to the original poster:
your error is here --

er.twi.fb wrote:let z=-5, then -15<m<-20 and suppose m=-16,so m+z=-5-16<0

"-15 < m < -20" is impossible; a number can't be both greater than -15 and less than -20 at once.
if this is not obvious, the obfuscation comes from the fact that the numbers are negative -- many people don't really have the proper intuition regarding negative numbers. however, the statement -15 < m < -20 is a lot like the statement 10 < m < 5; both are contradictory to themselves.

in fact, the statement 3z < m < 4z, by itself, proves that m and z are both positive, since "3z < 4z" is a false statement unless z is positive (and once you've established that z this positive, it follows that m must also be positive, since it's sandwiched between two positive values).

by the way, this problem is from GMATPREP, and it has not been reproduced faithfully.

the original of the problem is:

Is m + z > 0 ?
(1) m - 3z > 0
(2) 4z - m > 0

note that this original form makes it much easier to combine the statements: just add them together!

once you've figured out that the two individual statements are insufficient, add them together:
m - 3z > 0
4z - m > 0
--------------
z > 0

once you figure out that z > 0, then realize that m > 3z, so m is also positive.
therefore m and z are also positive, so m + z > 0.

lunarpower wrote:the original of the problem is:

Is m + z > 0 ?
(1) m - 3z > 0
(2) 4z - m > 0

just for fun, here's an awesome (but useless, in terms of takeaways/studying) solution!

* first, eliminate statements 1 and 2 individually

* then, some magic:
multiply statement (1) by 5, and multiply statement (2) by 4
then add them!
you get:
5m - 15z > 0
16z - 4m > 0
-----------------
m + z > 0

i will now return to providing solutions that are actually useful :)