Data Sufficiency

Is m + z > 0?

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

Question is from GMATPrep Software.

OA is C

vrn2vw wrote:Is m + z > 0?

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

Question is from GMATPrep Software.

OA is C

Statement 1: m - 3z >0
m =1 and z = -1 ==> m+z = 0
m=2 and z = -1 ==> m+z >0
NOT SUFFICIENT

Statement 2: 4z-m>0
m = -1 and z = 0.1 ==> m+z < 0
m=2 and z = 1 ==> m+z >0
NOT SUFFICIENT

Combining the two statements

m-3z + 4z -m >0
z > 0.... (P)
from 1, m > 3z and from 2, 4z > m
==> 3z < m < 4z... (Q)
from (P) and (Q) m+Z > 0

Answer: Option C

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Is m + z > 0?

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

There are 2 variables (m,z) and 2 equations are given by the 2 conditions, so there is high chance (C) will be the answer.
Looking at the conditions together,
from m-3z>0, 4z-m>0, and we can get m-3z+4z-m>0, z>0
Condition 1, m>3z>0 and m>0 which answers the question 'yes' and makes the condition sufficient.
The answer therefore becomes (C).

For cases where we need 2 more equations, such as original conditions with "2 variables", or "3 variables and 1 equation", or "4 variables and 2 equations", we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.

Hi Experts ,

I got stuck in this, please help me out.

From statement 1 : we get m>3z

From statement 2 : we get 4z>m

So we combine both the statement we get 3z<m<4z


Now what will be the next step?

Please advise

Thanks in advance.

SJ

vrn2vw wrote:Is m + z > 0?

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

Statement (1)
m-3z > 0
m > 3z
No info on the signs of m or z
Insufficient

Statement (2)
4z-m > 0
4z > m
No info on the signs of m or z
Insufficient

Adding statements (1) + (2)
(m-3z) + (4z-m) > 0 [Can add inequalities when their signs are in the same direction]
z > 0

if z > 0, then m > 0 [from statement (1)]
m + z > 0
Sufficient

Answer C

jain2016 wrote:Hi Experts ,

I got stuck in this, please help me out.

From statement 1 : we get m>3z

From statement 2 : we get 4z>m

So we combine both the statement we get 3z<m<4z


Now what will be the next step?

Please advise

Thanks in advance.

SJ

You've got it!

4z > 3z implies that z is positive.

m > 3z implies that m is also positive, since m > 3z > z > 0.

So m and z are BOTH positive, meaning that m + z is also positive.