What is the remainder when 91x92x93x94x95x96x97x98x99 is divided by 1261?
- A3
- B2
- C1
- 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:
- The number 91 is present. We know that 91 = 7 x 13. So, 13 is a factor of 91.
- 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.
Related questions
More UPSC Prelims practice from the same subject and topic.
- Prelims 2024CSATQuantitative Aptitude
What is the number of numbers of the form 0.xy, where x and y are distinct non-zero digits?
- Prelims 2024CSATQuantitative Aptitude
The sum of three consecutive integers is equal to their product. How many such possibilities are there?
- Prelims 2024CSATQuantitative Aptitude
15 × 14 × 13 × … × 3 × 2 × 1 = 3 m × n 12. 15 × 14 × 13 × … × 3 × 2 × 1 = 3 m × n Where m and n are positive integers, then what is the maximum value of m?
- Prelims 2024CSATQuantitative Aptitude
Consider the following statements in respect of two natural numbers p and q such that p is a prime number and q is a composite number: 1. p x q can be an odd number. 2. q / p can be a prime number. 3.…
- Prelims 2024CSATQuantitative Aptitude
Let p be a two-digit number and q be the number consisting of same digits written in reverse order. If p x q = 2430, then what is the difference between p and q?
- Prelims 2024CSATQuantitative Aptitude
What is the smallest number greater than 1000 that when divided by any one of the numbers 6, 9, 12, 15, 18 leaves a remainder of 3?