## Is m+z>0

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### Is m+z>0

by amirhakimi » Wed Nov 06, 2013 8:15 am
Is m+z>0

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

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by GMATGuruNY » Wed Nov 06, 2013 8:21 am
Is m+z > 0?

1) m-3z>0
2) 4z-m >0
Statement 1: m > 3z.
It's possible that z=1 and m=4.
In this case, m+z > 0.
It's possible that z=-10 and m=4.
In this case, m+z < 0.
INSUFFICIENT.

Statement 2: m < 4z
It's possible that z=1 and m=3.
In this case, m+z > 0.
It's possible that z=1 and m=-10.
In this case, m+z < 0.
INSUFFICIENT.

Statements combined:
One approach is to LINK together the inequalities.
Since 3z < m and m < 4z, we get:
3z < m < 4z
3z < 4z
0 < z.
Since z>0 and m > 3z, m > 0.
Thus, m+z > 0.
SUFFICIENT.

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by [email protected] » Wed Nov 06, 2013 8:25 am
amirhakimi wrote:Is m+z>0

(1) m - 3z > 0
(2) 4z - m > 0
Here's another way to handle the two statements combined....

Target question: Is m + z > 0?

Statement 1: m - 3z > 0
There are several sets of numbers that meet this condition. Here are two:
Case a: m = 4 and z = 1, in which case m + z is greater than 0
Case a: m = 4 and z = -10, in which case m + z is not greater than 0
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 4z - m > 0
There are several sets of numbers that meet this condition. Here are two:
Case a: m = 1 and z = 4, in which case m + z is greater than 0
Case a: m = -10 and z = 1, in which case m + z is not greater than 0
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined:
Rearrange statement 1 to get: -3z + m > 0
Statement 2: 4z - m > 0

Multiply both sides of -3z + m > 0 by 5 to get: -15z + 5m > 0
Multiply both sides of 4z - m > 0 by 4 to get: 16z - 4m > 0

Since both inequality signs are facing the same direction, we can ADD the two green inequalities to get: z + m > 0
Since we can answer the target question with certainty, the combined statements are SUFFICIENT