AAPL wrote:GMAT Prep
Are the integers \(z\) and \(f\) to the right of 0 on the number line?
1) The product of \(z\) and \(f\) is positive.
2) The sum \(z\) and \(f\) is positive.
OA C
So, we have to ascertain whether z and f positive numbers or not.
Let's take each statement one by one.
1) The product of \(z\) and \(f\) is positive.
Case 1: Say z and f both are positive, the product of \(z\) and \(f\) would be positive. The answer is yes.
Case 2: Say z and f both are negative, the product of \(z\) and \(f\) would be positive. The answer is no.
No unique answer. Insufficient.
2) The sum \(z\) and \(f\) is positive.
Case 1: Say z and f both are positive, the product of \(z\) and \(f\) would be positive. The answer is yes.
Case 3: Say z is positive and f is negative such that |z| > |f|, the sum of \(z\) and \(f\) = |z| - |f| would be positive. The answer is no.
No unique answer. Insufficient.
(1) and (2) together
Case 2 and Case 3 are not possible; thus, z and f both are to the right of 0 on the number line. Sufficient.
The correct answer:
C
Hope this helps!
-Jay
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