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

It is currently 20 Oct 2018, 22:59

Close

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
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.

Close

Request Expert Reply

Confirm Cancel

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

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

Hide Tags

Intern
Intern
avatar
Joined: 09 Apr 2010
Posts: 14
If x and y are positive integers, which of the following CAN  [#permalink]

Show Tags

New post 01 Jun 2010, 14:18
5
28
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

58% (01:44) correct 42% (01:50) wrong based on 359 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
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50007
Re: Another PS Question  [#permalink]

Show Tags

New post 07 Jun 2010, 10:04
1
6
bibha wrote:
Hey...
why am i not able to comprehend this question? somebody please 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 \(\frac{35x}{GCD}\) 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 \(20y\).

Answer: C.

Hope it's clear.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Most Helpful Community Reply
Manager
Manager
User avatar
Joined: 03 Feb 2010
Posts: 175
Concentration: Strategy
Schools: Northwestern (Kellogg) - Class of 2014
WE: Marketing (Computer Hardware)
Re: Another PS Question  [#permalink]

Show Tags

New post 01 Jun 2010, 14:41
2
4
priyanka116 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 reason the answer is C is because if you divide 35x/20x, you get 35/20, which isn't an integer. 35x and 20y can be divisible by 5, and 5(x-y) eg x=5, y=4. 35x/20y, if y = 7, and X=4, 20y/20y = 1. E also works, 35x/35x = 1, 20y/35x works when Y=7, X=4
General Discussion
Intern
Intern
avatar
Joined: 09 Apr 2010
Posts: 14
Re: Another PS Question  [#permalink]

Show Tags

New post 01 Jun 2010, 14:19
The correct answer is C though it beats me why. Any explanations will be very helpful.
Intern
Intern
avatar
Joined: 09 Apr 2010
Posts: 14
Re: Another PS Question  [#permalink]

Show Tags

New post 01 Jun 2010, 14:53
But 35x/20y is an integer where x=4 and y=1
Intern
Intern
avatar
Joined: 09 Apr 2010
Posts: 14
Re: Another PS Question  [#permalink]

Show Tags

New post 01 Jun 2010, 14:55
I must be shaken awake to see the obvious and obvious making a fool of myself! My bad... I get it.... its not 35x/20y its 35x/20x.. thanks !
Manager
Manager
avatar
Joined: 14 Apr 2010
Posts: 181
Re: Another PS Question  [#permalink]

Show Tags

New post 07 Jun 2010, 06:03
Hey...
why am i not able to comprehend this question? somebody please explain....:-(
Intern
Intern
User avatar
Affiliations: NYSSA
Joined: 07 Jun 2010
Posts: 32
Location: New York City
Schools: Wharton, Stanford, MIT, NYU, Columbia, LBS, Berkeley (MFE program)
WE 1: Senior Associate - Thomson Reuters
WE 2: Analyst - TIAA CREF
Re: Another PS Question  [#permalink]

Show Tags

New post 18 Jun 2010, 12:30
edoy56 wrote:
priyanka116 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 reason the answer is C is because if you divide 35x/20x, you get 35/20, which isn't an integer. 35x and 20y can be divisible by 5, and 5(x-y) eg x=5, y=4. 35x/20y, if y = 7, and X=4, 20y/20y = 1. E also works, 35x/35x = 1, 20y/35x works when Y=7, X=4


Hahaha. I'm so stupid... thats the 10 sec answer...
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12687
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 CAN  [#permalink]

Show Tags

New post 29 Dec 2014, 08:34
Hi All,

This question can be solved by TESTing VALUES. Here though, we'll be TESTing VALUES to prove which answers are POSSIBLE (so that we can eliminate them). This prompt is actually built around a few Number Properties and we can actually use the answer choices to our advantage (instead of just randomly TESTing VALUES until we knock out four of the answers).

We're told that X and Y are POSITIVE INTEGERS. We're asked which of the 5 answers CANNOT be the GCD of 35X and 20Y. This means that 4 of the answers COULD be the GCD under certain circumstances.

Before we TEST anything, there are some things to note about 35X and 20Y:

1) 20Y will ALWAYS be EVEN (20, 40, 60, 80, 100, etc.)
2) 35X can be EVEN or ODD (35, 70, 105, 140, etc.)

Looking at the list of answer choices, there are some that we can quickly eliminate...

IF
X = 1
Y = 1
Then we have 35 and 20, so the GCD = 5
Eliminate A.

X = 20
Y = 1
Then we have 700 and 20, so the GCD = 20
Eliminate D.

X = 1
Y = 35
Then we have 35 and 700, so the GCD = 35
Eliminate E.

With the remaining 2 answers, we have to think a little more.

To get a simple example of 5(X-Y) to be the GCD, we probably need 35X to be ODD

IF...
X = 3
Y = 2
Then we have 105 and 40, so the GCD = 5
5(X-Y) = 5(3-2) = 5
This can ALSO be the GCD
Eliminate B.

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Director
Director
User avatar
Joined: 07 Aug 2011
Posts: 540
Concentration: International Business, Technology
GMAT 1: 630 Q49 V27
GMAT ToolKit User
If x and y are positive integers, which of the following CAN  [#permalink]

Show Tags

New post 09 Jan 2015, 21:06
priyanka116 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


option
A) x=y=1; 5 is GCD.
2) x=3;y=2; 5(x-y) is GCD
3) 35x/20x cannot be an integer. ->Correct answer.
4) at X=20Y; 20y will be gcd.
5) at y=35x; 35x will be gcd.
_________________

Thanks,
Lucky

_______________________________________________________
Kindly press the Image to appreciate my post !! :-)

SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1829
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: If x and y are positive integers, which of the following CAN  [#permalink]

Show Tags

New post 13 Jan 2015, 22:34
In this type of question, we need to substitute value of "x" & "y" with positive integer as 2 & 1 etc.

Otherwise, we can end up in a wrong answer. Algebraic solution from the options is not possible

Answer = C = 20x
_________________

Kindly press "+1 Kudos" to appreciate :)

Manager
Manager
User avatar
Joined: 20 Dec 2013
Posts: 123
Re: If x and y are positive integers, which of the following CAN  [#permalink]

Show Tags

New post 13 Jan 2015, 22:40
priyanka116 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


Number divided by HCF should be an integer.

35x divided by 20x is not an integer hence 20x cannot be the HCF.
_________________

76000 Subscribers, 7 million minutes of learning delivered and 5.6 million video views

Perfect Scores
http://perfectscores.org
http://www.youtube.com/perfectscores

Intern
Intern
avatar
Joined: 18 Nov 2015
Posts: 7
Re: If x and y are positive integers, which of the following CAN  [#permalink]

Show Tags

New post 15 May 2016, 09:36
Property : GCD of any 2 numbers must divide those numbers completely.
Looking at the options : 20x can never divide 35x completely, all other options can be true.

Correct Answer : C
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 8496
Premium Member
Re: If x and y are positive integers, which of the following CAN  [#permalink]

Show Tags

New post 05 Feb 2018, 07:51
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Bot
Re: If x and y are positive integers, which of the following CAN &nbs [#permalink] 05 Feb 2018, 07:51
Display posts from previous: Sort by

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

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.