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

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What is the value of z, if z is not positive?  [#permalink]

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New post 18 Dec 2018, 00:27
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A
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E

Difficulty:

  55% (hard)

Question Stats:

59% (00:53) correct 41% (01:35) wrong based on 29 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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What is the value of z, if z is not positive?  [#permalink]

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New post 18 Dec 2018, 00:38
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.

Answer: A.
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What is the value of z, if z is not positive? &nbs [#permalink] 18 Dec 2018, 00:38
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