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M+z>0?

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M+z>0?

by Mormuse » Sat Mar 30, 2013 4:50 am
1) m-3z>0
2) 4z-m >0

I might do something wrong cause everytime i deal with this type of question, i get stuck after my first step. Actuaaly i almost always start by the following:
m>3z. If both m & z are positive then yes m+z is positive, if both are negative then no. If one of them is positive and the other negative, then no.
Same with the other statement and i usually cannot conclude.
What am i doing wrong? Is it possible to have a comprehensive approach of how to tackler these?
Many thx in advance.
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by rintoo22 » Sat Mar 30, 2013 5:07 am
hi claudayst,

I understand this is a DS question. You have posted the Statements and not the question. Kindly post the question.
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by Brent@GMATPrepNow » Sat Mar 30, 2013 5:12 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 GMATGuruNY » Sat Mar 30, 2013 6:14 am
claudayst wrote: 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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