max_subproblems": 0,
"max_output_chars": 207,
"theoretical_parallel_latency": 4.309345006942749
} | {
"prompt": "Jasmine drank 1.5 pints of water on the first 3 miles of her hike. If she continued at this rate, how many pints of water would she drink in the next 10 miles?\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Jasmine drank 1.5 pints of water on the... | 8 | 2 | 1 | Algebra | 5 | Jasmine drank 1.5 pints of water on the first 3 miles of her hike. If she continued at this rate, how many pints of water would she drink in the next 10 miles?
Please provide your final answer in the format \boxed{answer}. |
83 | Jasmine drank 1.5 pints of water on the first 3 miles of her hike. If she continued at this rate, how many pints of water would she drink in the next 10 miles?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{5} | null | {
"actual_latency_seconds": 4.020493030548096,
"total_llm_calls": 1,
"max_tree_depth": 0,
"max_subproblems": 0,
"max_output_chars": 215,
"theoretical_parallel_latency": 4.019701719284058
} | {
"prompt": "Jasmine drank 1.5 pints of water on the first 3 miles of her hike. If she continued at this rate, how many pints of water would she drink in the next 10 miles?\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Jasmine drank 1.5 pints of water on the... | 8 | 3 | 1 | Algebra | 5 | Jasmine drank 1.5 pints of water on the first 3 miles of her hike. If she continued at this rate, how many pints of water would she drink in the next 10 miles?
Please provide your final answer in the format \boxed{answer}. |
84 | Jasmine drank 1.5 pints of water on the first 3 miles of her hike. If she continued at this rate, how many pints of water would she drink in the next 10 miles?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{5} | null | {
"actual_latency_seconds": 4.614295959472656,
"total_llm_calls": 1,
"max_tree_depth": 0,
"max_subproblems": 0,
"max_output_chars": 235,
"theoretical_parallel_latency": 4.613529920578003
} | {
"prompt": "Jasmine drank 1.5 pints of water on the first 3 miles of her hike. If she continued at this rate, how many pints of water would she drink in the next 10 miles?\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Jasmine drank 1.5 pints of water on the... | 8 | 4 | 1 | Algebra | 5 | Jasmine drank 1.5 pints of water on the first 3 miles of her hike. If she continued at this rate, how many pints of water would she drink in the next 10 miles?
Please provide your final answer in the format \boxed{answer}. |
85 | Jasmine drank 1.5 pints of water on the first 3 miles of her hike. If she continued at this rate, how many pints of water would she drink in the next 10 miles?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{5} | null | {
"actual_latency_seconds": 4.513452053070068,
"total_llm_calls": 1,
"max_tree_depth": 0,
"max_subproblems": 0,
"max_output_chars": 236,
"theoretical_parallel_latency": 4.512455701828003
} | {
"prompt": "Jasmine drank 1.5 pints of water on the first 3 miles of her hike. If she continued at this rate, how many pints of water would she drink in the next 10 miles?\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Jasmine drank 1.5 pints of water on the... | 8 | 5 | 1 | Algebra | 5 | Jasmine drank 1.5 pints of water on the first 3 miles of her hike. If she continued at this rate, how many pints of water would she drink in the next 10 miles?
Please provide your final answer in the format \boxed{answer}. |
86 | Jasmine drank 1.5 pints of water on the first 3 miles of her hike. If she continued at this rate, how many pints of water would she drink in the next 10 miles?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{5}
Insight: For constant rate problems, the amount consumed is directly proportional to the distance, so we can use simple multiplication of rate by distance. | null | {
"actual_latency_seconds": 7.77403712272644,
"total_llm_calls": 1,
"max_tree_depth": 0,
"max_subproblems": 0,
"max_output_chars": 573,
"theoretical_parallel_latency": 7.773215293884277
} | {
"prompt": "Jasmine drank 1.5 pints of water on the first 3 miles of her hike. If she continued at this rate, how many pints of water would she drink in the next 10 miles?\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Jasmine drank 1.5 pints of water on the... | 8 | 6 | 1 | Algebra | 5 | Jasmine drank 1.5 pints of water on the first 3 miles of her hike. If she continued at this rate, how many pints of water would she drink in the next 10 miles?
