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.
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
