Though I have not started working on inequalities, so it is hard for me to understand the above solution posted by Camitava.

However, there is also another way to solve this problem without having much knowledge about inequalities. Here it goes:-

Statement 1: m - 3z > 0 => m > 3z
Statement 2: 4Z - m > 0 => 4z > m

From both statement as you deduce that 4z > m > 3z

Now lets check the solution with negative values to prove that m + z < 0

Lets take z = -1 (simplest one)
i.e -4 > m > -3
which is incorrect as -4 can't greater than -3.

Now lets check with some negative fractional value.
Lets take -1/12 (divisible by both 3 and 4)

therefore equation becomes, -0.33 > m > -0.25, which again incorrect, as -0.33 cannot be greater than -0.25

So, it means z cannot be negative. So, if z is not negative, then m also cannot be negative.

Therefore adding 2 positive number yields a positive number.
i.e. m + z > 0

There C is the answer

camitava wrote:
From this I deduced that 3z<m<4z> 0 or z > 0

Hi Camitava, Can you explain here how you have taken z > 0 ?

I didn't understand this point.

codesnooker wrote:

camitava wrote:
From this I deduced that 3z<m<4z> 0 or z > 0

Hi Camitava, Can you explain here how you have taken z > 0 ?

I didn't understand this point.

Sorry! I really don;t know how did I mess up while posting my last post.

I meant to say that - add the two equs : m-3z>0
and 4z-m>0.
So m - 3z + 4z - m > 0
or z > 0
From this m > 3z or m > 0
So m + z > 0

Got me, Codesnooker?

Ohhh! Got it now... Last time I forgot to uncheck the option - Disable HTML in this post or may be I messed up in some other way ...

Sure, thanks

Yes HTML code is ruining the answers in case of questions of inequalities. Disable them, before posting answers or questions of inequalities

Just as a general tip, you can turn html off under your profile and then just unclick the box if you ever decide you need it.

As a quick point on this discussion (if it's even needed anymore), Codesnooker got to:

From both statement as you deduce that 4z > m > 3z

From here, we can see that:

4z > 3z

which can only be true if z is positive.

And, since m > 3z, this means that m is also positive.

So, since both z and m are positive, it must be true that:

m + z

is also positive.

C is the answer.