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GATE 2026 CE (CE1) – Question 10

General Aptitude · Quantitative Aptitude: Arithmetic and Number Computation · 2 marks · Multiple choice

$P$ and $Q$ are two positive integers such that $P^2 = Q^2 + 13$. The product of the numbers $P$ and $Q$ is _________

  1. 13
  2. 26
  3. 39
  4. 42

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Show answer and explanation

Correct answer: (D) 42

Explanation

We have $P^2 - Q^2 = (P - Q)(P + Q) = 13$. Since 13 is prime and $P + Q > P - Q$, we need $P - Q = 1$ and $P + Q = 13$. So $P = 7$ and $Q = 6$, and the product is 42.