Is m + z > 0?
(1) m - 3z > 0
(2) 4z - m > 0
OA C
Source: GMAT Prep
Solve 700-Level Algebra Qs In 90 Secs!
Master 700-level Inequalities and Absolute Value Questions
Attend this free GMAT Algebra Webinar and learn how to master the most challenging Inequalities and Absolute Value problems with ease.
Is m + z > 0?
This topic has expert replies
-
- Moderator
- Posts: 7187
- Joined: Thu Sep 07, 2017 4:43 pm
- Followed by:23 members
GMAT/MBA Expert
- [email protected]
- GMAT Instructor
- Posts: 16201
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
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