If x + y + z > 0, is z > 1 ?
(1) z > x + y + 1
(2) x + y + 1 < 0
Answer: B
Source: Official Guide
If x + y + z > 0, is z > 1 ?
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Target question: Is z > 1BTGModeratorVI wrote: ↑Thu Mar 19, 2020 5:27 amIf x + y + z > 0, is z > 1 ?
(1) z > x + y + 1
(2) x + y + 1 < 0
Answer: B
Source: Official Guide
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
Answer: B
Cheers,
Brent

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Great solution above.
I had prepared a YouTube video for the same in case you are looking for a visual:
https://youtu.be/km49QKnuyoo
I had prepared a YouTube video for the same in case you are looking for a visual:
https://youtu.be/km49QKnuyoo
GMAT/MBA Coach (MBA, Columbia Business School)
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Free YouTube Videos: GMATByExample YouTube
https://GMATByExample.com
Free YouTube Videos: GMATByExample YouTube