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 Post subject: GMAT Algebra (Data Sufficiency)Posted: Thu Feb 03, 2011 10:18 am

Joined: Sun May 30, 2010 3:15 am
Posts: 424
Is x greater than 2?
(1) x² is greater than 4.
(2) x is between -1 and 3.

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) The statement (1) tells us that x² > 4. That means that x < -2 or x > 2. Therefore the statement (1) is not sufficient to answer the question.

The statement (2) tells us that -1 < x < 3. It is not sufficient to answer the question, because x can be 0, which is not greater than 2, or it can be 2.5, which is.

The both statements combined give the following system of the inequalities:
-1 < x < 3
x < -2 or x > 2

The solution to the system is:
2 < x < 3

Therefore x is definitely greater than 2. The correct answer is C.
----------
Could you please explain how combining the two statements yields 2 < x < 3?

1) x > 2 OR x < -2
2) -1< x <3

Thanks.

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 Post subject: Re: math (test 5, question 8): data sufficiency, inequalitiePosted: Thu Feb 03, 2011 10:59 am

Joined: Sun May 30, 2010 2:23 am
Posts: 498
In order to solve a system of inequalities, we need to find a set of all the possible values of the variable that satisfy all the original inequalities. Such set is the intersection of the solutions of each inequality.

It's easier to keep in mind the graphical interpretation on a number line:

1. The first inequality, x² > 4, results in:
x > 2 OR x < -2.

The solution is the red crosshatched region.

2. The second inequality, -1 < x < 3, results in:
-1 < x AND x < 3.

The solution to this inequality is the blue crosshatched region.

Therefore the solution of the system is the intersection:

2 < x < 3

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 Post subject: Re: math (test 5, question 8): data sufficiency, inequalitiePosted: Thu Feb 03, 2011 8:11 pm

Joined: Sun May 30, 2010 3:15 am
Posts: 424
Thanks, Great Explanation!

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