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?
- (a) 1
- (b) 2
- (c) 3 ✓ UPSC's answer
- (d) 4
Why the answer is (c)
• Units column: C + F must give 2, but since C and F are digits greater than 3, C + F = 12 with carry 1.
• Tens column: B + 2 + 1 = 0, so B + 3 = 10, giving B = 7 and carry 1.
• Hundreds column: 3 + E + 1 = 9, so E = 5 and there is no carry to the thousands column.
• Thousands column: A + D = 15, and A and D must be unused digits greater than 3, so they must be 6 and 9.
• Therefore, the difference between A and D is 3, which is option (c).
Why the other options are wrong
- (a) 1
- Option (a) is wrong because A and D must be 6 and 9, whose difference is 3, not 1.
- (b) 2
- Option (b) is wrong because two digits summing to 15 cannot differ by 2.
- (d) 4
- Option (d) is wrong because the only possible unused digit pair summing to 15 is 6 and 9, whose difference is 3, not 4.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2020, held on 4 October 2020. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.