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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, 05:17
2
1
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 \(x\): \(\frac{z}{3y}*x=integer*x\) --> \(\frac{zx}{3y}=x*integer=integer*integer=integer\).
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
1
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
_________________
“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”
Re: If x, y, and z are positive integers, x is a factor of 2y [#permalink]
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01 Nov 2012, 07:13
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: \(\frac{zx}{3y}=\frac{(3y*integer)*x}{3y}=integer*x=integer\).
Re: If x, y, and z are positive integers, x is a factor of 2y [#permalink]
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17 Jun 2017, 21:15
I have a doubt here. Option E is also possible. The answer option is zy/3x z is divisible by 3y. that means z/3 will always yield an integer. y/x will also give an integer. When we multiply these 2 the result should be an integer as all x,y,z are integers. Please clarify if I am missing something.
Re: If x, y, and z are positive integers, x is a factor of 2y [#permalink]
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18 Jun 2017, 03:07
laasshetty wrote:
I have a doubt here. Option E is also possible. The answer option is zy/3x z is divisible by 3y. that means z/3 will always yield an integer. y/x will also give an integer. When we multiply these 2 the result should be an integer as all x,y,z are integers. Please clarify if I am missing something.
You are not reading the question carefully.
The question asks: which of the following MUST also be an integer? Not COULD also be an integer?
_________________
Re: If x, y, and z are positive integers, x is a factor of 2y [#permalink]
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30 Jan 2018, 14:57
Hi All,
I'm a big fan of TESTing VALUES (which is showcased in several of the explanations) - it's perfect for these types of questions. In addition, the answer choices are written in such a way that you can answer this question using Number Property rules....
In the prompt, we're told that "3Y is a factor of Z." This is just a wordy way of saying Z/3Y is an INTEGER. We're also told that X, Y and Z are positive integers.
Looking at the answers, what do you notice about answer D?
ZX/3Y....
It's interesting that the letters in in the numerator are NOT in alphabetical order. I wonder why THAT is? Is it to hide the fact that this answer has Z/3Y in it? We already know that Z/3Y is an integer and we know that X is an integer too.
Answer D literally translates into (integer)(integer)....which is ALWAYS an integer.
close
66% (01:37) correct 
