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# If x is a positive integer, what is the value of x? (1) 2x = x! (2) x

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Math Expert
Joined: 02 Sep 2009
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If x is a positive integer, what is the value of x? (1) 2x = x! (2) x  [#permalink]

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06 Dec 2018, 04:50
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35% (medium)

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64% (00:59) correct 36% (00:57) wrong based on 128 sessions

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If x is a positive integer, what is the value of x?

(1) 2x = x!
(2) x^2 - 3x = 0

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Joined: 07 Dec 2017
Posts: 1153
Re: If x is a positive integer, what is the value of x? (1) 2x = x! (2) x  [#permalink]

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06 Dec 2018, 04:55
1) this is not true for x=1 (2=1) or x=2 (4=2), for which the left side is greater. it is true for x=3 (6=6). for x=4 (8=24) the right side is greater, and we can easily see that as we progress, the right side will increase even more in relation to the left side. In other words, there is no way there will be another value that works - only x=3. sufficient!
2) x(x-3)=0 ==> x=0, x=3 - but since we know x is a positive integer, only x=3 works. Sufficient!
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Re: If x is a positive integer, what is the value of x? (1) 2x = x! (2) x  [#permalink]

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06 Dec 2018, 05:12
Bunuel wrote:
If x is a positive integer, what is the value of x?

(1) 2x = x!
(2) x^2 - 3x = 0

x!= x * (x-1)

from 1
2x= x( x-1)
or x = 3 sufficient

From 2
we get x ( x-3)=0
x=0 and 3
since x is a +ve integer so x=3 is sufficient IMO D
Math Expert
Joined: 02 Sep 2009
Posts: 64220
Re: If x is a positive integer, what is the value of x? (1) 2x = x! (2) x  [#permalink]

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24 Dec 2018, 00:30
Bunuel wrote:
If x is a positive integer, what is the value of x?

(1) 2x = x!
(2) x^2 - 3x = 0

_________________
Re: If x is a positive integer, what is the value of x? (1) 2x = x! (2) x   [#permalink] 24 Dec 2018, 00:30