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If x, y, and z are positive integers, x is a factor of 2y, and 3y is a factor of z, which of the following must also be an integer?

A) \(\frac{y}{x}\)

B) \(\frac{2y}{6}\)

C) \(\frac{xy}{3z}\)

D) \(\frac{zx}{3y}\)

E) \(\frac{zy}{3x}\)

\(x\) is a factor of \(2y\), means that \(\frac{2y}{x}=integer\).

Similarly, \(3y\) is a factor of \(z\), means that \(\frac{z}{3y}=integer\). Multiply both sides of this equation by integer \(x\): \(\frac{z}{3y}*x=integer*x\) --> \(\frac{zx}{3y}=x*integer=integer*integer=integer\).

Re: If x, y, and z are positive integers, x is a factor of 2y [#permalink]

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31 Oct 2012, 06:12

Bunuel wrote:

LM wrote:

If x, y, and z are positive integers, x is a factor of 2y, and 3y is a factor of z, which of the following must also be an integer?

A) \(\frac{y}{x}\)

B) \(\frac{2y}{6}\)

C) \(\frac{xy}{3z}\)

D) \(\frac{zx}{3y}\)

E) \(\frac{zy}{3x}\)

\(x\) is a factor of \(2y\), means that \(\frac{2y}{x}=integer\).

Similarly, \(3y\) is a factor of \(z\), means that \(\frac{z}{3y}=integer\). Multiply both sides of this equation by integer \(x\): \(\frac{z}{3y}*x=integer*x\) --> \(\frac{zx}{3y}=x*integer=integer*integer=integer\).

Answer: D.

Hope it's clear.

Hello Bunuel,

Can we simplify the options and then attempt the Questions

For Option 5, ZY/3X can be simplified as 3Y*Y/3X --> Y*Y/X which may or may not be true. For example looking at option 4, ZX/3Y, if simplify it as ---> Z=3y and then the eqn becomes 3y*y/ 3y which gives x only

Please confirm
_________________

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If x, y, and z are positive integers, x is a factor of 2y, and 3y is a factor of z, which of the following must also be an integer?

A) \(\frac{y}{x}\)

B) \(\frac{2y}{6}\)

C) \(\frac{xy}{3z}\)

D) \(\frac{zx}{3y}\)

E) \(\frac{zy}{3x}\)

\(x\) is a factor of \(2y\), means that \(\frac{2y}{x}=integer\).

Similarly, \(3y\) is a factor of \(z\), means that \(\frac{z}{3y}=integer\). Multiply both sides of this equation by integer \(x\): \(\frac{z}{3y}*x=integer*x\) --> \(\frac{zx}{3y}=x*integer=integer*integer=integer\).

Answer: D.

Hope it's clear.

Hello Bunuel,

Can we simplify the options and then attempt the Questions

For Option 5, ZY/3X can be simplified as 3Y*Y/3X --> Y*Y/X which may or may not be true. For example looking at option 4, ZX/3Y, if simplify it as ---> Z=3y and then the eqn becomes 3y*y/ 3y which gives x only

Please confirm

We are not given that z=3y, we are given that z=3y*integer (3y is a factor of z). Now, if we substitute z in \(\frac{zx}{3y}\), we'l get: \(\frac{zx}{3y}=\frac{(3y*integer)*x}{3y}=integer*x=integer\).

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