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# Is nonnegative integer x odd? (1) x! = |x - 1|! (2) x! = (x + 1)!

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Joined: 02 Sep 2009
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Is nonnegative integer x odd? (1) x! = |x - 1|! (2) x! = (x + 1)!  [#permalink]

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03 Jul 2018, 09:48
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2
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Difficulty:

95% (hard)

Question Stats:

37% (01:48) correct 63% (01:43) wrong based on 57 sessions

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Is nonnegative integer x odd?

(1) x! = |x - 1|!
(2) x! = (x + 1)!

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Joined: 25 Apr 2016
Posts: 59
Is nonnegative integer x odd? (1) x! = |x - 1|! (2) x! = (x + 1)!  [#permalink]

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Updated on: 03 Jul 2018, 10:28
the trick is to not forget considering '0'. 0! =1 option =>b

Originally posted by attari92 on 03 Jul 2018, 09:53.
Last edited by attari92 on 03 Jul 2018, 10:28, edited 1 time in total.
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Re: Is nonnegative integer x odd? (1) x! = |x - 1|! (2) x! = (x + 1)!  [#permalink]

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03 Jul 2018, 10:22
attari92 wrote:
the trick is to not forget considering '0'. 0! =1 option =>d

IMO Option B.

(1) x can be 0 or 1. 0! = 1! = 1
If x = 0 then 0! = |0-1|! = |-1|! = 1! = 1
If x = 1, then 1! = |1-1|! = 0! = 1

Hence insufficient to say if x is odd or even since if x is 0, it is neither odd nor even.

(2) Only value (nonnegative integer) to satisfy the equation is x = 0. Hence sufficient to answer Yes/No type question stem.

Hence Option B.
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Joined: 25 Apr 2016
Posts: 59
Re: Is nonnegative integer x odd? (1) x! = |x - 1|! (2) x! = (x + 1)!  [#permalink]

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03 Jul 2018, 10:30
nkin wrote:
attari92 wrote:
the trick is to not forget considering '0'. 0! =1 option =>d

IMO Option B.

(1) x can be 0 or 1. 0! = 1! = 1
If x = 0 then 0! = |0-1|! = |-1|! = 1! = 1
If x = 1, then 1! = |1-1|! = 0! = 1

Hence insufficient to say if x is odd or even since if x is 0, it is neither odd nor even.

(2) Only value (nonnegative integer) to satisfy the equation is x = 0. Hence sufficient to answer Yes/No type question stem.

Hence Option B.

i stand corrected perhaps mistakenly typed 'd' instead of 'b'
Re: Is nonnegative integer x odd? (1) x! = |x - 1|! (2) x! = (x + 1)! &nbs [#permalink] 03 Jul 2018, 10:30
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