IMO C
These kind of problems think or draw a number line then try to put the possible values m and z without violating the inequalities.
from 1: m-3z>0 => m>3z
but we cannot say e=whether m and z are +ve or negative. (say m = -2,z=-1 then m>3z but m+z < 0)
from 2: 4z > m still we cannot say whether m+z > 0.
Combine 1 and 2 we can get 4z>m>3z. this pattern is only valid when m and z both are + ve. so m + z > 0
Hope this helps
GMAT Prep: Numbers
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Rahul@gurome
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(1) If m = 15 and z = 4, then m + z = 19 > 0
If m = -9 and z = -4, then m + z = -13 < 0
No unique answer.
So, (1) is NOT SUFFICIENT.
(2) If m = 2 and z = 1, then m + z = 3 > 0
If m = -9 and z = -2, then m + z = -11 < 0
No unique answer.
So, (2) is NOT SUFFICIENT.
Combining (1) and (2), m - 3z > 0 or m > 3z and 4z - m > 0 m < 4z
So, 3z < m < 4z
If we take z = -1, then 3z < m < 4z does not hold true. It is true only for positive values of z, and when z is positive, m is also positive. hence m + z > 0
The correct answer is [spoiler](C)[/spoiler].
If m = -9 and z = -4, then m + z = -13 < 0
No unique answer.
So, (1) is NOT SUFFICIENT.
(2) If m = 2 and z = 1, then m + z = 3 > 0
If m = -9 and z = -2, then m + z = -11 < 0
No unique answer.
So, (2) is NOT SUFFICIENT.
Combining (1) and (2), m - 3z > 0 or m > 3z and 4z - m > 0 m < 4z
So, 3z < m < 4z
If we take z = -1, then 3z < m < 4z does not hold true. It is true only for positive values of z, and when z is positive, m is also positive. hence m + z > 0
The correct answer is [spoiler](C)[/spoiler].
Rahul Lakhani
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Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
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GMATMadeEasy
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