What is the remainder when 85 × 87 × 89 × 91 × 95 × 96 is divided by 100?

1. B. 1
2. C. 2
3. D. 4

Answer: A

Explanation

To find the remainder when a product is divided by 100, we need to check for factors of 100 (which are 25 and 4). The given product is 85 × 87 × 89 × 91 × 95 × 96. Let’s identify factors of 5 and 2 within these numbers:
– 85 contains a factor of 5 (85 = 5 × 17).
– 95 contains a factor of 5 (95 = 5 × 19).
So, we have two factors of 5, which multiply to 25.
– 96 contains a factor of 4 (96 = 4 × 24).
Since the product contains factors of both 25 and 4, it means the entire product is divisible by 25 × 4 = 100. When a number is completely divisible by another number, the remainder is 0. This question tests basic number theory concepts related to divisibility and remainders, a fundamental part of CSAT quantitative aptitude.