Remainder of product divided by 100

To check for a remainder of 0 modulo 100, analyze the prime factors 2 and 5 within the continuous product expression : 85 = 5 × 17 \implies contains one factor of 5. 95 = 5 × 19 \implies contains one factor of 5. Total factors of 5 from these two odd numbers = 5 × 5 = 25.

Now scan for even terms: 96 = 32 × 3 = 2^5 × 3 \implies contains multiple factors of 2, specifically a multiple of 4.

Multiplying our extracted factors yields: ⟨MATH⟩25 × 4 = 100⟨/MATH⟩. Because the product contains 100 as an explicit factor, the entire expression is perfectly divisible by 100, leaving a remainder of exactly 0.

Answer: (a).