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GATE 2025 MT – Question 5

General Aptitude · Quantitative Aptitude: Arithmetic and Number Computation · 1 mark · Multiple choice

Let $p_1$ and $p_2$ denote two arbitrary prime numbers. Which statement is correct for all values of $p_1$ and $p_2$?

  1. $p_1+p_2$ is not a prime number.
  2. $p_1p_2$ is not a prime number.
  3. $p_1+p_2+1$ is a prime number.
  4. $p_1p_2+1$ is a prime number.

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Show answer and explanation

Correct answer: (B) $p_1p_2$ is not a prime number.

Explanation

Every prime is at least 2. Their product has a proper prime divisor and is therefore composite, even when the two primes coincide. The sum can be prime, for example 2+3=5, and the expressions with an added 1 are not always prime. **B**.