naveenhv wrote:Is M + Z > 0?
1) M - 3Z > 0
2) 4Z - M > 0
We can use counter-examples to quickly show that each statement alone is insufficient.
(1) If M - 3Z > 0 then:
case 1: M=4 and Z=1 --> M+Z
is greater than 0
case 2: M=4 and Z=-10 --> M+Z
is not greater than 0
Insufficient
(2) If 4Z - M > 0 then:
case 1: Z=4 and M=1 --> M+Z
is greater than 0
case 2: Z=1 and M=-10 --> M+Z
is not greater than 0
Insufficient
(1 and 2 combined)
First take statement 1 and rearrange:
M - 3Z > 0 -->
M > 3Z -->
3Z < M (I like ordering inequalities so that the larger value is on the right-hand side, just like on the number line)
Then take statement 2 and rearrange:
4Z - M > 0 -->
4Z > M -->
M < 4Z
We can now combine these to get:
3Z < M < 4Z
From here, we can conclude that 3Z < 4Z
Now, if we subtract 3Z from both sides, we get 0 < Z (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 must be positive, then X + Z
must be greater than 0
So, the statements combined are sufficient, which means the answer is
CBrent Hanneson - Creator of GMATPrepNow.com
