GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 16 Oct 2019, 08:48 GMAT Club Daily Prep

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

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.  If x and y are positive integers, which of the following

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Manager  Joined: 30 Dec 2008
Posts: 117
If x and y are positive integers, which of the following  [#permalink]

Show Tags

8
1
83 00:00

Difficulty:   75% (hard)

Question Stats: 54% (01:47) correct 46% (01:45) wrong based on 745 sessions

HideShow timer Statistics

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

Originally posted by cul3s on 18 Jan 2009, 22:40.
Last edited by Bunuel on 25 May 2013, 04:49, edited 2 times in total.
Edited the question and added the OA
Math Expert V
Joined: 02 Sep 2009
Posts: 58380
Re: greatest common divisor  [#permalink]

Show Tags

24
25
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 $$35x$$.

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.
_________________
Intern  Joined: 16 Jan 2009
Posts: 13
Re: greatest common divisor  [#permalink]

Show Tags

10
5
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.

so answer is C.

General Discussion
Director  Joined: 29 Nov 2012
Posts: 703
Re: If x and y are positive integers, which of the following  [#permalink]

Show Tags

would plugging in number a better strategy for such problems?
Math Expert V
Joined: 02 Sep 2009
Posts: 58380
Re: If x and y are positive integers, which of the following  [#permalink]

Show Tags

2
fozzzy wrote:
would plugging in number a better strategy for such problems?

Better strategy is the one that suits you best.
_________________
Director  Joined: 29 Nov 2012
Posts: 703
Re: greatest common divisor  [#permalink]

Show Tags

Bunuel wrote:
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 $$35x$$.

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?
Intern  Joined: 06 May 2008
Posts: 12
Concentration: Strategy, General Management
Re: If x and y are positive integers, which of the following  [#permalink]

Show Tags

1
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.
Director  Joined: 14 Dec 2012
Posts: 704
Location: India
Concentration: General Management, Operations
GMAT 1: 700 Q50 V34 GPA: 3.6
Re: greatest common divisor  [#permalink]

Show Tags

1
3
fozzzy wrote:
Bunuel wrote:
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 $$35x$$.

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

Originally posted by blueseas on 12 Jul 2013, 09:34.
Last edited by blueseas on 12 Jul 2013, 09:39, edited 1 time in total.
Math Expert V
Joined: 02 Sep 2009
Posts: 58380
Re: greatest common divisor  [#permalink]

Show Tags

fozzzy wrote:
Bunuel wrote:
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 $$35x$$.

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.
_________________
Senior Manager  Joined: 08 Apr 2012
Posts: 327
Re: greatest common divisor  [#permalink]

Show Tags

Bunuel wrote:
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 $$35x$$.

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,
Manager  Joined: 15 Aug 2013
Posts: 228
Re: greatest common divisor  [#permalink]

Show Tags

Bunuel wrote:
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 $$35x$$.

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?
Intern  Joined: 03 Jan 2014
Posts: 2
WE: Information Technology (Computer Software)
Re: If x and y are positive integers, which of the following  [#permalink]

Show Tags

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
Current Student D
Joined: 12 Aug 2015
Posts: 2568
Schools: Boston U '20 (M)
GRE 1: Q169 V154 Re: If x and y are positive integers, which of the following  [#permalink]

Show Tags

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.
_________________
EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15262
Location: United States (CA)
GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If x and y are positive integers, which of the following  [#permalink]

Show Tags

Hi All,

This question can be solved with math "theory" or by TESTing VALUES. Here's how to eliminate the 4 wrong answers by TESTing VALUES...

We're told that X and Y are POSITIVE INTEGERS. We're asked which of the following CANNOT be the greatest common divisor of 35x and 20y.

IF...X = 1, Y = 1...
35 and 20 have a GCD of 5.

IF...X = 3, Y = 2...
105 and 40 have a GCD of 5. 5(3-2) = 5

IF...X = 4, Y = 1...
140 and 20 have a GCD of 20. 20(1) = 2

IF...X = 2, Y = 7...
70 and 140 have a GCD of 70. 35(2) = 70

There's only one answer left....

GMAT assassins aren't born, they're made,
Rich
_________________
CEO  D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2977
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Re: If x and y are positive integers, which of the following  [#permalink]

Show Tags

cul3s wrote:
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

Please find the video solution oft eh question as attached here. Subscribe our youtube channel if you want more such concepts and video

Attachments

File comment: www.GMATinsight.com Screenshot 2018-10-21 at 12.17.36 PM.png [ 475.2 KiB | Viewed 9460 times ]

_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
CEO  D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2977
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
If x and y are positive integers, which of the following  [#permalink]

Show Tags

cul3s wrote:
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

The video solution is as available here.

Attachments

File comment: www.GMATinsight.com Screenshot 2019-03-17 at 11.38.07 AM.png [ 421.47 KiB | Viewed 6276 times ]

_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Intern  B
Joined: 13 Jul 2019
Posts: 26
Re: If x and y are positive integers, which of the following  [#permalink]

Show Tags

I have an alternate approach which will give you a quick answer in case you do not want to opt for plugging in.

In order to find the number which can not be a GCF of two numbers which are also product of some other two numbers, pick the number with the smaller coefficient and multiply it with the variable of the other term. That's it. SEE THE ATTACHMENT.

Please give kudos if you liked the solution. Deepti Singh
Master Trainer - GMAT
Manya - The Princeton Review

Attachments IMG_5989.jpg [ 49.91 KiB | Viewed 3056 times ] Re: If x and y are positive integers, which of the following   [#permalink] 19 Jul 2019, 04:21
Display posts from previous: Sort by

If x and y are positive integers, which of the following

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  