Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

If x and y are positive integers, which of the following CANNOT be the greatest common divisor of 35x and 20y?

a. 5 b. 5(x-y) c. 20x d. 20y e. 35x

We are looking for a choice that CANNOT be the greatest common divisor of 35x and 20y ...which means 35x and 20y when divided by the answer choice the quotient should not be a integer. lets check

a. 5 35x/5 = 7x and 20y/5 = 4y both are integers so eliminate b. 5(x-y) when x = 2 and y = 1 it could be be the greatest common divisor ..so eliminate c. 20x when x = 1 its 20 and 20 cannot be the greatest common divisor of 35x and 20y ... or 35x/20x = 7/4 which is not a integer.

If x and y are positive integers, which of the following CANNOT be the greatest common divisor of 35x and 20y? A. 5 B. 5(x – y) C. 20x D. 20y E. 35x

Greatest common divisor (GCD) of \(35x\) and \(20y\) obviously must be a divisor of both \(35x\) and \(20y\), which means that \(\frac{35x}{GCD}\) and \(\frac{20y}{GCD}\) must be an integer.

If \(GCD=20x\) (option C), then \(\frac{35x}{20x}=\frac{7}{4}\neq{integer}\), which means that \(20x\) cannot be GCD of \(35x\) and \(20y\) as it is not a divisor of \(35x\).

Answer: C.

How about the other choices, can they be GCD of \(35x\) and \(20y\)?

A. \(5\) --> if \(x=y=1\) --> \(35x=35\) and \(20y=20\) --> \(GCD(35,20)=5\). Answer is YES, \(5\) can be GCD of \(35x=35\) and \(20y\);

B. \(5(x-y)\) --> if \(x=3\) and \(y=2\) --> \(35x=105\) and \(20y=40\) --> \(GCD(105,40)=5=5(x-y)\). Answer is YES, \(5(x-y)\) can be GCD of \(35x\) and \(20y\);

D. \(20y\) --> if \(x=4\) and \(y=1\) --> \(35x=140\) and \(20y=20\) --> \(GCD(140,20)=20=20y\). Answer is YES, \(20y\) can be GCD of \(35x\) and \(20y\);

E. \(35x\) --> if \(x=1\) and \(y=7\) --> \(35x=35\) and \(20y=140\) --> \(GCD(35,140)=35=35x\). Answer is YES, \(35x\) can be GCD of \(35x\) and \(20y\).

If x and y are positive integers, which of the following CANNOT be the greatest common divisor of 35x and 20y? A. 5 B. 5(x – y) C. 20x D. 20y E. 35x

Greatest common divisor (GCD) of \(35x\) and \(20y\) obviously must be a divisor of both \(35x\) and \(20y\), which means that \(\frac{35x}{GCD}\) and \(\frac{20y}{GCD}\) must be an integer.

If \(GCD=20x\) (option C), then \(\frac{35x}{20x}=\frac{7}{4}\neq{integer}\), which means that \(20x\) cannot be GCD of \(35x\) and \(20y\) as it is not a divisor of \(35x\).

Answer: C.

In this question for the division does it mean that both X and Y must be divisible or if any one is divisible the solution works

In option D

\(\frac{35X}{20Y}\) doesn't work according to that strategy?
_________________

Click +1 Kudos if my post helped...

Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/

GMAT Prep software What if scenarios http://gmatclub.com/forum/gmat-prep-software-analysis-and-what-if-scenarios-146146.html

Re: If x and y are positive integers, which of the following [#permalink]

Show Tags

12 Jul 2013, 09:32

I proceeded like this:

35x can have following prime factors : 5 ,7, x [well, x can have > 1 prime factors too; if x=6, 2 and 3 will be added to the list of prime factors]

Similarly, 20y has following prime factors : 2, 5, y [Same theory holds good for y]

the GCF has to have one 5 for sure. [IF we found any answer choices that is not a multiple of 5, it could be omitted right away]

A. 5 => We already covered that GCF has 5. Eliminate B. 5 (x -y) => If x and y were 2 and 1 respectively, this would reduce to 5. (same as answer choice A). Eliminate. C. 20x prime factors are 2, 5 and x. For 2 to be part of GCF, it must have come from x as 35 in 35x doesn't have 2. [If x had 2's then, 20x= 4 x 5 x X as GCF would not tally because, there is only two 2's in 20y] D. 20y = 2 x 2 x 5 x y ... If x were 4, this would be very possible. E. 35x = 5 * 7 * x; If y=7 and x =4, this is also possible.