Please provide your final answer in the format \boxed{answer}. |
87 | Jasmine drank 1.5 pints of water on the first 3 miles of her hike. If she continued at this rate, how many pints of water would she drink in the next 10 miles?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{5} | null | {
"actual_latency_seconds": 23.409605264663696,
"total_llm_calls": 4,
"max_tree_depth": 1,
"max_subproblems": 2,
"max_output_chars": 1020,
"theoretical_parallel_latency": 23.408543348312378
} | {
"prompt": "Jasmine drank 1.5 pints of water on the first 3 miles of her hike. If she continued at this rate, how many pints of water would she drink in the next 10 miles?\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "\n\nTo solve this problem, I need to determine the rate of wa... | 8 | 7 | 1 | Algebra | 5 | Jasmine drank 1.5 pints of water on the first 3 miles of her hike. If she continued at this rate, how many pints of water would she drink in the next 10 miles?
Please provide your final answer in the format \boxed{answer}. |
88 | Jasmine drank 1.5 pints of water on the first 3 miles of her hike. If she continued at this rate, how many pints of water would she drink in the next 10 miles?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{5} | null | {
"actual_latency_seconds": 4.6861252784729,
"total_llm_calls": 1,
"max_tree_depth": 0,
"max_subproblems": 0,
"max_output_chars": 266,
"theoretical_parallel_latency": 4.685331583023071
} | {
"prompt": "Jasmine drank 1.5 pints of water on the first 3 miles of her hike. If she continued at this rate, how many pints of water would she drink in the next 10 miles?\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Jasmine drank 1.5 pints of water on the... | 8 | 8 | 1 | Algebra | 5 | Jasmine drank 1.5 pints of water on the first 3 miles of her hike. If she continued at this rate, how many pints of water would she drink in the next 10 miles?
Please provide your final answer in the format \boxed{answer}. |
89 | Jasmine drank 1.5 pints of water on the first 3 miles of her hike. If she continued at this rate, how many pints of water would she drink in the next 10 miles?
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{5}
Insight: When a rate is constant, the amount consumed over a distance is simply the rate multiplied by the distance. | null | {
"actual_latency_seconds": 4.982197046279907,
"total_llm_calls": 1,
"max_tree_depth": 0,
"max_subproblems": 0,
"max_output_chars": 304,
"theoretical_parallel_latency": 4.981405019760132
} | {
"prompt": "Jasmine drank 1.5 pints of water on the first 3 miles of her hike. If she continued at this rate, how many pints of water would she drink in the next 10 miles?\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Jasmine drank 1.5 pints of water on the... | 8 | 9 | 1 | Algebra | 5 | Jasmine drank 1.5 pints of water on the first 3 miles of her hike. If she continued at this rate, how many pints of water would she drink in the next 10 miles?
Please provide your final answer in the format \boxed{answer}. |
90 | Compute $139+27+23+11$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{200} | null | {
"actual_latency_seconds": 17.694568634033203,
"total_llm_calls": 4,
"max_tree_depth": 1,
"max_subproblems": 2,
"max_output_chars": 425,
"theoretical_parallel_latency": 17.69287919998169
} | {
"prompt": "Compute $139+27+23+11$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "\n\nI need to compute the sum of four numbers: 139, 27, 23, and 11. I can delegate this into two independent sub-sums to work in parallel. First, compute 139 + 27. Second, compute 23 + 11. These ar... | 9 | 0 | 1 | Algebra | 200 | Compute $139+27+23+11$.
Please provide your final answer in the format \boxed{answer}. |
91 | Compute $139+27+23+11$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{200}
Insight: When adding multiple numbers, grouping pairs that sum to round numbers can simplify mental calculation. | null | {
"actual_latency_seconds": 10.025477170944214,
"total_llm_calls": 1,
"max_tree_depth": 0,
"max_subproblems": 0,
"max_output_chars": 513,
"theoretical_parallel_latency": 10.02491307258606
} | {
"prompt": "Compute $139+27+23+11$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Compute $139+27+23+11$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "I need to compute 139+27+23+11. This is a... | 9 | 1 | 1 | Algebra | 200 | Compute $139+27+23+11$.
Please provide your final answer in the format \boxed{answer}. |
92 | Compute $139+27+23+11$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{200} | null | {
"actual_latency_seconds": 14.359508752822876,
"total_llm_calls": 4,
"max_tree_depth": 1,
"max_subproblems": 2,
"max_output_chars": 311,
"theoretical_parallel_latency": 14.358450174331665
} | {
"prompt": "Compute $139+27+23+11$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "\n\nWe need to compute 139 + 27 + 23 + 11. To break this down into independent sub-tasks, we can first sum two pairs: 139 + 27 and 23 + 11. These two sums are independent and can be computed in par... | 9 | 2 | 1 | Algebra | 200 | Compute $139+27+23+11$.
