GATE 2026 PI – Question 10
General Aptitude · Quantitative Aptitude: Data Interpretation, Arithmetic and Number Computation · 2 marks · Multiple choice
Positive integers P,Q satisfy $P^2=Q^2+13$. Find PQ.
- 13
- 26
- 39
- 42
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Show answer and explanation
Correct answer: (D) 42
Explanation
Factor $P^2-Q^2=(P-Q)(P+Q)=13$. Since 13 is prime and both factors are positive integers, $P-Q=1$ and $P+Q=13$. Thus P = 7, Q = 6, and **PQ = 42, D**.
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