There are simpler reasons already stated to say why C is the answer. But, for those who use prime factor trees to attach such problems, this is how I would explain.

If x and y are positive integers, which of the following CANNOT be the greatest common divisor of 35x and 20y? A. 5 B. 5(x – y) C. 20x D. 20y E. 35x

Greatest common divisor (GCD) of \(35x\) and \(20y\) obviously must be a divisor of both \(35x\) and \(20y\), which means that \(\frac{35x}{GCD}\) and \(\frac{20y}{GCD}\) must be an integer.

If \(GCD=20x\) (option C), then \(\frac{35x}{20x}=\frac{7}{4}\neq{integer}\), which means that \(20x\) cannot be GCD of \(35x\) and \(20y\) as it is not a divisor of \(35x\).

Answer: C.

In this question for the division does it mean that both X and Y must be divisible or if any one is divisible the solution works

In option D

\(\frac{35X}{20Y}\) doesn't work according to that strategy?

hi fozzy ,

i will say that best way to undersatand the defenetions of GCF and LCM.

GCF of 2 numbers means ...biggest number which is factor of those numbers.

now hers 35x==>prime factors 5/7...and others we dont know about x now 20y==>prime factors 2/2/5..and others we dont know as we dont about y

now as lets take options C: LETS SAY 20x is GCF...THEN IT MUST BE FACTOR OF BOTH...means..==>35x/20x==>this must be integer(according to defenetion of factor)==>but when we simplify that we are getting 7/4==>fraction===>hence we are sure 100 percent that this cant be a factor of both....hence it cant be GCF.

in rest all option we unknown variables are not getting cancelled...so we are not sure in that.

hope it helps
_________________

When you want to succeed as bad as you want to breathe ...then you will be successfull....

GIVE VALUE TO OFFICIAL QUESTIONS...

GMAT RCs VOCABULARY LIST: http://gmatclub.com/forum/vocabulary-list-for-gmat-reading-comprehension-155228.html learn AWA writing techniques while watching video : http://www.gmatprepnow.com/module/gmat-analytical-writing-assessment : http://www.youtube.com/watch?v=APt9ITygGss

Last edited by blueseas on 12 Jul 2013, 09:39, edited 1 time in total.

If x and y are positive integers, which of the following CANNOT be the greatest common divisor of 35x and 20y? A. 5 B. 5(x – y) C. 20x D. 20y E. 35x

Greatest common divisor (GCD) of \(35x\) and \(20y\) obviously must be a divisor of both \(35x\) and \(20y\), which means that \(\frac{35x}{GCD}\) and \(\frac{20y}{GCD}\) must be an integer.

If \(GCD=20x\) (option C), then \(\frac{35x}{20x}=\frac{7}{4}\neq{integer}\), which means that \(20x\) cannot be GCD of \(35x\) and \(20y\) as it is not a divisor of \(35x\).

Answer: C.

In this question for the division does it mean that both X and Y must be divisible or if any one is divisible the solution works

In option D

\(\frac{35X}{20Y}\) doesn't work according to that strategy?

Not sure I understand your question...

But notice that \(\frac{35x}{20y}=\frac{7x}{4y}\) could be an integer, for example if x=4 and y=1.
_________________

If x and y are positive integers, which of the following CANNOT be the greatest common divisor of 35x and 20y? A. 5 B. 5(x – y) C. 20x D. 20y E. 35x

Greatest common divisor (GCD) of \(35x\) and \(20y\) obviously must be a divisor of both \(35x\) and \(20y\), which means that \(\frac{35x}{GCD}\) and \(\frac{20y}{GCD}\) must be an integer.

If \(GCD=20x\) (option C), then \(\frac{35x}{20x}=\frac{7}{4}\neq{integer}\), which means that \(20x\) cannot be GCD of \(35x\) and \(20y\) as it is not a divisor of \(35x\).

Answer: C.

How about the other choices, can they be GCD of \(35x\) and \(20y\)?

A. \(5\) --> if \(x=y=1\) --> \(35x=35\) and \(20y=20\) --> \(GCD(35,20)=5\). Answer is YES, \(5\) can be GCD of \(35x=35\) and \(20y\);

B. \(5(x-y)\) --> if \(x=3\) and \(y=2\) --> \(35x=105\) and \(20y=40\) --> \(GCD(105,40)=5=5(x-y)\). Answer is YES, \(5(x-y)\) can be GCD of \(35x\) and \(20y\);

D. \(20y\) --> if \(x=4\) and \(y=1\) --> \(35x=140\) and \(20y=20\) --> \(GCD(140,20)=20=20y\). Answer is YES, \(20y\) can be GCD of \(35x\) and \(20y\);

E. \(35x\) --> if \(x=1\) and \(y=7\) --> \(35x=35\) and \(20y=140\) --> \(GCD(35,140)=35=35x\). Answer is YES, \(35x\) can be GCD of \(35x\) and \(20y\).