Please provide your final answer in the format \boxed{answer}. |
93 | Compute $139+27+23+11$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{200} | null | {
"actual_latency_seconds": 7.677954912185669,
"total_llm_calls": 1,
"max_tree_depth": 0,
"max_subproblems": 0,
"max_output_chars": 372,
"theoretical_parallel_latency": 7.6768574714660645
} | {
"prompt": "Compute $139+27+23+11$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Compute $139+27+23+11$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "I need to compute the sum of 139, 27, 23,... | 9 | 3 | 1 | Algebra | 200 | Compute $139+27+23+11$.
Please provide your final answer in the format \boxed{answer}. |
94 | Compute $139+27+23+11$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{200}
Insight: Adding numbers in pairs can simplify mental calculation. | null | {
"actual_latency_seconds": 4.055476903915405,
"total_llm_calls": 1,
"max_tree_depth": 0,
"max_subproblems": 0,
"max_output_chars": 198,
"theoretical_parallel_latency": 4.054578065872192
} | {
"prompt": "Compute $139+27+23+11$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Compute $139+27+23+11$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "I can compute the sum step by step. Start... | 9 | 4 | 1 | Algebra | 200 | Compute $139+27+23+11$.
Please provide your final answer in the format \boxed{answer}. |
95 | Compute $139+27+23+11$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{200} | null | {
"actual_latency_seconds": 3.561123847961426,
"total_llm_calls": 1,
"max_tree_depth": 0,
"max_subproblems": 0,
"max_output_chars": 168,
"theoretical_parallel_latency": 3.5603106021881104
} | {
"prompt": "Compute $139+27+23+11$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Compute $139+27+23+11$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "I can compute this sum by grouping number... | 9 | 5 | 1 | Algebra | 200 | Compute $139+27+23+11$.
Please provide your final answer in the format \boxed{answer}. |
96 | Compute $139+27+23+11$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{200} | null | {
"actual_latency_seconds": 9.198818445205688,
"total_llm_calls": 1,
"max_tree_depth": 0,
"max_subproblems": 0,
"max_output_chars": 411,
"theoretical_parallel_latency": 9.198036670684814
} | {
"prompt": "Compute $139+27+23+11$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Compute $139+27+23+11$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "We need to compute the sum of 139, 27, 23... | 9 | 6 | 1 | Algebra | 200 | Compute $139+27+23+11$.
Please provide your final answer in the format \boxed{answer}. |
97 | Compute $139+27+23+11$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{250} | null | {
"actual_latency_seconds": 21.756832599639893,
"total_llm_calls": 5,
"max_tree_depth": 1,
"max_subproblems": 3,
"max_output_chars": 623,
"theoretical_parallel_latency": 21.754706621170044
} | {
"prompt": "Compute $139+27+23+11$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "\n\nWe need to compute 139+27+23+11. To minimize errors, we can break the computation into smaller independent additions. Each pair addition is a trivial arithmetic operation that can be performed ... | 9 | 7 | 1 | Algebra | 200 | Compute $139+27+23+11$.
Please provide your final answer in the format \boxed{answer}. |
98 | Compute $139+27+23+11$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{200}
Insight: Breaking a larger sum into smaller independent additions allows for parallel computation, and the results can be combined straightforwardly. | null | {
"actual_latency_seconds": 16.928052186965942,
"total_llm_calls": 4,
"max_tree_depth": 1,
"max_subproblems": 2,
"max_output_chars": 388,
"theoretical_parallel_latency": 16.926332712173462
} | {
"prompt": "Compute $139+27+23+11$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "\n\nI need to compute the sum of four numbers: 139, 27, 23, and 11. I can break this into two independent additions: first, add 139 and 27, and second, add 23 and 11. These are simpler tasks that c... | 9 | 8 | 1 | Algebra | 200 | Compute $139+27+23+11$.
Please provide your final answer in the format \boxed{answer}. |
99 | Compute $139+27+23+11$.
Please provide your final answer in the format \boxed{answer}. | SUCCESS |
\boxed{200} | null | {
"actual_latency_seconds": 9.224208116531372,
"total_llm_calls": 1,
"max_tree_depth": 0,
"max_subproblems": 0,
"max_output_chars": 422,
"theoretical_parallel_latency": 9.223542213439941
} | {
"prompt": "Compute $139+27+23+11$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"fragment": "",
"main_problem": "Compute $139+27+23+11$.\n\nPlease provide your final answer in the format \\boxed{answer}.",
"parent_problem": "None",
"output": "To compute the sum \\(139+27+23+11\\), I ... | 9 | 9 | 1 | Algebra | 200 | Compute $139+27+23+11$.
Please provide your final answer in the format \boxed{answer}. |
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