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Explanation for example problem

Last updated: 23 Nov 2008

Now lets work through this example of a data sufficiency problem together.

Is $mathematical expression$ ?

$mathematical expression$
$mathematical expression$

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
EACH statement ALONE is sufficient
Statements (1) and (2) TOGETHER are NOT sufficient

To answer this we will have to examine each statement separately.

Is statement (1) sufficient to answer the question?

Statement (1) tells us that $mathematical expression$ .

This is true of any non-zero value of x, so x could be positive e.g. $mathematical expression$ which is greater than zero, but it could also be negative e.g. $mathematical expression$ which is also greater than zero.

Therefore statement (1) is not sufficient to answer the question.

Is statement (2) sufficient to answer the question?

Statement (2) tells us that $mathematical expression$ .

A cubing a number does not change it's sign so if $mathematical expression$ cubed is positive then $mathematical expression$ is positive.

Therefore statement (2) is sufficient to answer the question.

Putting it all together

We have just shown that statement (2) is sufficient to answer the question but statement (1) is not.

This matches answer B which must be the correct answer.

In answering this question we already are starting to make use of the key strategies for tackling data sufficiency problems so lets look at them in more detail.

Next page: Strategies for data sufficiency questions

Comments (5):

I didnt get the explanation for the cubic answer. Wouldn't be the same as the square. On the cubic the answer is always positive but X could be negative and positive.

kttboy8 on 9 Jul 2007 (permalink)
The cube of a positive number is positive, for example

$mathematical expression$

but the cube of a negative number is negative, for example

$mathematical expression$

So if x cubed is positive then x must be positive.

Does this make it clearer?

joel on 10 Jul 2007 (permalink)
So does the GMAT always assume that x will not be zero??

funk123 on 25 Sep 2008 (permalink)
You cannot, in general, assume that x is not zero in the GMAT.

In this question, statement 2. $mathematical expression$ , tells us that x is not zero.

joel on 25 Sep 2008 (permalink)
Can u add more examples

rahultripathi2005 on 1 Jul 2009 (permalink)