GMAT Math : DSQ: Understanding real numbers

Study concepts, example questions & explanations for GMAT Math

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Example Questions

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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: .

Possible Answers:

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.

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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