Find all School-related info fast with the new School-Specific MBA Forum

It is currently 07 Jul 2015, 00:02

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Which of the following CANNOT be the greatest common divisor

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
Manager
Manager
avatar
Joined: 04 Feb 2011
Posts: 64
Location: US
Followers: 2

Kudos [?]: 36 [1] , given: 42

Which of the following CANNOT be the greatest common divisor [#permalink] New post 08 Feb 2011, 00:43
1
This post received
KUDOS
4
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

81% (01:24) correct 19% (00:22) wrong based on 224 sessions
Which of the following CANNOT be the greatest common divisor of two positive integers x and y?

A. 1
B. x
C. y
D. x-y
E. x+y
[Reveal] Spoiler: OA
5 KUDOS received
Math Forum Moderator
avatar
Joined: 20 Dec 2010
Posts: 2028
Followers: 138

Kudos [?]: 1165 [5] , given: 376

Re: problem solving [#permalink] New post 08 Feb 2011, 01:55
5
This post received
KUDOS
1
This post was
BOOKMARKED
GCD of two postive numbers will always be less than or equal to the smaller of the two numbers.

If x and y are two +ve integers.

\(if (x < y)\)
\(GCD(x,y) <= x\)

\(if (y < x)\)
\(GCD(x,y) <= y\)

\(if (y = x)\)
\(GCD(x,y) = y = x\)

In any case;

GCD must be less than the sum of the two numbers

GCD(x,y) < (x+y)

Ans: "E"
_________________

~fluke

GMAT Club Premium Membership - big benefits and savings

Expert Post
3 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 28332
Followers: 4484

Kudos [?]: 45399 [3] , given: 6759

Re: problem solving [#permalink] New post 08 Feb 2011, 02:28
3
This post received
KUDOS
Expert's post
2
This post was
BOOKMARKED
Lolaergasheva wrote:
Which of the following cannot be the GCD of two positive integers x and y?
a 1
b x
c y
d x-y
e x+y


Divisor of a positive integer cannot be more than that integer (for example integer 4 doesn't have a divisor more than 4, the largest divisor it has is 4 itself), so greatest common divisor of two positive integers x and y can not be more than x or y.

Answer: E.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

Senior Manager
Senior Manager
avatar
Joined: 21 Mar 2010
Posts: 316
Followers: 5

Kudos [?]: 22 [0], given: 33

Re: problem solving [#permalink] New post 09 Feb 2011, 09:22
E.

X+y will be greater than either x or y and hence it cannot be the answer.
Expert Post
GMAT Tutor
avatar
Joined: 24 Jun 2008
Posts: 1171
Followers: 303

Kudos [?]: 963 [0], given: 4

Re: Could you explain? [#permalink] New post 26 Nov 2011, 06:15
Expert's post
The greatest common divisor of x and y must be a divisor of x, so it can't be larger than x. Since x+y is larger than x, it cannot be the greatest common divisor of x and y.
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

1 KUDOS received
Manager
Manager
User avatar
Joined: 13 Feb 2012
Posts: 147
Location: Italy
Concentration: General Management, Entrepreneurship
GMAT 1: 560 Q36 V34
GPA: 3.1
WE: Sales (Transportation)
Followers: 4

Kudos [?]: 3 [1] , given: 85

Re: Which of the following CANNOT be the greatest common divisor [#permalink] New post 24 Jul 2012, 09:42
1
This post received
KUDOS
Manhattan's way of visualizing the GCF comes in handy in this type of question. Even if you do not recall by theory that the GCF cannot be greater than either terms, you can figure that out.
_________________

"The Burnout" - My Debrief

Kudos if I helped you ;)


Andy

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 28332
Followers: 4484

Kudos [?]: 45399 [0], given: 6759

Re: Which of the following CANNOT be the greatest common divisor [#permalink] New post 31 Aug 2013, 05:28
Expert's post
2 KUDOS received
Intern
Intern
avatar
Joined: 01 Aug 2006
Posts: 35
Followers: 0

Kudos [?]: 19 [2] , given: 0

Re: Which of the following CANNOT be the greatest common divisor [#permalink] New post 07 Feb 2014, 20:49
2
This post received
KUDOS
Which of the following CANNOT be the greatest common divisor of two positive integers x and y?

method 1: use examples/counter examples.
A. 1 (x=2;y=3)
B. x (x=2; y = 4)
C. y (x=4; y = 2)
D. x-y (x = 4; y =2)
E. x+y -> NOT POSSIBLE.

