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CAT 2003 Slot 1 — QA Question 49

Number TheoryEasy

The number of positive integers n in the range 12 ≤ n ≤ 40 such that the product (n − 1)(n − 2)...3.2.1 is not divisible by n is

Answer & solution

Correct answer: 7

  • A

    5

  • 7

  • C

    13

  • D

    14

Solution

For (n − 1)(n − 2) … 3.2.1 to not be divisible by n, n should be a prime number.

But, there are 7 prime numbers in the range 12 ≤ n ≤ 40 are 7.

The prime numbers are 13, 17, 19, 23, 29, 31, 37.

Hence, option (b).

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CAT 2003 Slot 1 QA Q49: The number of positive integers n in the range 12 ≤ n ≤ 40 such that the product (n − 1)(n − — Solution | TheCATExam