GMAT Math : Real Numbers

Study concepts, example questions & explanations for GMAT Math

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Example Questions

Example Question #31 : Real Numbers

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: .

Possible Answers:

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

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

EITHER statement ALONE is sufficient to answer the question.

Correct answer:

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.

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