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Is m + z > 0? (1) m - 3z > 0 (2) 4z - m > 0

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Manager
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Is m + z > 0? (1) m - 3z > 0 (2) 4z - m > 0 [#permalink]  11 Feb 2009, 17:20
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Question Stats:

42% (04:10) correct 57% (01:41) wrong based on 7 sessions
Is m + z > 0?

(1) m - 3z > 0

(2) 4z - m > 0
Senior Manager
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Re: DS: From GMATPREP [#permalink]  11 Feb 2009, 20:57
1
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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Re: DS: From GMATPREP [#permalink]  12 Feb 2009, 03:38
2
KUDOS
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 3716 times ]

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

t75657_2.png [ 9.33 KiB | Viewed 3713 times ]

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

t75657_3.png [ 8.99 KiB | Viewed 3710 times ]

4. Now, use both conditions:
Attachment:

t75657_4.png [ 10.54 KiB | Viewed 3716 times ]

So, C is obvious after drawing as the statement is only true.
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Re: DS: From GMATPREP [#permalink]  12 Feb 2009, 09:27
great pictures.!!!! good alternative..
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Re: DS: From GMATPREP [#permalink]  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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Re: DS: From GMATPREP [#permalink]  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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Re: DS: From GMATPREP [#permalink]  19 Nov 2009, 21:05
C

I also used the adding two inequalities method. Have to learn the graphical approach...
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Re: DS: From GMATPREP [#permalink]  27 Dec 2009, 16:33
1
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]  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]  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.
Re: Is m + z > 0? (1) m - 3z > 0 (2) 4z - m > 0   [#permalink] 17 Jan 2012, 20:08
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