Is m + z > 0?
(1) m  3z > 0
(2) 4z  m > 0
OA C
Source: GMAT Prep
Is m + z > 0?
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Target question: Is m + z > 0?BTGmoderatorDC wrote: ↑Mon Sep 26, 2022 4:12 pmIs m + z > 0?
(1) m  3z > 0
(2) 4z  m > 0
OA C
Source: GMAT Prep
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
Answer: C