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# What is the value of z?

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What is the value of z? [#permalink]

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16 May 2013, 03:41
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What is the value of z?

(1) z^2= 25
(2) z = -|z|

Source Grockit but I think the answer they give is false. I will post my personal answer (I will wait for some responses) and tell me if I am wright or wrong...
[Reveal] Spoiler: OA
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Re: What is the value of z? [#permalink]

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16 May 2013, 03:49

1) Z = 5 or - 5

2) Z is negative or 0.

Combined Z = - 5
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Re: What is the value of z? [#permalink]

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16 May 2013, 04:45
What is the value of z?

(1) z^2= 25. This implies that z=5 or z=-5. Not sufficient.
(2) z = -|z|. This implies that $$z\leq{0}$$. Not sufficient.

(1)+(2) Since from (2) $$z\leq{0}$$, then from (1) z=-5. Sufficient.

P.S. Please indicate OA when posting.
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Re: What is the value of z? [#permalink]

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16 May 2013, 06:51
Thanks MacFauz and Bunuel. I understand your explanation and yes, OA is C.

However, can you tell me where I am wrong :
- Statement 1 is clearly not sufficient because z could be 5 or -5.
- Statement 2 is z = -|z|, you can rewrite the expression such as -z = IzI (wright?) if we multiply both side by -1. In that case the only possible value for z is 0 because the only possible solution is - 0 = I0I. So it is sufficient, no??

Thanks
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Re: What is the value of z? [#permalink]

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16 May 2013, 06:59
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tissime wrote:
Thanks MacFauz and Bunuel. I understand your explanation and yes, OA is C.

However, can you tell me where I am wrong :
- Statement 1 is clearly not sufficient because z could be 5 or -5.
- Statement 2 is z = -|z|, you can rewrite the expression such as -z = IzI (wright?) if we multiply both side by -1. In that case the only possible value for z is 0 because the only possible solution is - 0 = I0I. So it is sufficient, no??

Thanks

Yes, z = -|z| is the same as |z|=-z. But in this case z could be 0 or any negative number. For example, z=-2 --> |z|=|-2|=2 and -z=-(-2)=2 --> |z|=-z.

Absolute value properties:
When $$x\leq{0}$$ then $$|x|=-x$$, or more generally when $$some \ expression\leq{0}$$ then $$|some \ expression|\leq{-(some \ expression)}$$. For example: $$|-5|=5=-(-5)$$;

When $$x\geq{0}$$ then $$|x|=x$$, or more generally when $$some \ expression\geq{0}$$ then $$|some \ expression|\leq{some \ expression}$$. For example: $$|5|=5$$.

For more check Absolute Value chapter of Math Book: math-absolute-value-modulus-86462.html

DS questions on absolute value to practice: search.php?search_id=tag&tag_id=37
PS questions on absolute value to practice: search.php?search_id=tag&tag_id=58

Tough absolute value and inequity questions with detailed solutions: inequality-and-absolute-value-questions-from-my-collection-86939.html

Hope it helps.
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Re: What is the value of z? [#permalink]

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16 May 2013, 07:24
Thank you so much Bunuel. Your help is precious!
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Re: What is the value of z? [#permalink]

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24 Oct 2015, 07:48
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Re: What is the value of z?   [#permalink] 24 Oct 2015, 07:48
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