Consider a 3-digit number.
Question: What is the number?
- Statement-1: The sum of the digits of the number is equal to the product of the digits.
- Statement-2: The number is divisible by the sum of the digits of the number.
Which one of the following is correct in respect of the above Question and the Statements?
Answer & explanation
Answer: (d) The Question cannot be answered even by using both the Statements together.
Digits whose sum equals their product can only be 1, 2 and 3, so Statement 1 leaves six numbers. Adding Statement 2, the number must be divisible by 6, but both 132 and 312 qualify, so the number still cannot be fixed.
- Statement 1: for the digits of a 3-digit number, sum = product only for 1, 2, 3 (1 + 2 + 3 = 6 = 1 × 2 × 3).
- So the number is one of 123, 132, 213, 231, 312, 321 — not unique.
- Statement 2 alone: many numbers are divisible by their digit sum (for example 100, 102, 108) — not sufficient.
- Together: the digit sum is 6, so the number must be even and divisible by 3; both 132 and 312 work.
- Two answers remain, so the Question cannot be answered even with both Statements.
Remember · Data sufficiency needs one unique answer; two cases surviving both statements prove insufficiency.
Question and answer: UPSC's official GS Paper II (2023, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·