swerve wrote: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 of \(z\) and \(f\) is positive.

Target question: Are the integers z and f to the right of 0 on the number line?
This is a good candidate for rephrasing the target question.

If z and f to the right of 0 on the number line, then that means z and f are both POSITIVE
Let's now REPHRASE the target question....
REPHRASED target question: Are integers z and f both POSITIVE?

Aside: Here's a video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

Statement 1: The product of z and f is positive.
There are two possible scenarios that satisfy statement 1:
Case a: z and f are both positive. In this case, the answer to the REPHRASED target question is YES, z and f are both POSITIVE
Case b: z and f are both negative. In this case, the answer to the REPHRASED target question is NO, z and f are not both POSITIVE
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The sum of z and f is positive.
There are infinitely-many values of z and f that satisfy statement 2. Here are two:
Case a: z = 1 and f = 1. In this case, the answer to the REPHRASED target question is YES, z and f are both POSITIVE
Case b: z = -1 and f = 2. In this case, the answer to the REPHRASED target question is NO, z and f are not both POSITIVE
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
From statement 1, we concluded that EITHER z and f are both positive OR z and f are both negative
If z and f are both positive, then the sum of z and f will be POSITIVE
If z and f are both negative, then the sum of z and f will be NEGATIVE

Statement 2 tells us that The sum of z and f is positive.
AHA!
This means it must be the case that z and f are both positive
So, the answer to the REPHRASED target question is YES, z and f are both POSITIVE
Since we can answer the REPHRASED target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent

swerve wrote: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 of \(z\) and \(f\) is positive.

The OA is C

Source: GMAT Prep

In other words, we need to determine: are both z and f positive?

Statement One Alone:

The product of z and f is positive.

Since the product of z and f is positive, either z and f are both positive or both negative. However, we cannot determine on which side of the number line they fall. Statement one is not sufficient to answer the question.

Statement Two Alone:

The sum of z and f is positive

Although the sum is positive, either both z and f are positive or one is positive and one is negative. Thus, we cannot determine on which side of the number line they fall. Statement two is not sufficient to answer the question.

Statements One and Two Together:

Using the statements together, we see that the only possible scenario that works is when both z and f are positive.

Answer: C