\n ## Textual Document: Problem Solving Responses ### Overview The image presents a problem statement followed by three different responses generated by Large Language Models (LLMs): LLaMA-3-2-3B, LLaMA-3-1-8B, and AC (presumably an "Answer Check" or "Accuracy Check"). The problem involves calculating the cost of gift bags for a birthday party, considering that some invitees won't attend. ### Components/Axes The document is structured into the following sections: 1. **Question:** The initial problem statement. 2. **LLaMA-3-2-3B:** Response from the first LLM. 3. **LLaMA-3-1-8B:** Response from the second LLM. 4. **AC:** Response from the third source. ### Content Details **Question:** "Christina is planning a birthday party and needs .75 gift bags per invited guest, because 1/4 of attendees don't show up. She invited 16 friends. Gift bags are $2 each. How much will she spend?" **LLaMA-3-2-3B:** "Since 1/4 of attendees don't show up, we need to calculate 3/4 of the total invited guests to find out how many will attend. 3/4 of 16 is (3/4) * 16 = 12. Christina needs 0.75 gift bags per invited guest, so for 12 guests, she needs 0.75 * 12 = 9 gift bags. Each gift bag costs $2, so the total cost will be 9 gift bags * $2 per bag = $18." **LLaMA-3-1-8B:** "Christina invited 16 friends, but 1/4 of them won't show up. To find out how many will attend, we need to calculate 1/4 of 16 and subtract that from 16. To find 1/4 of 16, we divide 16 by 4. 16 / 4 = 4. Now that we know 4 guests won't come, we subtract 4 from the total number of guests invited. 16 - 4 = 12 guests will attend. Christina needs .75 gift bags per invited guest. Since she invited 16 friends, but only 12 will attend, we multiply .75 by 12. .75 * 12 = 9. Gift bags are $2 each. Since Christina needs 9 gift bags, we multiply 9 by 2. 9 * 2 = $18." **AC:** "1. Since 1/4 of the attendees don't show up, 3/4 of them will. To find the number of guests that will show up, we need to multiply the total number of invited guests by 3/4. So, 16 * 3/4 = 12 guests will show up. 2. Christina needs 0.75 gift bags per invited guest. Since she invited 16 friends, she needs 16 * 0.75 = 12 gift bags. 3. Each gift bag costs $2. Since she needs 12 gift bags, the total cost will be 12 * $2 = $24." ### Key Observations - There is a discrepancy in the final answer. LLaMA-3-2-3B and LLaMA-3-1-8B both arrive at a total cost of $18, while the AC calculates a total cost of $24. - The error in the AC's calculation lies in step 2, where it incorrectly calculates the number of gift bags needed based on the *total* number of invited guests (16) instead of the number of attendees (12). - LLaMA-3-1-8B provides a more verbose explanation of each step. - All responses correctly calculate the number of attendees as 12. ### Interpretation The document demonstrates the varying accuracy of different LLMs in solving a simple arithmetic word problem. While both LLaMA models provide the correct answer, the AC makes a logical error in its calculation, leading to an incorrect result. This highlights the importance of verifying the output of LLMs, even for seemingly straightforward tasks. The difference in verbosity between the models suggests different approaches to problem-solving and explanation generation. The AC's breakdown, while ultimately incorrect, attempts to provide a step-by-step rationale, which could be useful for debugging the error. The problem itself tests the ability to apply fractions, multiplication, and basic arithmetic in a real-world context. The discrepancy in the final answers underscores the need for careful attention to detail and logical consistency when using LLMs for problem-solving.