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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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New post 24 Oct 2012, 04:48
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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, 05:18, 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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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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New post 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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Re: If x, y, and z are positive integers, x is a factor of 2y [#permalink]

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New post 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: \(\frac{zx}{3y}=\frac{(3y*integer)*x}{3y}=integer*x=integer\).

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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New post 19 Sep 2015, 02:35
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]

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

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

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New post 18 Jun 2017, 21:32
Ok.. I get your point. Can you give me an example where E would not be an integer?
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Re: If x, y, and z are positive integers, x is a factor of 2y [#permalink]

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New post 18 Jun 2017, 21:48
laasshetty wrote:
Ok.. I get your point. Can you give me an example where E would not be an integer?


Yes.

\(x\) is a factor of \(2y\), means that \(\frac{2y}{x}=integer\). Say y = 2 and x = 1.

\(3y\) is a factor of \(z\), means that \(\frac{z}{3y}=integer\). Say z = 3 and y = 1.

E) \(\frac{zy}{3x}=\frac{3*1}{3*2}=\frac{1}{2} \neq integer\).

Hope it helps.
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Resources:
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: If x, y, and z are positive integers, x is a factor of 2y   [#permalink] 18 Jun 2017, 21:48
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