harsh.champ wrote:What is the remainder when P2 is divided by 12, where 'P' is a prime number?
A: P is of the form 4k + 3, where 'k' is a positive integer.
B: P is of the form 2k - 1, where 'k' is an integer greater than 1.

The OA is A.

A sufficient P can be 7, 11,19,23.... -- all have different remainder ....... 7 & 11, --- not sufficient
B unsufficient all odd nos. which are prime so remiander may be 5,7,11,1,3, ---not sufficient...
A and B gives same nos.as A

so combined is also insufficient
ANSE


Harsh will u please explain how ans is A

harsh.champ wrote:What is the remainder when P2 is divided by 12, where 'P' is a prime number?
A: P is of the form 4k + 3, where 'k' is a positive integer.
B: P is of the form 2k - 1, where 'k' is an integer greater than 1.

The OA is A.

With P2, do you mean P^2?

sanju09 wrote:

harsh.champ wrote:What is the remainder when P2 is divided by 12, where 'P' is a prime number?
A: P is of the form 4k + 3, where 'k' is a positive integer.
B: P is of the form 2k - 1, where 'k' is an integer greater than 1.

The OA is A.

With P2, do you mean P^2?

Yeah sanju I forgot the "^" sign over there. It would be P^2.

So,the question will be:-

What is the remainder when P2 is divided by 12, where 'P' is a prime number?
A: P is of the form 4k + 3, where 'k' is a positive integer.
B: P is of the form 2k - 1, where 'k' is an integer greater than 1.


Just check now if you are getting the correct answer.
Sorry for the inconvenience.

harsh.champ wrote:

sanju09 wrote:

harsh.champ wrote:What is the remainder when P2 is divided by 12, where 'P' is a prime number?
A: P is of the form 4k + 3, where 'k' is a positive integer.
B: P is of the form 2k - 1, where 'k' is an integer greater than 1.

The OA is A.

With P2, do you mean P^2?

Yeah sanju I forgot the "^" sign over there. It would be P^2.

So,the question will be:-

What is the remainder when P2 is divided by 12, where 'P' is a prime number?
A: P is of the form 4k + 3, where 'k' is a positive integer.
B: P is of the form 2k - 1, where 'k' is an integer greater than 1.


Just check now if you are getting the correct answer.
Sorry for the inconvenience.

alright

(1) If P = 4 k + 3 for some positive integer k, then P^2 = 16 k^2 + 24 k + 9. Now note that when P is prime, 16 k^2 leaves a remainder of 4, 24 k leaves 0 remainder, and 9 leaves 9 as remainder, when 16 k^2 + 24 k + 9 is divided by 12. Hence, when (4 + 0 + 9) or 13 is divided by 12, the remainder is 1. Sufficient

(2) If P = 2 k - 1 for some positive integer k, greater than 1, then P^2 = 4 k^2 - 4 k + 1. No fix remainders to the parts of 4 k^2 - 4 k + 1 when divided by 12. Insufficient

[spoiler]A[/spoiler]