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by DevB » Tue Jul 22, 2014 5:08 am
This question is from GMAT Prep so anyone planning to give the practice exam may avoid to see it here.

For others, Please help me in answering the below question:

Is m + z > 0 ?

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

Thanks in advance!
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Source: — Data Sufficiency |
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by GMATinsight » Tue Jul 22, 2014 5:46 am
DevB wrote:This question is from GMAT Prep so anyone planning to give the practice exam may avoid to see it here.

For others, Please help me in answering the below question:

Is m + z > 0 ?

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

Thanks in advance!
Question : Is m + z > 0 ?
Answer must be in the form of "YES" or "NO"

Statement 1) m - 3z > 0
Case 1: m = 10, z = 1 The answer to the question is YES
Case 2: m = -5, z = -3 The answer to the question is NO
INSUFFICIENT

Statement 2) 4z-m > 0

i.e. 4z > m
Case 1: m = 10, z = 1 The answer to the question is YES
Case 2: m = -5, z = -1 The answer to the question is NO
INSUFFICIENT

Combining the two statements
4z-m > 0 and m - 3z > 0
4z > m and m > 3z
Also

Adding the two equation
(4z-m)+(m-3z) > 0
i.e Z > 0

i.e. 4z>m>3z

Therefore both m and z are positive. therefore m+z>0

SUFFICIENT

Answer: Option C
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by Brent@GMATPrepNow » Tue Jul 22, 2014 5:56 am
Is m + z > 0?

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

Answer = C

Cheers,
Brent
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by GMATGuruNY » Tue Jul 22, 2014 6:03 am
Is m+z > 0?

(1) m-3z > 0
(2) 4z-m > 0
Statement 1: m > 3z.
m and z could both be positive, m and z could both be negative.
Insufficient.

Statement 2: m < 4z
m and z could both be positive, m and z could both be negative.
Insufficient.

Statements 1 and 2 combined:
Linking the inequalities, we get:
3z < m < 4z
3z < 4z.
0 < z.
Since z is positive, we know that m -- which is between 3z and 4z -- also is positive.
Thus, m+z > 0.
Sufficient.

The correct answer is C.
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