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CAT 1991 — QA Question 46

Number TheoryEasy

A positive integer is said to be a prime number if it is not divisible by any positive integer other than itself and 1. Let p be a prime number greater than 5. Then (p2 – 1) is

Answer & solution

Correct answer: always divisible by 24

  • A

    never divisible by 6

  • B

    always divisible by 6, and may or may not be divisible by 12

  • C

    always divisible by 12, and may or may not be divisible by 24

  • always divisible by 24

Solution

As each prime number greater than or equal 3 is of from 6k ± 1, here k is a natural number, p = 6k ± 1.

p2 - 1 = (6k ± 1)2 - 1 = 12k(3k ± 1)

Since k(3k ± 1) is an even number, above number is always divisible by 24 irrespective of value of k.

Hence, option (d).

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CAT 1991 QA Q46: A positive integer is said to be a prime number if it is not divisible by any positive integer other than itse — Solution | TheCATExam