# GMAT Math : DSQ: Understanding real numbers

## Example Questions

1 2 4 Next →

### Example Question #1260 : Data Sufficiency Questions

Define an operation  on the real numbers as follows:

If both  and  are both positive, then .

If both  and  are not both positive, then .

Evaluate .

Statement 1: .

Statement 2: .

BOTH statements TOGETHER are insufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

Explanation:

Assume both statements to be true. From Statement 1, , so  and  are each other's opposites. Either one is positive and one is negative, or both are equal to 0; either way, the definition of  for  and  not both positive is used, and

Statement 2 tells us nothing except that , so it can only be deduced that  is negative, and so is

With no further information,  cannot be evaluated.

1 2 4 Next →

Tired of practice problems?

Try live online GMAT prep today.