Explanation for example problem
Last updated: 23 Nov 2008
Now lets work through this example of a data sufficiency problem together.
Is ?
- 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 .
This is true of any non-zero value of x, so x could be positive e.g. which is greater than zero, but it could also be negative e.g.
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 .
A cubing a number does not change it's sign so if cubed is positive then
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.
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.
The cube of a positive number is positive, for example
but the cube of a negative number is negative, for example
So if x cubed is positive then x must be positive.
Does this make it clearer?
So does the GMAT always assume that x will not be zero??
You cannot, in general, assume that x is not zero in the GMAT.
In this question, statement 2.
, tells us that x is not zero.
Can u add more examples