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

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Source: — Data Sufficiency |
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by GMATGuruNY » Fri Dec 20, 2019 7:09 pm
BTGmoderatorDC wrote:If x + y + z > 0, is z > 1?

(1) z > x + y + 1
(2) x + y + 1 < 0
Inequalities can be ADDED TOGETHER.
One condition:
Before two inequalities can be added together, the inequality symbol must face the SAME DIRECTION in each inequality.

Statement 1:
Adding together x+y+z > 0 and z > x+y+1, we get:
x+y+z+z > 0+x+y+1
2z > 1
z > ½
If z = ¾, the answer to the question stem is NO.
If z = 2, the answer to the question stem is YES.
INSUFFICIENT.

Statement 2:
Inequality in the question stem:
x+y+z > 0
If we reverse x+y+1 < 0, we get:
0 > x+y+1
Since the inequality symbol is facing the same direction in the two blue inequalities, they can now be added:
x+y+z+0 > 0+x+y+1
z > 1
Thus, the answer to the question stem is YES.
SUFFICIENT.

The correct answer is B.
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by Brent@GMATPrepNow » Sat Dec 21, 2019 6:12 am
BTGmoderatorDC wrote:If x + y + z > 0, is z > 1?

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



OA B

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

Answer: B

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