I discussed this question here:

https://www.beatthegmat.com/is-m-z-0-t48172.html

pkw209 wrote:Is m + z > 0
a. m - 3z > 0
b. 4z - m > 0

a. m > 3z

If z is +ve, m is also +ve and m+z > 0. YES
If z is -ve, m is also -ve and m+z < 0. NO
Insufficient.

b. 4z > m

Same reasoning as stmt I. Insufficient.

Combined,

3z < M < 4z. In order to form this inequality, z must be greater than 0 (or positive). As M is greater than 3z, M is also positive. So, m+z > 0.
Sufficient.

Thanks guys. Sorry for the slow response, I've been extremely busy.

I got to C or E and my problem was that I subtracted the inequalities rather than add them as Testluv pointed out in his post.

However, I also tried picking numbers and that would satisfy both inequalities and couldn't find a pair that satisfied both. Considering that when you add the inequalities, the result is z>0, does that mean there are no two pairs but just that z is positive?

Also, I'm assuming it's ok if you simplify the question stem to is m>-z?

thanks.

Also, I'm assuming it's ok if you simplify the question stem to is m>-z?

Yes.

Once you combine, you know that z>0. And you know from (1) that m is bigger than z (ie, m>3z). Therefore, both must be positive; therefore, their sum is positive.

I just chose two positive numbers, z=2 and m=7 and the inequality worked. Not sure what I'm doing with some of these questions sometimes...

Anyway, thanks Testluv.