Remainder

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harsh.champ: Legendary Member; Posts: 1132; Joined: Mon Jul 20, 2009 3:38 amFollowed by: 6 members; Location: India; Thanked: 64 times; GMAT Score:760

by harsh.champ » Mon Feb 08, 2010 4:51 am

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.

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Source: Beat The GMAT — Data Sufficiency | Mon Feb 08, 2010 4:51 am

shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members; Location: Gandhinagar; Thanked: 41 times

by shashank.ism » Mon Feb 08, 2010 5:06 am

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

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Mon Feb 08, 2010 5:12 am

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?

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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harsh.champ: Legendary Member; Posts: 1132; Joined: Mon Jul 20, 2009 3:38 amFollowed by: 6 members; Location: India; Thanked: 64 times; GMAT Score:760

by harsh.champ » Mon Feb 08, 2010 5:17 am

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.

It takes time and effort to explain, so if my comment helped you please press Thanks button

Just because something is hard doesn't mean you shouldn't try,it means you should just try harder.

"Keep Walking" - Johnny Walker

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Mon Feb 08, 2010 5:33 am

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]

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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