Is m+z>0
(1) m - 3z > 0
(2) 4z - m > 0
Here's another way to handle the two statements combined....
Target question:
Is 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
Multiply both sides of
-3z + m > 0 by 5 to get:
-15z + 5m > 0
Multiply both sides of
4z - m > 0 by 4 to get:
16z - 4m > 0
Since both inequality signs are
facing the same direction, we can ADD the two
green inequalities to get:
z + m > 0
Since we
can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer =
C
Cheers,
Brent
