gmat preparation courses

It is currently Mon Oct 15, 2018 5:48 am

All times are UTC - 5 hours [ DST ]




Post new topic Reply to topic  [ 3 posts ] 
Author Message
 Post subject: GMAT Algebra (Data Sufficiency)
PostPosted: Tue Sep 20, 2011 5:47 pm 
Offline

Joined: Sun May 30, 2010 3:15 am
Posts: 424
If x is an integer such that x > 0, is it true that √x is an integer?
(1) 9 × √(16x) is an integer.
(2) √(6x) is not an integer.

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.

(A) Let’s evaluate each of the statements independently first. The question assumes that x is a positive integer. In order for (1) to be true, it should be obvious to the reader that x must be a perfect square. In other words we can break down (1), using the well-known properties of roots. Now, if 4√x is an integer, it must be true that √x is in fact an integer; there is no way that the product of an integer and an irrational number can give an integer. So, statement (1) is sufficient.

Now, let’s look at Statement (2). Sometimes it will answer the question, other times it won’t. For example, if x = 9 then √54 is not an integer. Yet, √9 = 3 is an integer. On the other hand, if x = 2 then √12 is not an integer and neither is√2. So, Statement (2) is insufficient, and the only reasonable answer choice is (A).
----------
I didn't understand the explanation of the answer, because in statement (1) I can write x = 1/4 and the answer will still be an integer.


Top
 Profile  
 
 Post subject: Re: math (t.3, qt. 30): algebra, data sufficiency
PostPosted: Tue Sep 20, 2011 6:10 pm 
Offline

Joined: Sun May 30, 2010 2:23 am
Posts: 498
Quote:
I didn't understand the explanation of the answer, because in statement (1) I can write x = 1/4 and the answer will still be an integer.
The basic question statement tells us that x must be an integer. So x = 1/4 is impossible.

The fact that x is a positive integer is highly important in this question. Let us analyse statement (1): 9 × √(16x) is an integer.

9 × √(16x) = 9 × 4 ×√x = a, where a is an integer
So √x = a / 36
x = (a / 36)²
Remember, that x is a positive integer, therefore a must be divisible by 36 and therefore √x = a / 36 is an integer as well.


Top
 Profile  
 
 Post subject: Re: math (t.3, qt. 30): algebra, data sufficiency
PostPosted: Wed Sep 21, 2011 3:30 am 
Offline

Joined: Sun May 30, 2010 3:15 am
Posts: 424
Thank you


Top
 Profile  
 
Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 3 posts ] 

All times are UTC - 5 hours [ DST ]


Who is online

Users browsing this forum: No registered users and 4 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