Explanation for example problem

Last updated: 2 Mar 2007

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

Is `x > 0`?

  1. `x^2 > 0`
  2. `x^3 > 0`
  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient
  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient
  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
  4. EACH statement ALONE is sufficient
  5. 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 `x^2 > 0`.

This is true of any non-zero value of x, so x could be positive e.g. `3^2 = 9` which is greater than zero, but it could also be negative e.g. `(-3)^2 = 9` 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 `x^3 > 0`.

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

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

Putting it all together

We have just shown that statement (2) is suffience 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 (2):

  1. 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)

  2. The cube of a positive number is positive, for example

    `2^3 = 2 xx 2 xx 2 = 8`

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

    `(-2)^3 = -2 xx -2 xx -2 = -8`

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

    Does this make it clearer?

    joel on 10 Jul 2007 (permalink)

You must log in or register to add a comment.

Creative Commons License