Let p1 and p2 denote two arbitrary prime numbers. Which one of the following statements is correct for all values of p1 and p2? A) p1 + p2 is not a prime number. B) p1 p2 is not a prime number. C) p1 + p2 + 1 is a prime number. D) p1 p2 + 1 is a prime number.

Official answer: B) p1 p2 is not a prime number.. Explanation: A prime number is an integer greater than 1 that has exactly two positive divisors: 1 and itself. Let p1 and p2 be any two prime numbers (p1 2 and p2 2). * Analysis of (B): The product p1 p2 is an integer 4. - If p1 p2, the positive divisors of p1 p2 are 1, p1, p2, and p1 p2 (at least four distinct divisors). - If p1 = p2 = p, the positive divisors of p2 are 1, p, and p2 (three distinct divisors). In both cases, p1 p2 has more than two distinct positive divisors, so p1 p2 is composite and never a prime number. * Counterexamples for other options: - (A) If p1 = 2 and p2 = 3, then p1 + p2 = 5, which is prime. - (C) If p1 = 3 and p2 = 5, then p1 + p2 + 1 = 9 = 32, which is not prime. - (D) If p1 = 3 and p2 = 5, then p1 p2 + 1 = 16 = 24, which is not prime. Therefore, statement (B) is correct for all values of p1 and p2.

A) p1 + p2 is not a prime number.

B) p1 p2 is not a prime number.

C) p1 + p2 + 1 is a prime number.

D) p1 p2 + 1 is a prime number.

General Aptitude · Quantitative Aptitude

Official IIT answer key · IIT Guwahati · Audited Aug 2026

Take topic test

GATE CSE 2025 Set 2 Q5 · MCQ · 1 mark

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 $p_2$ ?

Select an option to check

Key concept

Quantitative Aptitude

Step-by-step verified solution

Examiner trap & misconception

Topic notes

How GATE tests Quantitative Aptitude

Quantitative Aptitude in GATE CS evaluates foundational mathematical reasoning, arithmetic, algebra, combinatorics, elementary probability, and geometry through concise word problems and functional/graphical models. The questions emphasize direct application of core algebraic identities, logarithmic laws, rates, proportions, set intersections, and calculus-based optimization rather than heavy computation. Items are evenly distributed between 1-mark conceptual or single-step problems and 2-mark multi-step arithmetic, geometric, or conditional reasoning setups.

Full Quantitative Aptitude guide →

More on Quantitative Aptitude

All 53 questions on Quantitative Aptitude →

Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.

General Aptitude · Quantitative Aptitude

Official IIT answer key · IIT Guwahati · Audited Aug 2026

Take topic test

GATE CSE 2025 Set 2 Q5 · MCQ · 1 mark

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 $p_2$ ?

Select an option to check

Key concept

Quantitative Aptitude

Step-by-step verified solution

Examiner trap & misconception

Topic notes

How GATE tests Quantitative Aptitude

Full Quantitative Aptitude guide →

More on Quantitative Aptitude

All 53 questions on Quantitative Aptitude →

Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.

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 $p_2$ ?

Step-by-step verified solution

Check you can still solve Quantitative Aptitude under a clock

More from GATE CSE 2025 Set 2

More on Quantitative Aptitude

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 $p_2$ ?

Step-by-step verified solution

Check you can still solve Quantitative Aptitude under a clock

More from GATE CSE 2025 Set 2

More on Quantitative Aptitude

Let p1p_1p1​ and p2p_2p2​ denote two arbitrary prime numbers. Which one of the following statements is correct for all values of p1p_1p1​ and p2p_2p2​?

Step-by-step verified solution

Check you can still solve Quantitative Aptitude under a clock

More from GATE CSE 2025 Set 2

More on Quantitative Aptitude

Share this solution

Let p1p_1p1​ and p2p_2p2​ denote two arbitrary prime numbers. Which one of the following statements is correct for all values of p1p_1p1​ and p2p_2p2​?

Step-by-step verified solution

Check you can still solve Quantitative Aptitude under a clock

More from GATE CSE 2025 Set 2

More on Quantitative Aptitude

Share this solution

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 $p_2$ ?

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 $p_2$ ?