Is m + z > 0?
(1) m - 3z > 0
(2) 4z - m > 0
GMAT Prep Inequalities
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Statement 1: m > 3z.Is m+z > 0?
1) m-3z>0
2) 4z-m >0
It's possible that z=1 and m=4.
In this case, m+z > 0.
It's possible that z=-10 and m=4.
In this case, m+z < 0.
INSUFFICIENT.
Statement 2: m < 4z
It's possible that z=1 and m=3.
In this case, m+z > 0.
It's possible that z=1 and m=-10.
In this case, m+z < 0.
INSUFFICIENT.
Statements combined:
One approach is to LINK together the inequalities.
Since 3z < m and m < 4z, we get:
3z < m < 4z
3z < 4z
0 < z.
Since z>0 and m > 3z, m > 0.
Thus, m+z > 0.
SUFFICIENT.
The correct answer is C.
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Statement 1:prata wrote:Is m + z > 0?
(1) m - 3z > 0
(2) 4z - m > 0
Statement 1 looks insufficient. Try some positives and negatives to make sure that it is.
m = 6, z = 1
m - 3z = 3, 3 > 0
m + z = 7, 7 > 0
Answer to question is Yes.
m = 6, z = -10
m - 3z = 36, 36 > 0
m + z = -4, - 4 < 0
Answer to question is No.
Insufficient.
Statement 2:
This statement looks insufficient also. Use positive and negative values to confirm.
m = 1, z = 6
4z - m = 23, 23 > 0
m + z = 7, 7 > 0
Answer to the question is Yes.
m = -10, z = 6
4z - m = 34, 34 > 0
m + z = -4, - 4 < 0
Answer to the question is No.
Insufficient.
Statements Combined:
You can add inequalities that go the same way.
m - 3z > 0
4z - m > 0
----------
z > 0
If z > 0, then 3z > 0. If m - 3z > 0, then m > 3z > 0.
So m > 0, z > 0 and m + z > 0.
Sufficient.
The correct answer is C.
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Target question: m + z > 0Is 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.
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
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Here's a slight twist!
Rephrase the stem as
"Is m > -z ?"
S1:
m > 3z
So the question becomes "Is -z > 3z?" We can't say; INSUFFICIENT.
S2:
4z > m
So the question becomes "Is 4z > -z?" We can't say; INSUFFICIENT.
Together, we have 4z > m > 3z, or 4z > 3z. This means z > 0. Since m > 3z > 0 > -z, we know m > -z, and the two statements together are SUFFICIENT.
Rephrase the stem as
"Is m > -z ?"
S1:
m > 3z
So the question becomes "Is -z > 3z?" We can't say; INSUFFICIENT.
S2:
4z > m
So the question becomes "Is 4z > -z?" We can't say; INSUFFICIENT.
Together, we have 4z > m > 3z, or 4z > 3z. This means z > 0. Since m > 3z > 0 > -z, we know m > -z, and the two statements together are SUFFICIENT.