Numbers

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Numbers

by prat_agl » Mon Nov 12, 2012 9:45 pm
Is m + z > 0?
a) m - 3z >0
b) 4z - m >0

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by nisagl750 » Mon Nov 12, 2012 10:24 pm
IMO C

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by Brent@GMATPrepNow » Tue Nov 13, 2012 6:21 am
prat_agl wrote: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 now answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by prat_agl » Tue Nov 13, 2012 12:27 pm
Thanks for the detailed explanation Brent.