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Is m + z > 0 - ALGEBRAIC FORM

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venmic: Master | Next Rank: 500 Posts; Posts: 222; Joined: Mon Oct 13, 2008 4:04 pmFollowed by: 2 members; Thanked: 3 times

by venmic » Sat Jul 30, 2011 8:56 am

Is m + z > 0
(1) m - 3z > 0
(2) 4z - m > 0

I know this can be solved using numbers and I can do that

I need to know how to solve it algebraically ONLY

Appreciate your help

C

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Source: Beat The GMAT — Data Sufficiency | Sat Jul 30, 2011 8:56 am

MarkMeier20: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Wed Jul 27, 2011 5:41 am; Thanked: 1 times

by MarkMeier20 » Sat Jul 30, 2011 12:16 pm

Is m + z > 0
(1) m - 3z > 0
(2) 4z - m > 0

(1): m-3z>0 is equivalent to m+z>4z. Since we don't have any information about whether z is positive or negative, we can't conclude tan m+z>0
-> Insufficient

(2) 4z-m>0 is equivalent to m+z<5z. Since we don't have any information about whether z is positive or negative, we can't conclude tan m+z>0
-> Insufficient

(1)+(2):
If we add both equations, we get z>0. Since m-3z>0 is equivalent to m+z>4z and z>0 m+z>4z>0, Therefore C is the correct answer.

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