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

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ksrutisagar
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What is the value of z, if z is not positive? [#permalink] New post   18 Dec 2018, 01:27
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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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Bunuel
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What is the value of z, if z is not positive? [#permalink] New post   18 Dec 2018, 01:38
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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.

Answer: A.
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anmolsd1995
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Re: What is the value of z, if z is not positive? [#permalink] New post   24 Jan 2019, 10:39
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.
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Re: What is the value of z, if z is not positive? [#permalink] New post   24 Jan 2019, 11:25
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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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Re: What is the value of z, if z is not positive? [#permalink] New post   15 Sep 2022, 22:55
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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.


Hey anmolsd1995 ,
  • If you cancel \(z\) and go from \(z^3=25z\) to \(z^2=25\), you will get rid of a case where z can be equal to zero.
  • In equality, we should cancel terms iff we know that it is non zero.
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Re: What is the value of z, if z is not positive? [#permalink]
15 Sep 2022, 22:55
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