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# Let x, y, and z be positive integers such that y is a multiple of x.

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Math Expert
Joined: 02 Sep 2009
Posts: 58310
Let x, y, and z be positive integers such that y is a multiple of x.  [#permalink]

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10 Dec 2016, 06:29
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Difficulty:

25% (medium)

Question Stats:

74% (01:26) correct 26% (01:47) wrong based on 80 sessions

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Let x, y, and z be positive integers such that y is a multiple of x. Is y + z a multiple of x?

(1) z is a multiple of y.
(2) x is a prime.

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Joined: 12 Aug 2015
Posts: 2573
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Re: Let x, y, and z be positive integers such that y is a multiple of x.  [#permalink]

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10 Dec 2016, 08:52
1
1
Here is my solution to this one.
Given that y is a multiple of x=> y=kx
We need to check if y+z is a multiple of x.
Since y is already a multiple of x => y+z will be a multiple of x only if z is a multiple of x.
Else it wont be.

RULE -> Multiple +Multiple = Multiple
Multiple +Non Multiple = Non Multiple

Statement 1-->
Z=yk'=> xk*k'
Hence z is a multiple of x
Hence y+z will be multiple of x
Hence sufficient

Statement 2-->
No clue of z
Hence not sufficient

Hence A

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Re: Let x, y, and z be positive integers such that y is a multiple of x.  [#permalink]

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10 Apr 2019, 23:31
As per statement 1:$$z=yb$$
that implies $$y+yb=xm$$
that implies $$y(1+b)=xm$$,
hence $$y+z=xm$$.
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Re: Let x, y, and z be positive integers such that y is a multiple of x.   [#permalink] 10 Apr 2019, 23:31
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