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

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

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

(1) z > x + y +1
(2) x + y + 1 < 0
[Reveal] Spoiler: OA

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Re: DS- inequalities is Z>1? [#permalink]

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RisingForceX wrote:
If x+y+z > 0, is z > 1?

(1) z > x + y +1
(2) x + y + 1 < 0
[Reveal] Spoiler:
B


Remember we can add inequalities when their signs are in the same direction and subtract inequalities when their signs are in the opposite direction.

(1) z > x + y +1 and x+y+z > 0 --> adding inequalities x+y+z+z>x + y +1 --> z>1/2. Not sufficient.

(2) x + y + 1 < 0 and x+y+z > 0 --> subtract inequalities z-1>0 --> z>1. Sufficient.

Answer: B.
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Re: DS- inequalities is Z>1? [#permalink]

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RisingForceX wrote:
If x+y+z > 0, is z > 1?

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


B

1. we have x+y+z >0. given z > x + y +1
let x = -12 y = 10 and z= 3 then we have x+y+z >0, z > x + y +1 and also z>1
let x = -1 y = 1/2 z=3/4 then we have x+y+z >0, z > x + y +1 but z<1. hence insuff

2. x+y+1 < 0 or x+y < -1 given that x+y+z > 0 then z>1. hence suff

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

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

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Hello from the GMAT Club BumpBot!

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

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New post 16 Jul 2016, 19:36
I think it is B because it says that

x+y+1<0 or x+y<-1 therefore,
z has to to greater than 1 for for x+y+z>0

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

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New post 16 Jul 2016, 19:38
I think it is B because it says that

x+y+1<0 or x+y<-1 therefore,
z has to to greater than 1 for for x+y+z>0

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

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RisingForceX 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 =
[Reveal] Spoiler:
B


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

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New post 19 Aug 2017, 16:35
Hello from the GMAT Club BumpBot!

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

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New post 19 Aug 2017, 21:32
RisingForceX wrote:
If x + y + z > 0, is z > 1?

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


A.
x+y+z > 0 -------------1
z>x+y+1----------------2
Add 1 and 2

x+y+2z>x+y+1
z>1/2-------------------------------A--not sufficient

B.
x+y+1<0 = -X-Y-1 > 0----------3
add 1 and 3
z>1
Suff.

Hence B

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Re: If x + y + z > 0, is z > 1?   [#permalink] 19 Aug 2017, 21:32
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