Data Sufficiency

Is m + z > 0

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

Target question: 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
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.

For more on adding inequalities (and what you can and cannot do) see this video: https://www.gmatprepnow.com/module/gmat ... /video/982

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 answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent