2023 CSAT, all questions
UPSC Prelims 2023 · CSAT
Question 49: Logical Reasoning and Mental Ability
If today is Sunday, then which day is it exactly on 10^10 th day ?
aWednesday
bThursday
cFriday
dSaturday
AnswerUPSC’s answer is (a).
Find 10^10 mod 7. 10 leaves 3, and powers of 3 mod 7 repeat every 6: 3, 2, 6, 4, 5, 1. Since 10 = 6 + 4, 10^10 behaves like 3^4 = 81, which leaves 4. UPSC counts today, Sunday, as the first day, so the 10^10th day is 10^10 - 1 days later, which leaves 3 mod 7: Sunday + 3 = Wednesday.
Why each option is right or wrong
- (a) Right: counting today as day 1, the 10^10th day falls 3 days after Sunday.
- (b) Wrong under UPSC's counting: Thursday is 4 days after Sunday, which treats today as day 0.
- (c) Wrong: Friday is 5 days after Sunday.
- (d) Wrong: Saturday is 6 days after Sunday.
Worth knowing: If today is counted as day 0, the day 10^10 days later is Thursday; UPSC's key counts today as day 1, so the wording is ambiguous.
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.