UPSC Prelims 2022 · CSAT
Question 5: Basic Numeracy
An Identity Card has the number ABCDEFG, not necessarily in that order, where each letter represents a distinct digit (1, 2, 4, 5, 7, 8, 9 only). The number is divisible by 9. After deleting the first digit from the right, the resulting number is divisible by 6. After deleting two digits from the right of original number, the resulting number is divisible by 5. After deleting three digits from the right of original number, the resulting number is divisible by 4. After deleting four digits from the right of original number, the resulting number is divisible by 3. After deleting five digits from the right of original number, the resulting number is divisible by 2. Which of the following is a possible value for the sum of the middle three digits of the number?
AnswerUPSC’s answer is (a).
The seven digits sum to 36, so divisibility by 9 is automatic. E must be 5 (the first five digits form a number ending in 5). B, D and F are even, so they are 2, 4 and 8, leaving A, C and G from 1, 7 and 9. CD divisible by 4 forces D = 2. The first six digits summing to a multiple of 3 forces G = 9. ABC divisible by 3 forces B = 4, so F = 8. Then C is 1 or 7, and the middle three digits C, D, E sum to C + 7 = 8 or 14. Only 8 is offered.
Why each option is right or wrong
- (a) Correct: 7412589 meets every rule and its middle digits 1, 2, 5 sum to 8.
- (b) 9 would need C = 2, but 2 is fixed as D.
- (c) 11 would need C = 4, but 4 is fixed as B.
- (d) 12 would need C = 5, but 5 is fixed as E.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2022, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.