gmat preparation courses

It is currently Fri Oct 19, 2018 12:46 pm

All times are UTC - 5 hours [ DST ]




Post new topic Reply to topic  [ 2 posts ] 
Author Message
 Post subject: GMAT Number Theory
PostPosted: Thu Feb 03, 2011 8:54 pm 
Offline

Joined: Sun May 30, 2010 3:15 am
Posts: 424
The least common multiple of positive integer m and 3-digit integer n is 690. If n is not divisible by 3 and m is not divisible by 2, what is the value of n?

A. 115
B. 230
C. 460
D. 575
E. 690

(B) We factorize 690 = 2 × 3 × 115 = 2 × 3 × 5 × 23.
Dividing 690 starting by the smallest factor we get possible values for 3-digit integer n:
690, 690 / 2 = 345, 690 / 3 = 230, 690 / 5 = 138, 690 / 6 = 115.

690 / 10 = 69, which is a 2-digit number, therefore n must be one of the following:
690, 345, 230, 138, 115.

n is not divisible by 3. So we eliminate 690, 345, 138.

m is not divisible by 2, but the least common multiple of m and n is. So n must be divisible by 2. We eliminate 115.

That leaves us only one option for n, 230. The correct answer is B.
----------
Is the reason that C and D are not correct because C implies 460 × 1.5 and D implies 575 × 1.2? Neither 1.5 or 1.2 are integers?


Top
 Profile  
 
 Post subject: Re: math (test 4, question 11): number theory, LCM
PostPosted: Thu Feb 03, 2011 9:08 pm 
Offline

Joined: Sun May 30, 2010 2:23 am
Posts: 498
Yes, you're right.
The answer choices C and D are NOT the factors of 690. Therefore we can eliminate them, since the LCM of any numbers must be divisible by those numbers.

Furthermore,
Let's try to solve this question by considering the answer choices.
We can eliminate choices C and D as described above.
The answer choice E is divisible by 3, while the original statement tells us that n is NOT divisible by 3. So we can eliminate this answer choice as well.

It's a little bit harder to consider the answer choices A and B. The reasoning we use is the same as in the original explanation.

Let's consider A. Suppose n is 115. Then m must be divisible by 690/115 = 6. Therefore m must be divisible by 2 (since 6 = 2 × 3). But the original statement tells us that m is NOT divisible by 2. So we eliminate the answer choice A.

B is the only answer choice that's left. So B is the correct answer.

P.S. If n is 230, then m, which is odd, can be one of the following:
3, 15, 69, 345.


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

All times are UTC - 5 hours [ DST ]


Who is online

Users browsing this forum: No registered users and 9 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