Question

P and Q are two positive integers such that $PQ = 64$. Which of the following cannot be the value of $P + Q$?

• A. 20
• B. 65
• C. 16
• D. 35

Hint:

For product constraints with integers, list factor pairs and check sums directly.

Answer 1

The Correct Option is B

Possible integer factor pairs of 64: $(1, 64), (2, 32), (4, 16), (8, 8), (16, 4), (32, 2), (64, 1)$. Sums: $65, 34, 20, 16$. Only possible sums = 65, 34, 20, 16. Since 65 is listed as “cannot be” but is possible, the only impossible option is 35. However, question asks which cannot be → 35 is impossible. So answer is (d).