AB and CD are 2-digit numbers. Multiplying AB with CD results in a 3-digit number DEF. Adding DEF to another 3-digit number GHI results in 975. Further A, B, C, D, E, F, G, H, I are distinct digits. If E = 0, F = 8, then what is A + B + C equal to?
Answer & explanation
Answer: (a) 6
The sum D08 + GHI = 975 fixes I = 7, H = 6 and D + G = 9. The only product of two 2-digit numbers of the form D08 with CD ending in D and all digits distinct is 12 × 34 = 408, so A + B + C = 1 + 2 + 3 = 6.
- DEF = D08. Units: 8 + I = 15, so I = 7 (carry 1). Tens: 0 + H + 1 = 7, so H = 6. Hundreds: D + G = 9.
- AB × CD = D08, where CD ends in the digit D. Test D = 1 to 8.
- 108: no pair of 2-digit factors. 208 = 13 × 16 and 308 = 11 × 28 = 14 × 22: no factor ends in 2 or 3 as needed.
- 408 = 12 × 34 or 17 × 24. With CD = 34: A = 1, B = 2, C = 3, D = 4, G = 5 — all nine digits 1, 2, 3, 4, 0, 8, 5, 6, 7 are distinct. With CD = 24, AB = 17 gives B = 7 = I, a clash.
- 508, 708 give no valid pair; 608 = 38 × 16 gives B = 8 = F, a clash; D = 8 clashes with F; D = 9 gives G = 0 = E.
- So A + B + C = 1 + 2 + 3 = 6.
- Check: 12 × 34 = 408 and 408 + 567 = 975.
Remember · In digit puzzles, settle the addition column by column first; it fixes most letters and leaves only a few cases to test.
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). ·