What is the remainder when 51 × 27 × 35 × 62 × 75 is divided by 100?

Answer: (a) 50

Only the last two digits matter. 62 × 75 = 4650 ends in 50, and multiplying a number ending in 50 by any odd number again ends in 50. The other factors 51, 27 and 35 are all odd, so the remainder is 50.

1. 62 × 75 = 4650, which ends in 50.
2. 50 × (odd number) always ends in 50, since 50 × odd = 100k + 50.
3. 51 × 27 × 35 = 48195 is odd, so the whole product ends in 50.
4. Remainder = 50.

Remember · Remainder on division by 100 = last two digits; pair factors that quickly give a round ending like 50 or 00.

Question and answer: UPSC's official GS Paper II (2020, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). · Report an error