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

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by GMATQuantCoach » Sat Jul 11, 2009 2:11 pm
You will need to know how to add inequalities to isolate variables like you do when solving simultaneous linear equations.

x + y + z > 0 then z > - x - y (Let's call it inequality [1])

(1) z > x + y +1 (let's call it inequality [2])

Add inequality [1] with inequality [2] yields
2z > 1
z > 1/2

You can verify this answer by choosing z = 3/4, x = 0, y = -1/2 and z = 2, x = 0, y = -1/2.
Insufficient.

(2) x + y + 1 < 0
You can only add inequalities if the inequality signs are the same. Multiply -1 on both sides yields:
-(x + y + 1) > 0
-x - y - 1 > 0

Add the inequality above with x + y + z > 0. You get:
-1 + z > 0
z > 1
Sufficient.

The answer is B.
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by Musicolo » Mon Jul 13, 2009 1:51 am
GMATQuantCoach wrote:You will need to know how to add inequalities to isolate variables like you do when solving simultaneous linear equations.

x + y + z > 0 then z > - x - y (Let's call it inequality [1])

(1) z > x + y +1 (let's call it inequality [2])

Add inequality [1] with inequality [2] yields
2z > 1
z > 1/2

You can verify this answer by choosing z = 3/4, x = 0, y = -1/2 and z = 2, x = 0, y = -1/2.
Insufficient.

(2) x + y + 1 < 0
You can only add inequalities if the inequality signs are the same. Multiply -1 on both sides yields:
-(x + y + 1) > 0
-x - y - 1 > 0

Add the inequality above with x + y + z > 0. You get:
-1 + z > 0
z > 1
Sufficient.

The answer is B.
WOW i like your answer and explanation. I wish I new maths as good as you :)
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by Brent@GMATPrepNow » Sun Jul 17, 2016 11:10 am
sanjib wrote:If x + y + z > 0, is z > 1?

(1) z > x + y + 1
(2) x + y + 1 < 0
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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by Matt@VeritasPrep » Fri Jul 22, 2016 2:05 am
Brent with the surprise thread resurrection! ;) (The question is tough to resist, though.)
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