From 1 we get
m+z>4z...no information about sign of z..not sufficient

From 2
m+z<5z...no information about sign of z..not sufficient

combining
4z<m+z<5z...or 4z<5z..this is possible when z >0,,hence m+z>0...sufficient

Ans option C

sp.wonder2010 wrote:Is m+z >0 ?


1. M -3z >0
2. 4z-m>0

Statement I : Insufficient as info about sign of Z is not available

Stament II : same reason as above : Insufficient

Combining I & II

We can add both the equations if their inequality sign is same

therefore m-3z+4z-m>0

so z>0

From I: M-3z> 0

therefore M has to be positive

Z Positive (already proved)

Hence M+Z>0

HTH

The explanation below is pasted from a different thread


To be fair, this is a tough question, but it should teach you an important take-away: In general it's better to rephrase your equations so that you do not have leading negative signs in front of your variables. In this case, rewrite the statements as:
(1) m > 3z
(2) 4z > m.

Alone these give no information about signs. However when we put them together, we learn that 4z > 3z --> z > 0 and that will make all the difference (since m > 3z, m will also be > 0). The correct answer is C

This is QID 1020

-Patrick