Concept: Factors of a number are always less than or equal to that number. HCF of x and y can never be greater than the smaller number.
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 5393
Followers: 311

Kudos [?]: 60 [0], given: 0

Premium Member
Re: Which of the following CANNOT be the greatest common divisor [#permalink] New post 04 Mar 2015, 14:03
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

Expert Post
e-GMAT Representative
User avatar
Joined: 04 Jan 2015
Posts: 336
Followers: 52

Kudos [?]: 380 [0], given: 81

Which of the following CANNOT be the greatest common divisor [#permalink] New post 27 Apr 2015, 04:50
Expert's post
Bunuel wrote:
Bumping for review and further discussion.


Hi Everyone!

Here's a question to further test your understanding of the concept of GCD:

If A and B are distinct positive integers greater than 1 such that the GCD of A and B is A, then which of the following must be true?

(A) A is a prime number
(B) A and B have the same prime factors.
(C) A and B have the same even-odd nature
(D) All the factors of B are divisible by A
(E) The LCM of A and B is B


Will post the solution in this thread on May 1, 2015. Till then, happy solving! :-D

Regards
Japinder
_________________

https://e-gmat.com/courses/quant-live-prep/

Image

1 KUDOS received
Intern
Intern
avatar
Joined: 29 Mar 2015
Posts: 16
WE: Research (Other)
Followers: 0

Kudos [?]: 6 [1] , given: 17

GMAT ToolKit User
Which of the following CANNOT be the greatest common divisor [#permalink] New post 27 Apr 2015, 10:56
1
This post received
KUDOS
EgmatQuantExpert wrote:
Bunuel wrote:
Bumping for review and further discussion.


Hi Everyone!

Here's a question to further test your understanding of the concept of GCD:

If A and B are distinct positive integers greater than 1 such that the GCD of A and B is A, then which of the following must be true?

(A) A is a prime number
(B) A and B have the same prime factors.
(C) A and B have the same even-odd nature
(D) All the factors of B are divisible by A
(E) The LCM of A and B is B


Will post the solution in this thread on May 1, 2015. Till then, happy solving! :-D

Regards
Japinder



I think B, C and E are valid for the above question.
Expert Post
e-GMAT Representative
User avatar
Joined: 04 Jan 2015
Posts: 336
Followers: 52

Kudos [?]: 380 [0], given: 81

Re: Which of the following CANNOT be the greatest common divisor [#permalink] New post 01 May 2015, 05:13
Expert's post
EgmatQuantExpert wrote:
Bunuel wrote:
Bumping for review and further discussion.


Hi Everyone!

Here's a question to further test your understanding of the concept of GCD:

If A and B are distinct positive integers greater than 1 such that the GCD of A and B is A, then which of the following must be true?

(A) A is a prime number
(B) A and B have the same prime factors.
(C) A and B have the same even-odd nature
(D) All the factors of B are divisible by A
(E) The LCM of A and B is B


Will post the solution in this thread on May 1, 2015. Till then, happy solving! :-D

Regards
Japinder


The correct answer is Option E.

PFB the correct solution for this question:

We are given that A and B are distinct positive integers greater than 1 such that the GCD of A and B is A

The important thing to note is that the question is asking about must be true statements. Must be true statements are those that will hold for all possible values of A and B, without exception.

So, our approach here will be to see if we can find any exceptions to the 5 given statements. Let's see.

(A) A is a prime number
Consider A = 20 and B = 60. In this case, GCD(A,B) = A but A is not a prime number. Since we have found an exception to Statement A, it is clearly not a must be true statement.

(B) A and B have the same prime factors.
Once again, consider the case of A = 20 and B= 60. The prime factors of A are 2 and 5. The prime factors of B are 2, 3 and 5. So, clearly Statement B doesn't hold true for all possible values of A and B, and therefore, cannot be a must be true statement.

(C) A and B have the same even-odd nature
Consider A = 3 and B = 6. Here too, GCD(A,B) = A but the even-odd nature of A and B is opposite. So, Statement C is ruled out as well.

(D) All the factors of B are divisible by A
In the case of A= 20 and B = 60, 15 is a factor of B that is not divisible by A.
Similarly, in the case of A = 3 and B = 6, 1 is a factor of B that is not divisible by A

The existence of these exceptions indicates that Statement D is not a must be true statement.

(E) The LCM of A and B is B
We know that LCM(A,B)*GCD(A,B) = A*B . . . (1)

Given: GCD(A,B) = A . . . (2)

On substituting (2) in (1), we get:
LCM(A,B) = B

Therefore, Statement E will always be true, for all values of A and B.

