Positive/Negative Inequality Algebra

[NMencia09]

"Is m + z > 0?

"(1) m - 3z > 0
"(2) 4z - m > 0"

Question: I quickly realized neither (1) nor (2) are sufficient using theory, then when deciding between C and E, I ran into this question.

Combining inequalities: Is this approach correct:
1) add these two inequalities, leading to z>0
2) reason that if, as per statement (1), m-3z>0, and since z must be positive, that m must be positive too.
3) if both m and z are positive, m+z>0. (C) Sufficient together.

Is this a logical approach? i.e. to determine something that must be true according to the prompts, and then use that to deduce something about another variable in one of the prompts?

Hmm...?

[abemartin87]

your logic is right dude m>3z>z>0
and yes if statment 1) is saying one thing like z>0 that carries over into the other statement
don't worry, be happy.

http://www.youtube.com/watch?v=yHFDa9efCQU

[shubham_sagijain]

yes, the logic and the approach is very much correct...
Another way to approach is :

S1 : It gives m > 3z
S2 : it gives m < 4z

So, from S 1 and S 2, we know 3z< m < 4z.

Now, the only way 4z can be greater than 3z is when z is positive.

Hence the answer is C :)

Thanks,
Shubh

[NMencia09]

many thanks, Gentlemen!

[RonPurewal]

nice.

if you really get bored, you can also notice that ...
* multiplying statement 1 by 5
* multiplying statement 2 by 4
* adding the results
... actually gives m + z directly.
how 'bout that?

[NMencia09]

You just blew my mind, dude.
nice.

[RonPurewal]

here's another thread on this problem.
post41615.html#p41615