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GMAT Tutor B
Joined: 07 Nov 2016
Posts: 56
GMAT 1: 760 Q51 V42 What is the value of z, if z is not positive?  [#permalink]

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3 00:00

Difficulty:   75% (hard)

Question Stats: 45% (01:28) correct 55% (01:38) wrong based on 76 sessions

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What is the value of z if z is not positive ?

(1) |x-2| + |x+y-5| + |x+y+z| = 0
(2) z^3 – 25z = 0

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Math Expert V
Joined: 02 Sep 2009
Posts: 58421
What is the value of z, if z is not positive?  [#permalink]

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What is the value of z if z is not positive ?

(1) |x-2| + |x+y-5| + |x+y+z| = 0

Absolute value is always non-negative, so the above to be true all three terms must be 0 (the sum of non-negative terms to be 0, all the terms must be 0).
x + y - 5 = 0, thus x + y = 5.
x + y + z = 0. Since from above, x + y = 5, then 5 + z = 0 --> z = -5.

Sufficient.

(2) z^3 – 25z = 0.

z(z^2 - 25) = 0.

z = 0 or z = -5 or z = 5. Given that z is not positive, we are left with z = 0 or z = -5. Not sufficient.

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Intern  B
Joined: 17 Apr 2017
Posts: 11
Re: What is the value of z, if z is not positive?  [#permalink]

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I tried to solve second equation this way:

z^3-25z=0

z^3=25z

z^2=25

z= +/-5

Since z is not positive it must be -5 then.

can anyone please correct me where i am going wrong.
Director  G
Joined: 09 Mar 2018
Posts: 994
Location: India
Re: What is the value of z, if z is not positive?  [#permalink]

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1
anmolsd1995 wrote:
I tried to solve second equation this way:

z^3-25z=0

z^3=25z

z^2=25

z= +/-5

Since z is not positive it must be -5 then.

can anyone please correct me where i am going wrong.

If its not positive it could have been that it is 0 or -ive, so by taking the value to RHS, you removed a case in which z could have been 0

z^3-25z=0
z (z^2-25) = 0

Now z can be 0 or z can be +/- 5

But then it cant be +ive, it can be 0 or -5, Since 0 is neither positive nor negative
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Many of life's failures happen with people who do not realize how close they were to success when they gave up. Re: What is the value of z, if z is not positive?   [#permalink] 24 Jan 2019, 11:25
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