UPSC Prelims 2024·CSAT·Quantitative Aptitude·Number System

What is the remainder when 91x92x93x94x95x96x97x98x99 is divided by 1261?

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Last updated 23 May 2026, 3:31 pm IST
  1. A3
  2. B2
  3. C1
  4. D0Correct

Explanation

The divisor is 1261. First, factorize 1261. We find that 1261 = 13 x 97. Now, examine the numbers in the product: 91x92x93x94x95x96x97x98x99. Within this product, we can see two numbers that are crucial: 1. The number 91 is present. We know that 91 = 7 x 13. So, 13 is a factor of 91. 2. The number 97 is present. Since the product contains 91 (which has 13 as a factor) and it also contains 97 as a factor, the entire product is a multiple of (13 x 97). Therefore, the product 91x92x...x99 is a multiple of 1261. When a number is a multiple of the divisor, the remainder is 0. The final answer is D) 0.
Quantitative Aptitude: What is the remainder when 91x92x93x94x95x96x97x98x99 is divided by 1261?

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