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Is m + z > 0?

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Is m + z > 0? [#permalink] New post 11 Feb 2009, 16:20
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

55% (02:07) correct 44% (01:47) wrong based on 65 sessions
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, 03:36, edited 1 time in total.
Added the OA.
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Re: DS: From GMATPREP [#permalink] New post 11 Feb 2009, 19:57
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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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Re: DS: From GMATPREP [#permalink] New post 12 Feb 2009, 02:38
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Expert's post
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
t75657_1.png [ 6.27 KiB | Viewed 4987 times ]


2. Now, cut a bit of the cake by first condition:
Attachment:
t75657_2.png
t75657_2.png [ 9.33 KiB | Viewed 4982 times ]


3. cut a bit of the cake by second condition:
Attachment:
t75657_3.png
t75657_3.png [ 8.99 KiB | Viewed 4978 times ]


4. Now, use both conditions:
Attachment:
t75657_4.png
t75657_4.png [ 10.54 KiB | Viewed 4983 times ]


So, C is obvious after drawing as the statement is only true.
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Re: DS: From GMATPREP [#permalink] New post 12 Feb 2009, 08:27
great pictures.!!!! good alternative..
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Re: DS: From GMATPREP [#permalink] New post 12 Feb 2009, 09:02
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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Re: DS: From GMATPREP [#permalink] New post 12 Nov 2009, 19:01
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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Re: DS: From GMATPREP [#permalink] New post 19 Nov 2009, 20:05
C

I also used the adding two inequalities method. Have to learn the graphical approach...
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Re: DS: From GMATPREP [#permalink] New post 27 Dec 2009, 15:33
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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] New post 17 Jan 2012, 18:41
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] New post 17 Jan 2012, 19:08
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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Re: DS: From GMATPREP [#permalink] New post 29 Aug 2013, 21:06
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.


Thanks in advance :-)
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Re: DS: From GMATPREP [#permalink] New post 30 Aug 2013, 03:38
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Expert's post
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.


Thanks in advance :-)


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.

Answer: C.

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, 03:38
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