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m+z>0?

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Source: — Data Sufficiency |
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by GMATGuruNY » Fri Jan 01, 2016 8:36 am
Is m+z > 0?

1) m-3z>0
2) 4z-m >0
Statement 1: m > 3z.
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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by Brent@GMATPrepNow » Fri Jan 01, 2016 8:45 am
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

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by Matt@VeritasPrep » Fri Jan 08, 2016 2:22 pm
I'd just add the two together:

(m - 3z) + (4z - m) > 0 + 0

z > 0

Since m > 3z, we also have m > 0.

So m + z = the sum of two positives, and we're set!
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