If the sum of the two-digit numbers AB and CD is the three-digit number 1CE, where the letters A, B, C, D, E denote distinct digits, then what is the value of A?
Answer & explanation
Answer: (a) 9
Two two-digit numbers add up to at most 197, so the leading 1 of 1CE is a carry. In the tens column A + C + carry = 10 + C, which forces A = 9 with a carry of 1 from the units column.
- AB + CD ≤ 99 + 98 = 197, so the sum 1CE lies between 100 and 197.
- Tens column: A + C + c = C + 10, where c (0 or 1) is the carry from the units column.
- So A + c = 10. A is a single digit, so c = 1 and A = 9.
- Check: 97 + 35 = 132 fits, with A = 9, B = 7, C = 3, D = 5, E = 2 all different.
Remember · In digit-sum puzzles, write each column as an equation with its carry; the leftmost column usually fixes a digit at once.
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). ·