Gmat Prep - Number Line

[dubeystuts]

Are the integers z and f to the right of 0 on the number line?
1) product of z and f is positive
2) sum of z and f is positive

I chose e.

From 1. for product to be positive, either z and f are both positive or both negative. Not Suffcient

From 2. for some to be positive, either z and f are both positive or both negative. Not sufficient.

Combing 1 and 2 I think it is still insufficient but the correct answer is C. Can someone please explain?

[DanaJ]

You did a pretty good job when ruling out A, but not for stmt 2.
For a sum of two numbers to be positive, you have three options:
a. z is positive and f is negative. Example: z is 6 and f is -1. z + f = 5 >0.
b. z is negative and f is positive. Example: z is -3 and f is 5. z + f = 2 > 0.
c. both numbers are positive, which means that their sum will always be positive.
Now, you can NEVER add two negatives and have a positive sum, since both of them are negative!
So, by using stmt 2, you get nowhere.

But when you combine the two, you get that z and f are both positive, since it is the only common case for the two statements. So C is correct.

[dubeystuts]

Many Thanks.

Yes you are right. I did not evaluate statement 2 properly.

Thanks a lot for your help.