The difference between a 2-digit number and the number obtained by interchanging the positions of the digits is 54.
Consider the following statements:
- 1.The sum of the two digits of the number can be determined only if the product of the two digits is known.
- 2.The difference between the two digits of the number can be determined.
Which of the above statements is/are correct?
Answer & explanation
Answer: (b) 2 only
A 2-digit number and its reverse differ by 9 times the difference of the digits, so 54 means the digits differ by 6 — that is fixed. The digit sum could be 6, 8, 10 or 12; a known product would settle it, but so would other information, so 'only if the product is known' is not true.
- (10a + b) − (10b + a) = 9(a − b), so 9 × (difference of digits) = 54.
- The digits differ by 6 — Statement 2 is correct.
- Possible numbers: 60, 71, 82, 93 (or 17, 28, 39 the other way round), with digit sums 6, 8, 10, 12.
- Knowing the product (0, 7, 16 or 27) would fix the sum, but so would other clues, such as the larger digit — the product is not the only way, so Statement 1 is incorrect.
- ✗ 1. The product is one way to fix the sum, not the only way, so 'only if' makes the statement false.
- ✓ 2. 9 × (difference of digits) = 54 gives a difference of 6.
Remember · Number − its reverse = 9 × (difference of digits); number + its reverse = 11 × (sum of digits).
Question and answer: UPSC's official GS Paper II (2021, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·