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# Is m + z > 0?

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Manager
Joined: 09 Jul 2008
Posts: 112
Location: Dallas, TX
Schools: McCombs 2011
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Kudos [?]: 36 [0], given: 1

Is m + z > 0? [#permalink]

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11 Feb 2009, 17:20
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Difficulty:

65% (hard)

Question Stats:

60% (01:54) correct 40% (01:38) wrong based on 196 sessions

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Is m + z > 0?

(1) m - 3z > 0
(2) 4z - m > 0

OPEN DISCUSSION OF THIS QUESTION IS HERE: is-m-z-0-1-m-3z-0-2-4z-m-106381.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 30 Aug 2013, 04:36, edited 1 time in total.
Senior Manager
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11 Feb 2009, 20:57
3
KUDOS
I will go with C.

From clue 1, m-3z > 0 here m, z can be positive or negative. So cannot say whether m + z > 0. Hence Insufficient.

From clue 2, 4z-m > 0, here m, z can be positive or negative. So cannot say whether m + z > 0. Hence Insufficient.

Cosider both the clues.

m-3z>0--->Ine1
4z-m>0 --->ine2

Add both the inequalities, z > 0.
m-3z > 0 ==> m > 3z. Since Z is positive m also should be positive.

So we can say that m+z > o. Hence sufficient.
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12 Feb 2009, 03:38
8
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It is also possible to solve it by drawing:

1. Let's draw our statement using two colors: red (statement is false) and green (statement is true). We will have two color cake:
Attachment:

t75657_1.png [ 6.27 KiB | Viewed 10529 times ]

2. Now, cut a bit of the cake by first condition:
Attachment:

t75657_2.png [ 9.33 KiB | Viewed 10526 times ]

3. cut a bit of the cake by second condition:
Attachment:

t75657_3.png [ 8.99 KiB | Viewed 10518 times ]

4. Now, use both conditions:
Attachment:

t75657_4.png [ 10.54 KiB | Viewed 10525 times ]

So, C is obvious after drawing as the statement is only true.
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12 Feb 2009, 09:27
great pictures.!!!! good alternative..
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Manager
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12 Feb 2009, 10:02
OA is C. I am not familiar with this picture method. I ended up doing addition of inequalities and got the answer on the test and I probably spent 2-3 min on this question.
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12 Nov 2009, 20:01
1) m>3Z not sufficient;
2) m<4Z not sufficient;

1) and 2) adding together => Z>0 -> m+Z >0

C
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Manager
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19 Nov 2009, 21:05
C

I also used the adding two inequalities method. Have to learn the graphical approach...
Intern
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27 Dec 2009, 16:33
2
KUDOS
Q : m + z > 0 ?

1. m-3z > 0

m+z > 4z

For this to be sufficient, z > 0 should be known, but we don't know that, hence insufficient.

2. 4z-m > 0

m+z > 5/4 m OR 4z > m

For this to be sufficient, m > 0 should be known, but we don't know that, hence insufficient.

Combining 1 & 2 :

m+z > 4z > m

m+z-m > 4z-m > m-m

z > 4z-m > 0. This solves our question in 1. Hence sufficient. => C
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Re: Is m + z > 0? (1) m - 3z > 0 (2) 4z - m > 0 [#permalink]

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17 Jan 2012, 19:41
I am learning graphical approach..is it useful for all the Inequalities Q?
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Re: Is m + z > 0? (1) m - 3z > 0 (2) 4z - m > 0 [#permalink]

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17 Jan 2012, 20:08
Is m + z > 0?

(1) m - 3z > 0

m > 3z

Not sufficient

(2) 4z - m >0

4z > m

Not sufficient

1 + 2

z > 0

From 1
m > 3z

so both m and z are positive, hence their sum is positive.
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29 Aug 2013, 22:06
Can you explain after drawing graphs how to interpret them.?

I am able to draw all but how to interpret while taking two lines at a time, I am not getting it.Please advise.

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30 Aug 2013, 04:38
2
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Expert's post
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ygdrasil24 wrote:
Can you explain after drawing graphs how to interpret them.?

I am able to draw all but how to interpret while taking two lines at a time, I am not getting it.Please advise.

Explained here: graphic-approach-to-problems-with-inequalities-68037-80.html

Is m+z > 0

(1) m - 3z > 0. Insufficient on its own.
(2) 4z - m > 0. Insufficient on its own.

(1)+(2) Remember we can add inequalities with the sign in the same direction --> $$m-3z+4z-m>0$$ --> $$z>0$$, so $$z$$ is positive. From (1) $$m>3z=positive$$, so $$m$$ is positive too ($$m$$ is more than some positive number $$3z$$, so it's positive) --> $$m+z=positive+positive>0$$. Sufficient.

OPEN DISCUSSION OF THIS QUESTION IS HERE: is-m-z-0-1-m-3z-0-2-4z-m-106381.html
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Re: DS: From GMATPREP   [#permalink] 30 Aug 2013, 04:38
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