UPSC Prelims 2023 · CSAT
Question 76: Basic Numeracy
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 ?
AnswerUPSC’s answer is (a).
DEF = D08 is the product AB x CD, and D is also the units digit of CD. Try D = 1 to 9. D = 4 gives 408 = 12 x 34 or 17 x 24, with CD ending in 4. D = 6 gives 608 = 38 x 16, but B = 8 repeats F = 8. No other D gives such a pair. Then GHI = 975 - 408 = 567. With AB = 17, I = 7 repeats B, so reject it. With AB = 12 and CD = 34 all digits are distinct. A + B + C = 1 + 2 + 3 = 6.
Why each option is right or wrong
- (a) Right: AB = 12, CD = 34 and 1 + 2 + 3 = 6.
- (b) Wrong: the only valid case gives 6.
- (c) Wrong: the only valid case gives 6.
- (d) Wrong: the only valid case gives 6.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2023, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.