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

It is currently 28 Aug 2014, 01:49

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

What is the greatest common factor of "a" and "b"? 1) The

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
avatar
Joined: 28 Feb 2003
Posts: 100
Followers: 1

Kudos [?]: 3 [0], given: 0

GMAT Tests User
What is the greatest common factor of "a" and "b"? 1) The [#permalink] New post 15 May 2003, 05:38
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
What is the greatest common factor of "a" and "b"?

1) The greatest common factor of a/2 and b/2 is 5
2) The greatest common factor of 2a and 2b is 10
SVP
SVP
User avatar
Joined: 03 Feb 2003
Posts: 1613
Followers: 5

Kudos [?]: 44 [0], given: 0

 [#permalink] New post 15 May 2003, 23:57
An interesting one.
I think the problem works for the least common multiple as well.
Manager
Manager
avatar
Joined: 28 Feb 2003
Posts: 100
Followers: 1

Kudos [?]: 3 [0], given: 0

GMAT Tests User
 [#permalink] New post 16 May 2003, 00:18
ya, I think it works for LCM also

Can we generalise :?: :?: :?:

that if GCF of "x*a" and "x*b" is Z, then GCF of "a" and "b" will be x*Z,

where x is a positive integer or fraction.

similarly for LCM :?: :?: :?: :?:
SVP
SVP
User avatar
Joined: 03 Feb 2003
Posts: 1613
Followers: 5

Kudos [?]: 44 [0], given: 0

 [#permalink] New post 16 May 2003, 00:38
You mean
If GCD of AX and BX is ZX, then GCD of A and B is Z, and vice versa.
I think it should be the same for LCM.
Looks like a new theorem.
Senior Manager
Senior Manager
avatar
Joined: 11 Nov 2003
Posts: 356
Location: Illinois
Followers: 1

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

GMAT Tests User
This one is for Stolyar or brstorewala [#permalink] New post 06 Feb 2004, 08:54
brstorewala wrote:
ya, I think it works for LCM also

Can we generalise :?: :?: :?:

that if GCF of "x*a" and "x*b" is Z, then GCF of "a" and "b" will be x*Z,

where x is a positive integer or fraction.

similarly for LCM :?: :?: :?: :?:




Applying this rule, statement (1) and (2) will give different values for "GCF of a and b". Are you sure about this?
Director
Director
avatar
Joined: 03 Jul 2003
Posts: 656
Followers: 2

Kudos [?]: 13 [0], given: 0

GMAT Tests User
Re: This one is for Stolyar or brstorewala [#permalink] New post 06 Feb 2004, 15:46
gmatblast wrote:
Applying this rule, statement (1) and (2) will give different values for "GCF of a and b". Are you sure about this?


Yes ! The answers is different for (1) & (2). But, the concept, IMO,
should be OK!
Manager
Manager
avatar
Joined: 25 Jan 2004
Posts: 92
Location: China
Followers: 1

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

 [#permalink] New post 06 Feb 2004, 21:58
Probably the following might be helpful. I hope you won't say 'what are you trying to demonstrate here' for adding my reply.

let a = p1^k1 * p2^k2 * ... pn^kn
b = p2^m1 * p2^m2 * ... pn^mn

gcd(a,b) = p1^min(k1, m1) * p2^min(k2, m2) * ... pn^min(kn, mn)
lcm(a,b) = p1^max(k1, m1) * p2^max(k2, m2) * ... pn^max(kn, mn)

min(c, d)+max(c,d) = c +d

hence gcd(a,b)*lcm(a,b) = a*b
Director
Director
avatar
Joined: 03 Jul 2003
Posts: 656
Followers: 2

Kudos [?]: 13 [0], given: 0

GMAT Tests User
 [#permalink] New post 06 Feb 2004, 23:11
Zhung Gazi wrote:

min(c, d)+max(c,d) = c +d



I've lost you at this step. Would you elaborate?
Manager
Manager
avatar
Joined: 25 Jan 2004
Posts: 92
Location: China
Followers: 1

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

 [#permalink] New post 06 Feb 2004, 23:32
if c < d then min(c,d) = c , max(c,d) =d min(c,d)+max(c,d) = c+d
if c >= d then min(c,d) = d, max(c, d) = c and min(c,d)+max(c,d) = c+d

max(c,d) - min(c,d) = |c-d|

Further you can have algebraic equivalents as follows
max(c,d) = (1/2)(c+d+|c-d|)
min(c,d) = (1/2)(c+d-|c-d|)
  [#permalink] 06 Feb 2004, 23:32
    Similar topics Author Replies Last post
Similar
Topics:
Experts publish their posts in the topic What is the greatest common divisor of a and b? (1) a is rafi 3 17 Sep 2010, 03:07
What is the greatest common divisor of (2^a) - 1 and (2^b) - az780 1 15 Mar 2008, 01:50
pls sho working.... What is the greatest common factor of FN 2 31 May 2005, 10:12
What is the greatest common factor of the positive integers crackgmat04 2 09 Dec 2004, 03:08
What is the greatest common factor of positive integers x venksune 5 19 Sep 2004, 12:42
Display posts from previous: Sort by

What is the greatest common factor of "a" and "b"? 1) The

  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®.