2022 CSAT, all questions
UPSC Prelims 2022 · CSAT
Question 58: Basic Numeracy
What is the remainder when 91×92×93×94×95×96×97×98×99 is divided by 1261?
a3
b2
c1
d0
AnswerUPSC’s answer is (d).
1261 = 13 × 97. The product 91 × 92 × ... × 99 contains 91 = 7 × 13, so 13 divides it, and it contains 97, so 97 divides it. Since 13 and 97 are distinct primes, their product 1261 divides the product exactly. The remainder is 0. No multiplication is needed: when a modulus splits into distinct prime factors, check each factor in turn.
Why each option is right or wrong
- (a) 3 is wrong: both prime factors of 1261 appear in the product.
- (b) 2 is wrong for the same reason.
- (c) 1 is wrong for the same reason.
- (d) Correct: 13 (in 91) and 97 both appear, so the remainder is 0.
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.