Let A3BC and DE2F be four-digit numbers where each letter represents a different digit greater than 3. If the sum of the numbers is 15902, then what is the difference between the values of A and D?
Answer & explanation
Answer: (c) 3
Working column by column from the units, the carries force B = 7 and E = 5, and C and F must be 4 and 8. That leaves 6 and 9 for A and D, whose difference is 3.
- Units: C + F ends in 2; both are at least 4, so C + F = 12, carry 1.
- Tens: B + 2 + 1 ends in 0, so B + 3 = 10 and B = 7, carry 1.
- Hundreds: 3 + E + 1 ends in 9, so E = 5, carry 0.
- Thousands: A + D = 15.
- Digits left from 4–9 after B = 7, E = 5: {4, 6, 8, 9}. C + F = 12 needs {4, 8}; so A and D are 6 and 9 (6 + 9 = 15).
- Difference = 9 − 6 = 3.
- Check: 6374 + 9528 = 15902.
Remember · In letter-addition puzzles, start from the units column, track every carry, and use 'different digits' to fix the pairs.
Question and answer: UPSC's official GS Paper II (2020, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·