• Board contributors include instructors with "800" GMAT scores.
  • 95% of posts have replies within 24 hours.
  • Join for discounts with 800score, VeritasPrep and ManhattanGMAT


FAQ  - Register  - Search - Login 

All times are UTC - 7 hours




Post new topic Reply to topic  [ 2 posts ] 
Author Message
 Post subject: GMAT Number Theory
PostPosted: Fri May 03, 2013 10:05 am 
Offline
User avatar

Joined: Tue Apr 13, 2010 8:48 am
Posts: 483
If m and n are different positive integers, then how many prime numbers are in set {m, n, m + n}?
(1) mn is prime.
(2) m + n is even.

A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.
D. Either statement BY ITSELF is sufficient to answer the question.
E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, meaning that further information would be needed to answer the question.

(C) Statement (1) tells us that mn is prime. The product of two integers can be prime only if one integer is 1 and the other one is prime. Otherwise the product would be divisible by more factors than just itself and 1. We can plug in some small prime numbers to see that statement (1) by itself is NOT sufficient. The set can be {1, 2, 3} – 2 prime numbers, or it can be {1, 3, 4} – 1 prime number.

Statement (2) tells us that m + n is even. Therefore the integers are both odd or both even. Clearly, there are many options possible: {2, 4, 6} – 1 prime number, {4, 6, 8} – no prime numbers, {3, 5, 8} – 2 prime numbers. Therefore statement (2) by itself is NOT sufficient.

If we use the both statements together, the set is {1, n, n + 1}, where n is prime and odd. If n is odd, then n + 1 is even. So n + 1 is NOT prime. Therefore the set contains exactly one prime number. Statements (1) and (2) taken together are sufficient to answer the question, even though neither statement by itself is sufficient. The correct answer is C.
----------
In case of {1, n, n + 1}, what if n = 2, then n + 1 = 3. This makes the set as {1, 2, 3}. Thus 2 prime numbers. Hence this too is insufficient. Hence, the answer should be E.


Top
 Profile  
 
 Post subject: Re: GMAT Number Theory
PostPosted: Fri May 03, 2013 10:05 am 
Offline
User avatar

Joined: Fri Apr 09, 2010 2:11 pm
Posts: 459
Quote:
In case of {1, n, n + 1}, what if n = 2, then n + 1 = 3. this makes the set as {1, 2, 3}. Thus 2 prime numbers. Hence this too is insufficient. Hence, the answer should be E.
Statement (2) implies, that n + 1 must be even. So the proposed example is NOT possible.


Top
 Profile  
 
Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 2 posts ] 

All times are UTC - 7 hours


Who is online

Users browsing this forum: No registered users and 3 guests


You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot post attachments in this forum

Search for:
Jump to:  
cron
Powered by phpBB © 2000, 2002, 2005, 2007 phpBB Group
Template made by DEVPPL -
phpBB SEO
 
GMAT(TM) and GMAT CAT (TM) are registered trademarks of the Graduate Management Admission Council(TM). The Graduate Management Admission Council(TM) does not endorse, nor is affiliated in any way with the owner or any content of this site.