It is currently Mon Oct 22, 2018 12:47 am

 All times are UTC - 5 hours [ DST ]

 Page 1 of 1 [ 2 posts ]
 Print view Previous topic | Next topic
Author Message
 Post subject: GMAT Number Theory (data sufficiency)Posted: Sun Dec 09, 2012 5:19 pm

Joined: Mon Nov 26, 2012 5:39 pm
Posts: 11
Is √(56x) an integer?
(1) x is a multiple of 14.
(2) 28 is not a factor of x.

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.

(E) We could pick numbers here, but it seems impractical given that, after multiplying, the numbers would be so large that it would be difficult to tell whether they were perfect squares.

Let’s try to simplify the question stem by taking the prime factorization of 56:
√(56x) = √(2 × 2 × 2 × 7x)
= √(2 × 2) √(2 × 7x)
= 2√(14x).

So, the question is really asking whether 2√(14x) is an integer.

Statement (1) is insufficient. There are certain multiples of 14 (like 14 or 56) that would make 2√(14x) an integer. In fact, the multiples that will work here are the cases where x equals 14 times a perfect square. There are other multiples of 14, like 28, that would not make it an integer.

Statement (2) is also insufficient. Most values of x that do not have 28 as a factor, such as 5, won't make 2√(14x) an integer, but there are some that will: 28 is not a factor of 14, yet setting x equal to 14 will make 2√(14x) an integer. So Statement (2) is also insufficient.

Combined, the two statements are still insufficient. As shown, x could be 14, and 2√(14x) would be an integer. But if x were 42, both statements would be satisfied, but 2√(14x) would not be an integer.

Since both statements are insufficient, even when combined, the correct answer is choice (E).
----------
So if both conditions are true then we can conclude that √(56x) is not an integer, correct? Shouldn't answer be C?

e.g. :
x = 42
(1) and (2) satisfied hence √(56) not an integer

However x = 28 (1) true but not (2) then we cannot say √(56x) is an integer or not

Top

 Post subject: Re: GMAT Number Theory (data sufficiency)Posted: Sun Dec 09, 2012 5:35 pm

Joined: Sun May 30, 2010 2:23 am
Posts: 498
Quote:
So if both conditions are true then we can conclude that √(56x) is not an integer, correct?
No. For example these two values fit the both statements:

x = 14
(1) x = 14 is a multiple of 14
(2) 28 is not a factor of x = 14

and x = 42
(1) x = 42 is a multiple of 14
(2) 28 is not a factor of x = 42

And these two values yield different answers to the main question "Is √(56x) an integer?"
IF x = 14, then √(56x) = 28 . It is an integer!
√(56 × 14) = √(14 × 4 × 14) = 14 × 2 = 28

IF x = 42, then √(56x) = 28√3 . It is NOT an integer!
√(56 × 42) = √(14 × 4 × 14 × 3) = 14 × 2 × √3 = 28√3

So the both statements combined are NOT sufficient to give a definite answer to the main question.

Top

 Display posts from previous: All posts1 day7 days2 weeks1 month3 months6 months1 year Sort by AuthorPost timeSubject AscendingDescending
 Page 1 of 1 [ 2 posts ]

 All times are UTC - 5 hours [ DST ]

#### Who is online

Users browsing this forum: No registered users and 5 guests

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

Search for:
 Jump to:  Select a forum ------------------ GMAT    GMAT: Quantitative Section (Math)    GMAT: Verbal Section    GMAT: Integrated Reasoning    GMAT: General Questions GRE    GRE: Quantitative Reasoning (Math)    GRE: Verbal Reasoning    GRE: General Questions General questions    Other questions