# Confused with a Problem Involving sums and products of numerators/denominators

Here is the problem: if the product of the numerator and denominator of a proper fraction in simplest form is 24, what is the maximum possible sum of its numerator and denominator?

When we try to solve, the possible numerators and denominators in simplest form that would give a product of 24 would be 1,6; 2,3; 3,8; and 1,24. Thus, the factors that would give the maximum possible sum would be 1 and 24, and the sum being 25.

However, the answer key gives us 3,8 as the factors with the sum being 11. We are confused as to why this is the case that is correct. Thanks in advance for any help

• Your list is messed up; neither $1\cdot6=24$ nor $2\cdot3=24$. As regards your question: On the face of it, you seem to be right. However, experience shows that these sorts of problems often arise because people misunderstand questions and present them here in the misunderstood form, so the problem isn't visible here. The only way to tell for sure whether the error is in the text or in your work is if you quote/show the problem verbatim. – joriki Jul 5 '18 at 10:00
• Hi, the problem is quoted verbatim. My list of possible numerator-denominator factors included 1,6 and 2,3 becasue 2 x 12 = 24 and 4 x 6 = 24. Though I may have made a mistake there. Assuming these 2 pairs aren't acceptable, that leaves 1 x 24 and 3 x 8 as the possible answer. For some reason the answer key gives 3 and 8 as the factors because the final answer (sum) is 11. Thanks again for replying hope to hear your thoughts further. – RC Wong Jul 5 '18 at 15:19