text: If x, y, and z are positive integers, x is a factor of 2y : GMAT Problem Solving (PS)
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  # If x, y, and z are positive integers, x is a factor of 2y
  
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  If x, y, and z are positive integers, x is a factor of 2y [#permalink]
  
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  24 Oct 2012, 03:48
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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) $$\frac{zy}{3x}$$
  [Reveal] Spoiler: OA
  
  Last edited by Bunuel on 24 Oct 2012, 04:18, edited 2 times in total.
  Renamed the topic and edited the question.
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  Re: If x, y, and z are positive integers, x is a factor of 2y [#permalink]
  
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  24 Oct 2012, 04:17
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  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.
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  Re: If x, y, and z are positive integers, x is a factor of 2y [#permalink]
  
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  31 Oct 2012, 05:12
  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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  Re: If x, y, and z are positive integers, x is a factor of 2y [#permalink]
  
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  01 Nov 2012, 06:13
  mridulparashar1 wrote:
  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
  
  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: $$\frac{zx}{3y}=\frac{(3y*integer)*x}{3y}=integer*x=integer$$.
  
  Hope it helps.
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  Re: If x, y, and z are positive integers, x is a factor of 2y [#permalink]
  
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  19 Sep 2015, 01:35
  if we take x=4, y=2 and z=12...
  x(=2) is factor of 2y(=4)
  and 3y(=6) is a factor of z(=12)......
  D it is.......
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  Re: If x, y, and z are positive integers, x is a factor of 2y   [#permalink] 19 Sep 2015, 01:35
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  # If x, y, and z are positive integers, x is a factor of 2y
  
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