A Question is given followed by two Statements I and II. Consider the Question and the Statements.
- Question: What are the values of m and n, where m and n are natural numbers?
- Statement–I: m + n > mn and m > n.
- Statement–II: The product of m and n is 24.
Which one of the following is correct in respect of the above Question and the Statements?
Answer & explanation
Answer: (c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
m + n > mn with m > n forces n = 1, but leaves m open; mn = 24 alone allows several pairs. Together, n = 1 and m = 24.
- m + n > mn is the same as mn − m − n + 1 < 1, i.e. (m − 1)(n − 1) < 1.
- For natural numbers this means (m − 1)(n − 1) = 0; since m > n ≥ 1, n = 1. Statement I fixes n = 1 but any m ≥ 2 works, so it is not sufficient.
- Statement II alone: mn = 24 allows (24, 1), (12, 2), (8, 3), (6, 4) and their reversals, so it is not sufficient.
- Together: n = 1 and mn = 24 give m = 24. Check: 24 + 1 = 25 > 24.
Remember · Rewrite m + n > mn as (m − 1)(n − 1) < 1; with natural numbers, one of them must be 1.
Question and answer: UPSC's official GS Paper II (2024, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·