BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Remainder

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Legendary Member
Posts: 1132
Joined: Mon Jul 20, 2009 3:38 am
Location: India
Thanked: 64 times
Followed by:6 members
GMAT Score:760

Remainder

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.
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 :P
Top
Source: — Data Sufficiency |
User avatar
Legendary Member
Posts: 1022
Joined: Mon Jul 20, 2009 11:49 pm
Location: Gandhinagar
Thanked: 41 times
Followed by:2 members

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
My Websites:
www.mba.webmaggu.com - India's social Network for MBA Aspirants

www.deal.webmaggu.com -India's online discount, coupon, free stuff informer.

www.dictionary.webmaggu.com - A compact free online dictionary with images.

Nothing is Impossible, even Impossible says I'm possible.
Top
User avatar
GMAT Instructor
Posts: 3650
Joined: Wed Jan 21, 2009 4:27 am
Location: India
Thanked: 267 times
Followed by:80 members
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
Top
User avatar
Legendary Member
Posts: 1132
Joined: Mon Jul 20, 2009 3:38 am
Location: India
Thanked: 64 times
Followed by:6 members
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 :P
Top
User avatar
GMAT Instructor
Posts: 3650
Joined: Wed Jan 21, 2009 4:27 am
Location: India
Thanked: 267 times
Followed by:80 members
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
Top
Post new topic Post Reply
• Page 1 of 1