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22 Jul 2009, 06:17
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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?
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?
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22 Jul 2009, 06:38
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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.
So answer is A.
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.
So answer is A.
22 Jul 2009, 06:54
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I got A as well
y = 1*2*3*4*...*x + x/z
y = x*(1/z + 1*2*3*4*...)
y/x = 1/z + 1*2*3*4 ------->> Final Expression
1) Since y/x and 1*2*3*4*... are both integers, then 1/z must be integer. The only value for z, such as 1/z is an integer is 1. Thus SUFF.
2) Using the same final expression, the fact that z<x does not help in anything.
A.
y = 1*2*3*4*...*x + x/z
y = x*(1/z + 1*2*3*4*...)
y/x = 1/z + 1*2*3*4 ------->> Final Expression
1) Since y/x and 1*2*3*4*... are both integers, then 1/z must be integer. The only value for z, such as 1/z is an integer is 1. Thus SUFF.
2) Using the same final expression, the fact that z<x does not help in anything.
A.
We can find z. 
We can find z.
