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

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

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New post 01 Sep 2010, 19:25
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D
E

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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
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Re: Please help explain Factors problem  [#permalink]

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New post 01 Sep 2010, 20:25
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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.

Answer: I and II (only).

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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New post 21 Apr 2018, 02:42
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Re: If x and y are nonzero integers and 450x = 120y then which &nbs [#permalink] 21 Apr 2018, 02:42
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