A 3-digit number ABC, on multiplication with D gives 37DD where A, B, C and D are different non-zero digits. What is the value of A + B + C ?
- (a) 18 ✓ UPSC's answer
- (b) 16
- (c) 15
- (d) Cannot be determined due to insufficient data
Why the answer is (a)
• ABC × D = 37DD means ABC × D = 3700 + 11D, so ABC = (3700 + 11D) ÷ D must be a whole 3-digit number.
• D = 1, 2 or 3 makes ABC too large (over 999); so try D = 4 to 9.
• D = 4: 3744 ÷ 4 = 936 — digits 9, 3, 6 and 4 are all different and non-zero, so it works.
• D = 5 gives 751, which repeats the digit 5; D = 6, 7, 8, 9 do not divide evenly.
• So ABC = 936 and A + B + C = 9 + 3 + 6 = 18, option (a).
Why the other options are wrong
- (b) 16
- Option (b) 16 is incorrect because the only valid combination of digits yields a sum of 18, not 16.
- (c) 15
- Option (c) 15 is incorrect because the calculated sum of the digits A, B, and C is 18, not 15.
- (d) Cannot be determined due to insufficient data
- Option (d) is incorrect because the constraints of distinct non-zero digits and the specific product structure uniquely determine the value of D and the digits A, B, C.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2023, held on 28 May 2023. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.