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# If x,y, and z are positive integers such that x is a factor

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Manager
Joined: 28 Jan 2005
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If x,y, and z are positive integers such that x is a factor [#permalink]  31 Jan 2005, 17:23
If x,y, and z are positive integers such that x is a factor of y, and x is a multiple of z, which of the following is NOT necessarily an integer?

A x+z/z
B y+z/x
C x + y/z
D xy/z
E yz/x
VP
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[#permalink]  31 Jan 2005, 17:36
"B".

Given .....y/x = l and x/z = k ....k,l r integers

also from above we have y/z = kl

A. x + 1...integer
B y+z/x --------------y + 1/k..........may not be an integer
C x + y/z ----------x + kl.....integer
D xy/z -----------x(kl)...........integer
E yz/x -----------z(y/x)..........z(l)........integer
Current Student
Joined: 28 Dec 2004
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Location: New York City
Schools: Wharton'11 HBS'12
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[#permalink]  31 Jan 2005, 17:37
B it is...

y=mx
x=nz z=x/n

B) y+z/x

mx + (x/n)1/x= mx+ 1/n

1/n may not be an integer...
CIO
Joined: 09 Mar 2003
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Re: Number Properties [#permalink]  31 Jan 2005, 18:57
tareks wrote:
If x,y, and z are positive integers such that x is a factor of y, and x is a multiple of z, which of the following is NOT necessarily an integer?

A x+z/z
B y+z/x
C x + y/z
D xy/z
E yz/x

Yup, I'm with b too.

From the statement, y/x is an integer, and x/z is an integer. All the combinations have that in one way or another except b, which has z/x. We don't know about z over x.
Manager
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[#permalink]  31 Jan 2005, 22:06
fast and clean :
two sets of integers

y x z
6 3 1
8 4 2

you ve got b
Manager
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[#permalink]  31 Jan 2005, 22:18
Quote:
From the statement, y/x is an integer, and x/z is an integer. All the combinations have that in one way or another except b, which has z/x. We don't know about z over x

What a simple and quick solution. Any more examples of this?

B is right.
VP
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[#permalink]  31 Jan 2005, 23:04
i agree with all you guys...........
CIO
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[#permalink]  31 Jan 2005, 23:15
tareks wrote:
Quote:
From the statement, y/x is an integer, and x/z is an integer. All the combinations have that in one way or another except b, which has z/x. We don't know about z over x

What a simple and quick solution. Any more examples of this?

B is right.

Yes. I just posted one: http://www.gmatclub.com/phpbb/viewtopic.php?p=81302#81302
[#permalink] 31 Jan 2005, 23:15
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# If x,y, and z are positive integers such that x is a factor

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