2021 CSAT, all questions
UPSC Prelims 2021 · CSAT
Question 6: Basic Numeracy
The number 3798125P369 is divisible by 7. What is the value of the digit P ?
a1
b6
c7
d9
AnswerUPSC’s answer is (b).
Split the number as 3798125 × 10^4 + P × 1000 + 369 and reduce each part modulo 7. 3798125 leaves 2 and 10^4 leaves 4, so the first part leaves 8, i.e. 1. 1000 leaves 6, so P contributes 6P. 369 leaves 5. The total is 6P + 6, which must be a multiple of 7, so P + 1 must be a multiple of 7 and P = 6. Check: 6 × 6 + 6 = 42. Remember: modular arithmetic beats long division for divisibility by 7.
Why each option is right or wrong
- (a) P = 1 gives 6 + 6 = 12, remainder 5 on division by 7, so not divisible.
- (b) Right: P = 6 gives 6 × 6 + 6 = 42, a multiple of 7.
- (c) P = 7 gives 6 × 7 + 6 = 48, remainder 6 on division by 7.
- (d) P = 9 gives 6 × 9 + 6 = 60, remainder 4 on division by 7.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2021, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.