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# What is the value of non-zero integer z? (1) |z|^3 = 3^z (2) z^z = z^3

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Math Expert
Joined: 02 Sep 2009
Posts: 60779
What is the value of non-zero integer z? (1) |z|^3 = 3^z (2) z^z = z^3  [#permalink]

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01 Oct 2019, 03:13
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65% (hard)

Question Stats:

48% (01:43) correct 52% (01:21) wrong based on 69 sessions

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What is the value of non-zero integer z?

(1) $$|z|^3 = 3^z$$

(2) $$z^z = z^3$$

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Joined: 31 May 2018
Posts: 461
Location: United States
Concentration: Finance, Marketing
Re: What is the value of non-zero integer z? (1) |z|^3 = 3^z (2) z^z = z^3  [#permalink]

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01 Oct 2019, 05:21
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Z is a non-zero integer

STATEMENT (1) - $$|z|^3$$ = $$3^z$$
--here z cant be negative because if z = -ve then $$|z|^3$$ = fraction which is not possible (since z is an integer $$|z|^3$$ must be an integer)
--so from here we know z is +ve integer
z = 3 is the only positive integer satisfying the equation
SUFFICIENT

STATEMENT (2) -$$z^z$$= $$z^3$$

if z = 1 then $$z^z$$= $$z^3$$
if z = 3 then $$z^z$$= $$z^3$$
we cant get definite value of z
so, INSUFFICIENT

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Re: What is the value of non-zero integer z? (1) |z|^3 = 3^z (2) z^z = z^3  [#permalink]

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19 Nov 2019, 06:35
Bunuel wrote:
What is the value of non-zero integer z?

(1) $$|z|^3 = 3^z$$

(2) $$z^z = z^3$$

$$z=integer≠0$$

(1) $$|z|^3 = 3^z$$ sufic

$$3^z≥0…z≠0…3^z>0…|z|^3>0…z>0…(z)^3=3^z…z=3$$

(2) $$z^z = z^3$$ insufic

$$z=(1,-1,3)$$

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Joined: 12 Nov 2019
Posts: 6
Re: What is the value of non-zero integer z? (1) |z|^3 = 3^z (2) z^z = z^3  [#permalink]

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19 Nov 2019, 06:43
Thank you very much for the answers. I could not have done it without you, since it is difficult for me at this level of my progress.
Re: What is the value of non-zero integer z? (1) |z|^3 = 3^z (2) z^z = z^3   [#permalink] 19 Nov 2019, 06:43
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