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Find all its solutions. (|2*Z|)!–|Z|=Z

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SVP
Joined: 03 Feb 2003
Posts: 1603

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Find all its solutions. (|2*Z|)!–|Z|=Z [#permalink]

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19 Jun 2003, 00:10
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82% (02:06) correct 18% (03:21) wrong based on 62 sessions

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Find all its solutions. (|2*Z|)!–|Z|=Z

Kudos [?]: 299 [2], given: 0

SVP
Joined: 03 Feb 2003
Posts: 1603

Kudos [?]: 299 [0], given: 0

Re: Find all its solutions. (|2*Z|)!–|Z|=Z [#permalink]

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19 Jun 2003, 22:41
now it is correct.
it is imperative that you sovle the question, not simply guess it.

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Manager
Joined: 24 Jun 2003
Posts: 145

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Location: India
Re: Find all its solutions. (|2*Z|)!–|Z|=Z [#permalink]

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26 Jun 2003, 06:45
The LHS equation always gives positive values. Therefore, solution cannot lie in Z<0

Now for Z>=0, the equation can be rewritten as

(2Z)!-Z=Z

which gives (2Z-1)!=1 which is only possible for
(2Z-1) = 0 or 1. This leads to values of Z as 1 or 1/2

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GMAT Club Legend
Joined: 09 Sep 2013
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Re: Find all its solutions. (|2*Z|)!–|Z|=Z [#permalink]

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24 Oct 2014, 12:39
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Hello from the GMAT Club BumpBot!

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Manager
Joined: 21 Sep 2012
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Location: United States
Concentration: Finance, Economics
Schools: CBS '17
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WE: General Management (Consumer Products)
Re: Find all its solutions. (|2*Z|)!–|Z|=Z [#permalink]

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25 Oct 2014, 00:03
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(|2*Z|)!–|Z|=Z

since |2z|!>|z|, LHS has to be >0, therefore RHS(Z)>0
|2z|!-|z|=z
|2z|!=z+|z|
|2z|!=2z
2z*(2z-1)=2z
since z>0, cancel 2z from both sides
2z-1=1
2z=2
z=1

Kudos [?]: 195 [2], given: 31

Re: Find all its solutions. (|2*Z|)!–|Z|=Z   [#permalink] 25 Oct 2014, 00:03
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