Multiple choice general knowledge math & puzzles

Two whole numbers, m and n, have been chosen. Both are unequal to 1 and the sum of them is less than 100. The product, m × n, is given to mathematician X. The sum, m + n, is given to mathematician Y. Then both mathematicians have the following conversation: X: "I have no idea what your sum is, Y." Y: "That's no news to me, X. I already knew you didn't know that." X: "Ahah! Now I know what your sum must be, Y!" Y: "And now I also know what your product is, X!" The Question: What are the smallest values of m and n?

  1. 5, 25

  2. 4, 13

  3. 17, 11

  4. 3, 10
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B Correct answer
Explanation

This is the classic Sum and Product Puzzle. The unique solution for the sum being less than 100 and the conversation holding true is $m = 4$ and $n = 13$, where their sum is 17 and product is 52. Other options fail the logical constraints of the mathematicians' statements.

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