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Source: Beat The GMAT — Data Sufficiency |
GMAT/MBA Expert
-
Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Location: Vancouver, BC
- Thanked: 5254 times
- GMAT Score:770
Target question: m + z > 0prat_agl wrote:Is m + z > 0?
1) m - 3z >0
2) 4z - m >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
Since both inequality signs are facing the same direction, we can add the two given inequalities to get: z > 0
In other words, z is positive.
If z is positive, then 3z is positive, and if 3z is positive then m must be positive (since we know that 3z < m)
If z and m are both positive, then m + z must be greater than 0
Since we can now answer the target question with certainty, the combined statements are SUFFICIENT
Answer = C
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
