v1gnesh wrote:
Prime numbers are of the form 6n+1 or 6n-1. The first part of each of the terms contains a 6,and hence is a multiple of 6. We only need to factor out 6's from the 2nd part of each option. If you're left with a number greater than one, then that's the answer . In this case, that would be B.
Don't get your solution...
The property you are referring to is: any prime number p greater than 3 could be expressed as p=6n+1 or p=6n+5 (p=6n-1), where n is an integer >1.
That's because any prime number p greater than 3 when divided by 6 can only give remainder of 1 or 5 (remainder can not be 2 or 4 as in this case p would be even and remainder can not be 3 as in this case p would be divisible by 3).
But:
Note that, not all number which yield a remainder of 1 or 5 upon division by 6 are primes, so vise-versa of above property is not correct. For example 25 (for n=4) yields a remainder of 1 upon division by 6 and it's not a prime number.