GMAT Math : DSQ: Understanding real numbers
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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: .
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.
BOTH statements TOGETHER are insufficient to answer the question.
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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