## If x + y + z > 0, is z > 1 ?

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### If x + y + z > 0, is z > 1 ?

by BTGModeratorVI » Thu Mar 19, 2020 5:27 am
If x + y + z > 0, is z > 1 ?

(1) z > x + y + 1
(2) x + y + 1 < 0

Source: Official Guide

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### Re: If x + y + z > 0, is z > 1 ?

by [email protected] » Sat Mar 21, 2020 5:59 am
BTGModeratorVI wrote:
Thu Mar 19, 2020 5:27 am
If x + y + z > 0, is z > 1 ?

(1) z > x + y + 1
(2) x + y + 1 < 0

Source: Official Guide
Target question: Is z > 1

Given: x + y + z > 0

Statement 1: z > x + y +1
Let's create a similar inequality to x + y + z > 0
Take z > x + y +1 and subtract x and y from both sides to get: z - x - y > 1
We now have two inequalities with the inequality signs facing the same direction.
z - x - y > 1
x + y + z > 0
ADD them to get: 2z > 1
Divide both sides by 2 to get: z > 1/2
So, z COULD equal 2, in which case z > 1
Or z COULD equal 3/4, in which case z < 1
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x + y + 1 < 0
Let's use the same strategy.
This time, let's multiply both sides by -1 to get: -x - y - 1 > 0
We now have two inequalities with the inequality signs facing the same direction.
-x - y - 1 > 0
x + y + z > 0
ADD them to get: z - 1 > 0
Add 1 to both sides to get z > 1
Perfect!!!
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com

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### Re: If x + y + z > 0, is z > 1 ?

by gmatbyexample » Tue Aug 17, 2021 12:10 pm
Great solution above.

I had prepared a YouTube video for the same in case you are looking for a visual:

https://youtu.be/km49QKnuyoo
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