Thanks and Best Regards

Japinder
_________________

https://e-gmat.com/courses/quant-live-prep/

Image

Expert Post
e-GMAT Representative
User avatar
Joined: 04 Jan 2015
Posts: 336
Followers: 52

Kudos [?]: 380 [0], given: 81

Re: Which of the following CANNOT be the greatest common divisor [#permalink] New post 01 May 2015, 05:19
Expert's post
nailgmat2015 wrote:

I think B, C and E are valid for the above question.


Dear nailgmat2015

Thank you for attempting this question. Please go through the solution posted above and let me know if you have any doubts about it.

See you around! :)

Japinder
_________________

https://e-gmat.com/courses/quant-live-prep/

Image

Intern
Intern
avatar
Joined: 29 Mar 2015
Posts: 16
WE: Research (Other)
Followers: 0

Kudos [?]: 6 [0], given: 17

GMAT ToolKit User
Re: Which of the following CANNOT be the greatest common divisor [#permalink] New post 01 May 2015, 06:25
EgmatQuantExpert wrote:
nailgmat2015 wrote:

I think B, C and E are valid for the above question.


Dear nailgmat2015

Thank you for attempting this question. Please go through the solution posted above and let me know if you have any doubts about it.

See you around! :)

Japinder



Thanks Jaspinder...

I want to clarify two things which are what is the level of this question? and how to approach number system questions (I mean substituting values and working through is the best way to approach questions)?
Expert Post
e-GMAT Representative
User avatar
Joined: 04 Jan 2015
Posts: 336
Followers: 52

Kudos [?]: 380 [0], given: 81

Re: Which of the following CANNOT be the greatest common divisor [#permalink] New post 04 May 2015, 03:08
Expert's post
nailgmat2015 wrote:


Thanks Jaspinder...

I want to clarify two things which are what is the level of this question? and how to approach number system questions (I mean substituting values and working through is the best way to approach questions)?


Dear nailgmat2015

Thank you for your questions. :) PFB my response.

1. This question is of GMAT 650- difficulty level. That said, I don't think the difficulty-level of a question is an important number. During the preparation stage, one should focus on the learning that one can glean from a question. And, every question that can teach you something - whether a conceptual point or a takeaway on how to attempt questions better - is an important question. By focusing in this manner on

i) building concepts
ii) learning to solve questions methodically in a step-by-step manner
iii) learning from the mistakes that one makes along the way

even the questions of the GMAT 700+ difficulty level will start seeming easy to you. :)

2. I am not too big a fan of solving questions by substituting numbers. This approach certainly appears appealing at the first look because it seemingly allows you to bypass conceptual understanding. And precisely there lies the problem with this approach - if, during your preparation, you solve questions by substituting numbers, you're depriving yourself of an opportunity to hone your conceptual understanding.

I always advise my students to work through questions from the first principles.

Since your question was specifically about Number Properties, I can actually share with you a tangible sample of what I mean:

Our Number Properties Live Classroom session is a free session and likewise, its recording too is freely accessible by all. Please click here to go to the recording (the video takes about 45 seconds to load). The Number Properties part begins from the 20th minute onwards. In this session, you'll find both basic and very advanced questions from Even-Odd numbers, Prime Numbers and LCM-GCD. And, you'll see for yourself how even the most difficult Number Properties questions can be solved by applying, in a step-by-step manner, the basic concepts that you already know.

I hope you found this discussion useful. Please let me know if I can be of any further help :)

Best Regards

Japinder
_________________

https://e-gmat.com/courses/quant-live-prep/

Image

Re: Which of the following CANNOT be the greatest common divisor   [#permalink] 04 May 2015, 03:08
    Similar topics Author Replies Last post
Similar
Topics:
2 Experts publish their posts in the topic Which of the following CANNOT be the least common multiple of two posi PareshGmat 1 09 Sep 2014, 01:09
5 Experts publish their posts in the topic Which of the following CANNOT be the greatest common divisor Bunuel 6 17 Feb 2014, 02:42
1 Experts publish their posts in the topic Which of the following cannot be the least common multiple goodyear2013 2 06 Feb 2014, 02:24
2 If x=8y+11 then which of the following cannot be a divisor guerrero25 4 02 Oct 2013, 18:13
Which of the following CANNOT be the greatest common divisor rahulraao 2 03 Sep 2005, 05:02
Display posts from previous: Sort by

Which of the following CANNOT be the greatest common divisor

  Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.