1. m > 3z
m + z > 4z

We need to know whether z > 0. Insuff

2. m < 4z
m + z < 5z, Insufficient


Combined. z > 0 and m > 0. Sufficient.

hpgmat wrote:is M+Z > 0?

A) m - 3z>0
B) 4Z-m >0

We need to know whether m + z>0

With inequalities, if you are dividing or multiplying by a negative you have to flip the inequality sign. But other than that you can treat inequalities the same way you would treat an equal sign. Here, we don't have to worry about division or multiplication.

Therefore, the first statement is just telling us that m>3z. This can happen with m and z both being negative or both positive. So, with the information in this statement, the answer to the question can be either yes or no: Insufficient.

Statement two: 4z>m. Similar reasoning. Insufficient.(when analyzing this statement, we can't refer to the information in the other statement).

Combo:


When the inequality arrows are poining in the same direction, we can add the inequalities.

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

So z is positive. Statement one tells us that m>3z. The only way m can be greater than (three times) a positive number is if m is also positive.

If both m and z are positive, then definitely their sum m+z is positive.

Therefore, the answer to the question is yes, and the statements, although insufficient in isolation, are sufficient in combination.

Choose C.

When the inequality arrows are pointing in the same direction, we can add the inequalities.

Can you also subtract in this situation or can you only add?

pkw209 wrote:

When the inequality arrows are pointing in the same direction, we can add the inequalities.

Can you also subtract in this situation or can you only add?

No subtraction. Reason: we do not know which one is greater.

see this :

1) 3 > 0
2) 4 > 0


is (1) - (2) > 0 ?

But of course, their addition : 7, will also be greater than 0.

Harsha's correct.

Technically, we can subtract when the inequality arrows are pointing in opposite directions. However, there are many exceptions to this rule, so for the GMAT you're better off staying away from it. If the arrows are in opposite directions, you can divide (or multiply) one of the inequalities by negative one, which will flip the sign. Then, the arrows will point in the same direction, and you can add.

We can also "connect" or "chain-up" multiple inequalities (providing there is at least one shared variable).

(1) tells us that m > 3z

(2) tells us that 4z > m

Thus: 4z > m > 3z

Thus: 4z > 3z

Thus: z is positive (4z's will be greater than 3 z's when z is positive; if z were negative, then 4 of them would be smaller than 3 of them; in other words, if z were negative, the inequality sign would be the other way around)

And because m > 3z, m is also positive.

m+z>0

A m-3z>0
b. 4z-m>0


a. m-3z doest not give anything that can prove m+z>0
b.4z-m>0 also doest not give any information

now combing a n b m-3z+4z-m>0
z>0

when z>0
and m>3z

so m>0

m+z>0

so C