What is the remainder when 85 × 87 × 89 × 91 × 95 × 96 is divided by 100 ?
- (a) 0 ✓ UPSC's answer
- (b) 1
- (c) 2
- (d) 4
Why the answer is (a)
• The remainder on division by 100 is the last two digits of the product.
• 85 = 5 × 17 and 95 = 5 × 19 supply two factors of 5, and 96 = 2⁵ × 3 supplies more than two factors of 2.
• So 5² × 2² = 100 divides the product.
• Hence the remainder is 0, option (a).
Why the other options are wrong
- (b) 1
- The product contains factors 85 and 95 (both multiples of 5) and 96 (a multiple of 4), making the total product divisible by 100, so the remainder cannot be 1.
- (c) 2
- The product is divisible by 100 because it contains at least two factors of 5 (from 85 and 95) and at least two factors of 2 (from 96), resulting in a remainder of 0, not 2.
- (d) 4
- The product is divisible by 100 as established by the presence of sufficient factors of 2 and 5, so the remainder is 0, not 4.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2023, held on 28 May 2023. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.