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If x,y,z are positive integers,and x!+x/z=y,then what is the [#permalink]
22 Jul 2009, 05:17
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If x,y,z are positive integers,and x!+x/z=y,then what is the value of z? 1. x is a factor of y 2. z<x
Guys,plugging in got me no where..Ijust went blindly plugging in random nos,didnt succeed and ended up getting the answer wrong.any ideas? _________________
Re: x,y,z are positive integers [#permalink]
22 Jul 2009, 05:38
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1 is suff. y = 1.2.3....x + x/z y= x( 1.2.3..(x-1)+1/z) so if x is a factor of y then 1/z must be integer so z=1
2 is insuff. since x! is integer and y is integer x/z must be integer. And x>=z. This only says that x is not equal to z. We can not find the value of z.
Re: x,y,z are positive integers [#permalink]
23 Jul 2009, 04:18
No. z can not be any integer.
Based on the equation you found; if x = z then equation becomes (x! + 1). But x can only be the factor of y when the value of x = 1, z=1 and y=2. In other values of x; x can not be a factor of y because x! and x!+1 are coprimes (numbers that do not have any divisors other than 1). So z becomes 1 We can find z.
Re: x,y,z are positive integers [#permalink]
23 Jul 2009, 04:59
maliyeci wrote:
No. z can not be any integer.
Based on the equation you found; if x = z then equation becomes (x! + 1). But x can only be the factor of y when the value of x = 1, z=1 and y=2. In other values of x; x can not be a factor of y because x! and x!+1 are coprimes (numbers that do not have any divisors other than 1). So z becomes 1 We can find z.
Agree with you. Have totally missed the condition that x is a factory of y.
gmatclubot
Re: x,y,z are positive integers
[#permalink]
23 Jul 2009, 04:59