GATE CSE 2025 Session 2 Q5: Which statement about two primes always holds

Let $p_1$ and $p_2$ denote two arbitrary prime numbers. Which one of the following statements is correct for all values of $p_1$ and $p_2$ ?

Try it: multiple choice: exactly one correct option

Wrong answer costs 1/3 mark in GATE.

Show answer and explanation

Answer: B (official GATE 2025 final answer key)

Concept used: Definition of a prime, and disproving the other claims with small counterexamples.

First step: Try $p_1 = 2, p_2 = 3$ and $p_1 = p_2 = 3$ on each option; a product of two primes always has a factor other than 1 and itself.

Full step-by-step solution

Detailed working, common mistakes and linked mock tests will be available with a free GATEiit account. Log-in is coming soon.

Share this question

Source: official GATE 2025 Session 2 CS question paper and final answer key, organised by IIT Roorkee. Question paper · Answer key