Question 48

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 $$(p^2-1)$$ is

Solution

Let the Prime number be 6n+1.

So $$(p^2 - 1)$$ = 6n(6n+2) = 12n(3n+1)

For any value of n , n(3n+1) will have a factor of 2

Hence given equation will be always be divisible by 24

Create a FREE account and get:

All Quant CAT complete Formulas and shortcuts PDF
35+ CAT previous papers with video solutions PDF
5000+ Topic-wise Previous year CAT Solved Questions for Free

CAT Quant Questions | CAT Quantitative Ability

CAT Quadratic Equations Questions CAT Inequalities Questions CAT Averages Questions CAT Linear Equations Questions CAT Percentages Questions

CAT DILR Questions | LRDI Questions For CAT

CAT Quant Based DI Questions CAT Table with Missing values Questions CAT Selection With Condition Questions CAT Charts Questions CAT Routes And Networks Questions

CAT Verbal Ability Questions | VARC Questions For CAT

CAT Reading Comprehension Questions CAT Verbal Ability Questions CAT Critical Reasoning Questions CAT Odd One Out Questions CAT Vocabulary Questions

Related Formulas With Tests

Divisibility by different numbers

Follow us on

Boost your Prep!

Download App