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YOU ARE A LLM JUDGE DETERMINING IF THE FOLLOWING MODEL GENERATED ANSWER IS THE SAME AS THE CORRECT ANSWER.
Model's Answer (last 100 chars): lowest terms $\frac{m}{n}$. Here, $ m = 1 $, $ n = 115 $.
So:
$$
m + n = 1 + 115 = \boxed{116}
$$
Correct Answer: 116
```json
{ "correctness": true/false }
```
To determine if the model's answer is the same as the correct answer, we need to compare the final result provided by the model with the correct answer.
The model's answer concludes with:
$$
m + n = 1 + 115 = \boxed{116}
$$
The correct answer is:
116
Both the model's answer and the correct answer are the same, as they both conclude with the value 116.
```json
{ "correctness": true }
```
true
[{"role":"user","content":"YOU ARE A LLM JUDGE DETERMINING IF THE FOLLOWING MODEL GENERATED ANSWER IS THE SAME AS THE CORRECT ANSWER.\nModel's Answer (last 100 chars): lowest terms $\\frac{m}{n}$. Here, $ m = 1 $, $ n = 115 $.\n\nSo:\n\n$$\nm + n = 1 + 115 = \\boxed{116}\n$$\nCorrect Answer: 116\n```json\n{ \"correctness\": true/false }\n```"}]
gpt-4o-2024-08-06
<openai.resources.chat.completions.completions.Completions object at 0x7f789a76e4d0>
0
N/A
YOU ARE A LLM JUDGE DETERMINING IF THE FOLLOWING MODEL GENERATED ANSWER IS THE SAME AS THE CORRECT ANSWER.
Model's Answer (last 100 chars): $, where $m = 25$, $n = 8$, and they are relatively prime.
Thus:
$$
m + n = 25 + 8 = \boxed{33}
$$
Correct Answer: 33
```json
{ "correctness": true/false }
```
```json
{ "correctness": true }
```
true
[{"role":"user","content":"YOU ARE A LLM JUDGE DETERMINING IF THE FOLLOWING MODEL GENERATED ANSWER IS THE SAME AS THE CORRECT ANSWER.\nModel's Answer (last 100 chars): $, where $m = 25$, $n = 8$, and they are relatively prime.\n\nThus:\n\n$$\nm + n = 25 + 8 = \\boxed{33}\n$$\nCorrect Answer: 33\n```json\n{ \"correctness\": true/false }\n```"}]
gpt-4o-2024-08-06
<openai.resources.chat.completions.completions.Completions object at 0x7f789a76e4d0>
0
N/A
YOU ARE A LLM JUDGE DETERMINING IF THE FOLLOWING MODEL GENERATED ANSWER IS THE SAME AS THE CORRECT ANSWER.
Model's Answer (last 100 chars): m = 71, n = 24
\Rightarrow m + n = 71 + 24 = \boxed{95}
$$
---
### Final Answer
$$
\boxed{95}
$$
Correct Answer: 33
```json
{ "correctness": true/false }
```
```json
{ "correctness": false }
```
true
[{"role":"user","content":"YOU ARE A LLM JUDGE DETERMINING IF THE FOLLOWING MODEL GENERATED ANSWER IS THE SAME AS THE CORRECT ANSWER.\nModel's Answer (last 100 chars): m = 71, n = 24\n\\Rightarrow m + n = 71 + 24 = \\boxed{95}\n$$\n\n---\n\n### Final Answer\n\n$$\n\\boxed{95}\n$$\nCorrect Answer: 33\n```json\n{ \"correctness\": true/false }\n```"}]
gpt-4o-2024-08-06
<openai.resources.chat.completions.completions.Completions object at 0x7fc3af8708e0>
0
N/A
1-50