## Is m + z > 0?

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### Is m + z > 0?

by BTGmoderatorDC » Mon Sep 26, 2022 4:12 pm

00:00

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## Global Stats

Is m + z > 0?

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

OA C

Source: GMAT Prep

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### Re: Is m + z > 0?

by [email protected] » Wed Sep 28, 2022 7:19 am

00:00

A

B

C

D

E

## Global Stats

BTGmoderatorDC wrote:
Mon Sep 26, 2022 4:12 pm
Is m + z > 0?

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

OA C

Source: GMAT Prep
Target question: Is m + z > 0?

Statement 1: m - 3z > 0
There are several values of m and z that satisfy statement 1. Here are two:
Case a: m = 10 and z = 1. In this case, the answer to the target question is YES, m + n is greater than zero
Case b: m = 1 and z = -2. In this case, the answer to the target question is NO, m + n is not greater than zero
Since we can’t answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 4z - m > 0
There are several values of m and z that satisfy statement 2. Here are two:
Case a: m = 1 and z = 1. In this case, the answer to the target question is YES, m + n is greater than zero
Case b: m = -5 and z = 1. In this case, the answer to the target question is NO, m + n is not greater than zero
Since we can’t answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that m - 3z > 0
Statement 2 tells us that 4z - m > 0

To make things clearer, let's rearrange the terms in the first inequality to get:
-3z + m > 0
4z - m > 0

Since the inequality symbols are facing the SAME direction, we can ADD the inequalities to get: z > 0
Perfect! We now know that z is positive, but we still need information about the value of m.
There are several ways to accomplish this. My approach is to take the system:
-3z + m > 0
4z - m > 0

Multiply both sides of the top inequality by 4, and multiply both sides of the bottom inequality by 3 to get the following equivalent system:
-12z + 4m > 0
12z - 3m > 0

Since the inequality symbols are facing the SAME direction, we can ADD the inequalities to get: m > 0

We now know that m and z are both positive, which means m + z > 0
Since we can answer the target question with certainty, the combined statements are SUFFICIENT