GMAT Prep Question - Inequality

[dongkim2]

M + Z > 0?

(1) M - 3Z > 0

(2) 4Z - M > 0

OA: C

[spoiler]Since I couldn't answer for the above based on (1) and (2) individually, I combined (subtraction is not allowed) both inequalities and came up with Z > 0. Based on (1), I came up with M > 3Z > 0. Therefore, I concluded M + Z is greater than 0. Please let me know my reasoning was correct. Thanks![/spoiler]

[asamaverick]

Your reasoning is perfectly fine.

There is another way to do this.
Multiply (1) by 5 to get - > 5M - 15Z > 0
Multiply (2) by 4 to get - > 16Z - 4M > 0

Add the two and you get:
M + Z > 0

[jube]

1) M > 3Z - insuff
2) 4Z > M - insuff.

1&2 combined: 4Z > M > 3Z. So, if:

both M &Z are +ve and M+Z>0
both M&Z are -ve and M+Z<0

Isn't this also insuff. since M+Z can be either positive or negative?

[gmatmachoman]

1) M > 3Z - insuff
2) 4Z > M - insuff.

1&2 combined: 4Z > M > 3Z. So, if:

both M &Z are +ve and M+Z>0
both M&Z are -ve and M+Z<0

Isn't this also insuff. since M+Z can be either positive or negative?

I liked ur way of "out of box " reasoning..But but there is a glitch!

U said very clearly 4Z>M and 4Z> 3Z

So as per ur second statement both M&Z are -ve and M+Z<0

Z cannot be Negative !!

If Z is <0 then 4Z cannot be greater that 3Z..That would violate the deductions!!

So for 4Z to be greater than 3Z, Z has to be greater than zero!!

It becomes like 4z>3Z>0 !!

[jube]

1) M > 3Z - insuff
2) 4Z > M - insuff.

1&2 combined: 4Z > M > 3Z. So, if:

both M &Z are +ve and M+Z>0
both M&Z are -ve and M+Z<0

Isn't this also insuff. since M+Z can be either positive or negative?

I liked ur way of "out of box " reasoning..But but there is a glitch!

U said very clearly 4Z>M and 4Z> 3Z

So as per ur second statement both M&Z are -ve and M+Z<0

Z cannot be Negative !!

If Z is <0 then 4Z cannot be greater that 3Z..That would violate the deductions!!

So for 4Z to be greater than 3Z, Z has to be greater than zero!!

It becomes like 4z>3Z>0 !!

Ahh!! I see the mistake I was making! Thank you!