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# Is m+z > 0? 1) m-3z >0 2) 4z-m >0 According to me,

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Is m+z > 0? 1) m-3z >0 2) 4z-m >0 According to me, [#permalink]

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14 Oct 2011, 12:47
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25% (medium)

Question Stats:

84% (01:52) correct 16% (00:57) wrong based on 19 sessions

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

[Reveal] Spoiler: Doubt
According to me, the answer should be E.

According to GMAT Prep, answer is C. If we consider both the statements, it will end up as 3z<m<4z. How can we confirm that m+z>0 until and unless we know the value of z (+ve or -ve)

Pls help me on this one.
[Reveal] Spoiler: OA
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Re: GMAT Prep quant Doubt [#permalink]

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14 Oct 2011, 13:12
1
KUDOS
rvind wrote:
Is m+z > 0?
1) m-3z >0
2) 4z-m >0

According to me, the answer should be E.

According to GMAT Prep, answer is C. If we consider both the statements, it will end up as 3z<m<4z. How can we confirm that m+z>0 until and unless we know the value of z (+ve or -ve)

Pls help me on this one.

If you consider z negative than equation will be -> 3z>m>4z
consider z=-1, and assume m= - 3.5, these values doesn't fit the above equation. Hence negative value is not be a right for z amd m in this question. hence, C.
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Re: GMAT Prep quant Doubt [#permalink]

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14 Oct 2011, 13:28
Ajay369 wrote:

If you consider z negative than equation will be -> 3z>m>4z
consider z=-1, and assume m= - 3.5, these values doesn't fit the above equation. Hence negative value is not be a right for z amd m in this question. hence, C.

Ajay,

Though now that you have old that 3z<m<4z can only imply positive value of z i fully agree and feel i have always known this fact, but otherwise I wouldn't have picked this relation if i saw in question format. thanks so much for this.

however i did solved this question and got the right answer c but through different method(which took me about 1.75mins), can you tell me if my way was right. I solved like this
Is m+z > 0?
1) m-3z >0
2) 4z-m >0

as both inequalities have same side, I added both LHS and RHS sides to get z > o

After that I multiplied inequality 1 by 4 to get 4m -12z >0 and inequality 2 by 3 to get 12z -3m..........again I added both t get m > 0.....can you tell me if my multiplying any inequality by a positive number is correct or not ? especially when RHS side contains 0 ?
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Re: GMAT Prep DS: Is m+z > 0 [#permalink]

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14 Oct 2011, 13:33
1
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rvind wrote:
Is m+z > 0?
1) m-3z >0
2) 4z-m >0

1)
m-3z>0
m>3z
3z<m----------1
m=-1; z=-1; m+z=-2<0
m=4; z=1; m+z=5>0
Not Sufficient.

2)
4z-m>0
4z>m
OR
m<4z--------------2
m=1; z=1; m+z=2>0
m=-5; z=-1; m+z=-6<0
Not Sufficient.

Putting together:
m-3z+4z-m>0
z>0

From 1 and 2:
We know; 3z<m<4z AND z=+ve; 3z=+ve; m is some +ve greater than 3z.
Sufficient.

Ans: "C"
*******************************

A graph would also be a good way to solve this if someone care to put that down. I know walker is an expert.
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Re: GMAT Prep DS: Is m+z > 0 [#permalink]

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14 Oct 2011, 13:57
fluke wrote:
rvind wrote:
Is m+z > 0?
1) m-3z >0
2) 4z-m >0

1)
m-3z>0
m>3z
3z<m----------1
m=-1; z=-1; m+z=-2<0
m=4; z=1; m+z=5>0
Not Sufficient.

2)
4z-m>0
4z>m
OR
m<4z--------------2
m=1; z=1; m+z=2>0
m=-5; z=-1; m+z=-6<0
Not Sufficient.

Putting together:
m-3z+4z-m>0
z>0

From 1 and 2:
We know; 3z<m<4z AND z=+ve; 3z=+ve; m is some +ve greater than 3z.
Sufficient.

Ans: "C"
*******************************

A graph would also be a good way to solve this if someone care to put that down. I know walker is an expert.

Awesome explanation Fluke , yet again
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Re: GMAT Prep DS: Is m+z > 0 [#permalink]

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14 Oct 2011, 14:36
I picked E, but I understand why C is the answer.

Stm1) m-3z>0....m+z>4z...m and z can take any value
Not Sufficient.

Stm2) 4z-m>0...m+z<5z...m and z can take any value
Not Sufficient.

Combined Stm1 and Stm2:
4z<m+z<5z
AND if (m-3z>0) + (4z-m>0) = z>0
then m+z>0 therefore Sufficient.
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Re: GMAT Prep quant Doubt [#permalink]

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14 Oct 2011, 17:38
Aj85 wrote:
Ajay369 wrote:

If you consider z negative than equation will be -> 3z>m>4z
consider z=-1, and assume m= - 3.5, these values doesn't fit the above equation. Hence negative value is not be a right for z amd m in this question. hence, C.

Ajay,

Though now that you have old that 3z<m<4z can only imply positive value of z i fully agree and feel i have always known this fact, but otherwise I wouldn't have picked this relation if i saw in question format. thanks so much for this.

however i did solved this question and got the right answer c but through different method(which took me about 1.75mins), can you tell me if my way was right. I solved like this
Is m+z > 0?
1) m-3z >0
2) 4z-m >0

as both inequalities have same side, I added both LHS and RHS sides to get z > o

After that I multiplied inequality 1 by 4 to get 4m -12z >0 and inequality 2 by 3 to get 12z -3m..........again I added both t get m > 0.....can you tell me if my multiplying any inequality by a positive number is correct or not ? especially when RHS side contains 0 ?

@Aj85 - your method is also right but as you said, it takes time. while solving any inequality i always prefer to put relevant numerical values and check. In this question its very easy to figure out that when z is negative the equation is -> 3z>m>4z and when z is positive than equation is -> 3z<m<4z. Put z=-1, and m= - 3.5 and z=1, and m= 3.5 respectively.

Hope it helps.
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Re: GMAT Prep DS: Is m+z > 0 [#permalink]

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15 Oct 2011, 00:44
ans C ..add 2 options u wil get ans
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Re: GMAT Prep DS: Is m+z > 0 [#permalink]

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17 Oct 2011, 14:42
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Expert's post
Here is a graph. Two statements define the light green area. For each point of the area m+z>0 is true. So, sufficient.

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graphs_122011.png [ 10.72 KiB | Viewed 1496 times ]

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Re: GMAT Prep DS: Is m+z > 0   [#permalink] 17 Oct 2011, 14:42
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# Is m+z > 0? 1) m-3z >0 2) 4z-m >0 According to me,

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