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# If x and y are nonzero integers and 450x = 120y then which

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Manager
Status: Current MBA Student
Joined: 19 Nov 2009
Posts: 89
Concentration: Finance, General Management
GMAT 1: 720 Q49 V40
If x and y are nonzero integers and 450x = 120y then which  [#permalink]

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01 Sep 2010, 18:25
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65% (hard)

Question Stats:

61% (02:08) correct 39% (02:08) wrong based on 232 sessions

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If x and y are nonzero integers and 450x = 120y then which of the following must be an integer?

I. xy/60
II. 15x/4y
III. 4x/15y

A. I only
B. II only
C. I and III
D. I and II
E. I, II, and III
Math Expert
Joined: 02 Sep 2009
Posts: 64237

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01 Sep 2010, 19:25
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5
tonebeeze wrote:
Hello,

I need a more detailed explanation than one provided in the Veritas Advanced Word Problems Book. I would appreciate the help.

If x and y are nonzero integers and 450x = 120y then which of the following must be an integer?

I. xy/60
II. 15x/4y
III. 4x/15y

a. I only
b. II only
c. I and III
d. I and II
e. I, II, and III

$$450x=120y$$ --> reduce by 30 --> $$15x=4y$$ --> $$x$$ is a multiple of 4 ($$y=\frac{15x}{4}$$ so $$x$$ must be multiple of 4 for $$y$$ to be an integer) and $$y$$ is a multiple of 15 ($$x=\frac{4y}{15}$$ $$y$$ must be multiple of 15 for $$x$$ to be an integer).

I. xy/60 --> always true, as $$xy$$ will be multiple of 4*15=60;

II. 15x/4y --> as $$4y=15x$$ then $$\frac{15x}{4y}=\frac{15x}{15x}=1={integer}$$, so this option is also always true;

III. 4x/15y --> as $$x=\frac{4y}{15}$$ then $$\frac{4x}{15y}=\frac{16}{225}\neq{integer}$$, so this option is never true.

Hope it helps.
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Re: If x and y are nonzero integers and 450x = 120y then which  [#permalink]

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28 Mar 2020, 23:57
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Re: If x and y are nonzero integers and 450x = 120y then which   [#permalink] 28 Mar 2020, 23:57