Oct 20 07:00 AM PDT  09:00 AM PDT Get personalized insights on how to achieve your Target Quant Score. Oct 22 08:00 PM PDT  09:00 PM PDT On Demand for $79. For a score of 4951 (from current actual score of 40+) AllInOne Standard & 700+ Level Questions (150 questions) Oct 23 08:00 AM PDT  09:00 AM PDT Join an exclusive interview with the people behind the test. If you're taking the GMAT, this is a webinar you cannot afford to miss!
Author 
Message 
TAGS:

Hide Tags

Director
Joined: 03 Sep 2006
Posts: 639

If x, y, and z are positive integers, x is a factor of 2y
[#permalink]
Show Tags
Updated on: 24 Oct 2012, 05:18
Question Stats:
65% (02:05) correct 35% (02:21) wrong based on 225 sessions
HideShow timer Statistics
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) \(\frac{zy}{3x}\)
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by LM on 24 Oct 2012, 04:48.
Last edited by Bunuel on 24 Oct 2012, 05:18, edited 2 times in total.
Renamed the topic and edited the question.




Math Expert
Joined: 02 Sep 2009
Posts: 58449

Re: If x, y, and z are positive integers, x is a factor of 2y
[#permalink]
Show Tags
24 Oct 2012, 05:17
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.
_________________




Director
Joined: 25 Apr 2012
Posts: 660
Location: India
GPA: 3.21
WE: Business Development (Other)

Re: If x, y, and z are positive integers, x is a factor of 2y
[#permalink]
Show Tags
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
_________________
“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.”



Math Expert
Joined: 02 Sep 2009
Posts: 58449

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



Intern
Joined: 21 Mar 2014
Posts: 22

Re: If x, y, and z are positive integers, x is a factor of 2y
[#permalink]
Show Tags
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.......
_________________
kinaare paaon phailane lage hian, nadi se roz mitti kat rahi hai....



Intern
Joined: 23 Sep 2014
Posts: 6

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



Math Expert
Joined: 02 Sep 2009
Posts: 58449

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



Intern
Joined: 23 Sep 2014
Posts: 6

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



Math Expert
Joined: 02 Sep 2009
Posts: 58449

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



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15281
Location: United States (CA)

Re: If x, y, and z are positive integers, x is a factor of 2y
[#permalink]
Show Tags
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. Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
Contact Rich at: Rich.C@empowergmat.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★



eGMAT Representative
Joined: 04 Jan 2015
Posts: 3074

Re: If x, y, and z are positive integers, x is a factor of 2y
[#permalink]
Show Tags
31 Jan 2018, 04:25
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) \(\frac{zy}{3x}\) Solution • Given: x is factor of 2y.
o Thus, we can write \(2y = k * x\), where k is an integer
o \(\frac{x}{y} = \frac{2}{k}\) • Given: 3y is a factor of z.
o Thus, we can write \(z = q * 3y\), where q is an integer
o \(\frac{y}{z} = \frac{1}{3q}\) • Thus \(x : y : z = 2: k: 3qk\)
Now let us consider the options one by one and check which of the following MUST be an integer 1. \(\frac{y}{x} = \frac{k}{2}\)
a. We cannot be sure, since we do not know the value of k 2. \(\frac{2y}{6} = \frac{k}{3}\)
a. Again, we cannot be sure, since we do not know the value of k 3. \(\frac{xy}{3z} = \frac{2k}{9qk} = \frac{2}{9q}\)
a. Again, we cannot be sure, since we do not know the value of q 4. \(\frac{zx}{3y} = \frac{3qk*2}{3k} = 2q\)
a. This has to be an integer, since 2q is an integer At this point, we can stop and mark the answer as D, but just to be sure, let’s check the last option.
5. \(\frac{zy}{3x} = \frac{3qk*k}{3*2}= \frac{qk^2}{2}\)
a. We cannot be sure this is an integer, since we do not know the value of k or q. Correct Answer: Option DRegards, Saquib Quant Expert eGMAT
_________________



NonHuman User
Joined: 09 Sep 2013
Posts: 13270

Re: If x, y, and z are positive integers, x is a factor of 2y
[#permalink]
Show Tags
16 Feb 2019, 04:00
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________




Re: If x, y, and z are positive integers, x is a factor of 2y
[#permalink]
16 Feb 2019, 04:00