Hope it's clear.

Hi Bunuel, Is there a way to do this using prime factorization of 35 and 20? That's the first thing that comes to mind, but I can see how to proceed from there. Thanks,

If x and y are positive integers, which of the following CANNOT be the greatest common divisor of 35x and 20y? A. 5 B. 5(x – y) C. 20x D. 20y E. 35x

Greatest common divisor (GCD) of \(35x\) and \(20y\) obviously must be a divisor of both \(35x\) and \(20y\), which means that \(\frac{35x}{GCD}\) and \(\frac{20y}{GCD}\) must be an integer.

If \(GCD=20x\) (option C), then \(\frac{35x}{20x}=\frac{7}{4}\neq{integer}\), which means that \(20x\) cannot be GCD of \(35x\) and \(20y\) as it is not a divisor of \(35x\).

Answer: C.

How about the other choices, can they be GCD of \(35x\) and \(20y\)?

A. \(5\) --> if \(x=y=1\) --> \(35x=35\) and \(20y=20\) --> \(GCD(35,20)=5\). Answer is YES, \(5\) can be GCD of \(35x=35\) and \(20y\);

B. \(5(x-y)\) --> if \(x=3\) and \(y=2\) --> \(35x=105\) and \(20y=40\) --> \(GCD(105,40)=5=5(x-y)\). Answer is YES, \(5(x-y)\) can be GCD of \(35x\) and \(20y\);

D. \(20y\) --> if \(x=4\) and \(y=1\) --> \(35x=140\) and \(20y=20\) --> \(GCD(140,20)=20=20y\). Answer is YES, \(20y\) can be GCD of \(35x\) and \(20y\);

E. \(35x\) --> if \(x=1\) and \(y=7\) --> \(35x=35\) and \(20y=140\) --> \(GCD(35,140)=35=35x\). Answer is YES, \(35x\) can be GCD of \(35x\) and \(20y\).

Hope it's clear.

Hi Bunuel,

The steps here are easy to follow but one thing that bugs me is the number selection. It's almost as if you had to KNOW the answer to select the numbers to prove the statements worth. On the GMAT, that might be a little challenging.

is there a way to do this algebraically by using Prime Boxes? Meaning, 35 has 7 and 5 as it's PF and 20 has xxx?

Re: If x and y are positive integers, which of the following [#permalink]

Show Tags

26 Jun 2014, 00:14

How i did this (using prime factors/prime boxes)

35x will have following prime factors (pf) : 5 ,7, x (x could be anything but we leave that for now)

20y will have following prime factors (pf) : 2, 5, y (Again y could be anything but we leave that for now)

So : GCF - 5 or 5xy

A. 5 => Eliminate as GCF can be 5

B. 5 (x -y) => Leave the option for now or pick numbers to check. I left it for later (there was no need to come back to this and check as i got C as an answer)

C. 20x = 2 * 2 * 5 * x. GCF could be 5xy but 20y already has two 2's so ideally this should have come from 35x for 2*2 to be in the GCF and hence this is the answer as this can never be the GCF

D. 20y = 2 * 2 * 5 * y ; GCF could be 5xy and if x=4 (we pick this number to prove this option incorrect), this would be true

E. 35x = 5 * 7 * x; GCF could be 5xy and if y=7 (we pick this number to prove this option incorrect), this would be true

Re: If x and y are positive integers, which of the following [#permalink]

Show Tags

30 Jun 2015, 22:44

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 and y are positive integers, which of the following [#permalink]

Show Tags

14 Mar 2016, 02:24

i was able to arrive at C as for all the value i was able to portray the GCD but C was not coming to be true hence I choose C then i realized then 20x caanot be the GCD as x must be greater than 4x which is impossible.
_________________

Re: If x and y are positive integers, which of the following [#permalink]

Show Tags

12 Jul 2017, 01:12

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.
_________________

Version 8.1 of the WordPress for Android app is now available, with some great enhancements to publishing: background media uploading. Adding images to a post or page? Now...

“Keep your head down, and work hard. Don’t attract any attention. You should be grateful to be here.” Why do we keep quiet? Being an immigrant is a constant...

“Keep your head down, and work hard. Don’t attract any attention. You should be grateful to be here.” Why do we keep quiet? Being an immigrant is a constant...