It is currently 10 Dec 2017, 21:17

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

What is the gcd of a, b, and 3a+23b 1. a = 4 2. gcd(a, b,

  post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
Senior Manager
Senior Manager
avatar
Joined: 02 Mar 2004
Posts: 327

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

Location: There
What is the gcd of a, b, and 3a+23b 1. a = 4 2. gcd(a, b, [#permalink]

Show Tags

New post 12 Apr 2004, 12:41
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 5 sessions

HideShow timer Statistics

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

What is the gcd of a, b, and 3a+23b

1. a = 4
2. gcd(a, b, 23a+3b) = 4

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

Intern
Intern
avatar
Joined: 27 Mar 2004
Posts: 4

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

Re: DS-42 [#permalink]

Show Tags

New post 16 Apr 2004, 04:29
hallelujah1234 wrote:
What is the gcd of a, b, and 3a+23b

1. a = 4
2. gcd(a, b, 23a+3b) = 4


say i take a = b = 2
then 23a + 3b = 3a + 23b = 52

so B is sufficient

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

Senior Manager
Senior Manager
avatar
Joined: 11 Nov 2003
Posts: 356

Kudos [?]: 5 [0], given: 0

Location: Illinois
Re: DS-42 [#permalink]

Show Tags

New post 15 May 2004, 18:37
abeautifulmind wrote:
hallelujah1234 wrote:
What is the gcd of a, b, and 3a+23b

1. a = 4
2. gcd(a, b, 23a+3b) = 4


say i take a = b = 2
then 23a + 3b = 3a + 23b = 52

so B is sufficient


if you take a = b = 2, then how does that satisfy given second statement? The gcd in that case will be 2.

I would solve the question by applying the halle..'s methodology. Halle can then approve wether this solution is correct or not.


gcd(a, b, 23a+3b) = 4

=> a = 4m, where m > 0 (integer)
=> b = ak + 4 = (4m)k + 4 = 4mk + 4, where k >=0; integer
=> 3a+23b = 3(4m) + 23(4mk+4) = 4 [3m + 23(mk+1)]

So the gcd (a, b, 3a+23b) = 4

So the answer is B.

Kudos [?]: 5 [0], given: 0

Senior Manager
Senior Manager
avatar
Joined: 02 Mar 2004
Posts: 327

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

Location: There
 [#permalink]

Show Tags

New post 15 May 2004, 18:44
1
This post was
BOOKMARKED
gcd(a, b, ax+by) = gcd(a, b) (obvious)

B says, gcd(a,b) = 4. So, gcd(a, b, 3a+23b) = 4.

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

Senior Manager
Senior Manager
avatar
Joined: 02 Feb 2004
Posts: 344

Kudos [?]: 72 [0], given: 0

 [#permalink]

Show Tags

New post 15 May 2004, 18:58
hallelujah1234 wrote:
gcd(a, b, ax+by) = gcd(a, b) (obvious)



let
a=3
b=2
x=5
y=7

ax+by=15+14=29
gcd of 2, 3, 29 isn't 6 :panel

Kudos [?]: 72 [0], given: 0

Senior Manager
Senior Manager
avatar
Joined: 02 Mar 2004
Posts: 327

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

Location: There
 [#permalink]

Show Tags

New post 15 May 2004, 19:02
mirhaque wrote:
hallelujah1234 wrote:
gcd(a, b, ax+by) = gcd(a, b) (obvious)



let
a=3
b=2
x=5
y=7

ax+by=15+14=29
gcd of 2, 3, 29 isn't 6 :panel


gcd(2, 3) = 1; gcd(2, 3, 29) = 1 = gcd(2, 3)

The proof is based on the fact: that gcd(a, b, c, ...) is the least positive integer in the set {am1+bm2+cm3+ ... | mi is an integer}

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

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 14955

Kudos [?]: 287 [0], given: 0

Premium Member
Re: What is the gcd of a, b, and 3a+23b 1. a = 4 2. gcd(a, b, [#permalink]

Show Tags

New post 13 Aug 2017, 03:07
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

Kudos [?]: 287 [0], given: 0

Re: What is the gcd of a, b, and 3a+23b 1. a = 4 2. gcd(a, b,   [#permalink] 13 Aug 2017, 03:07
Display posts from previous: Sort by

What is the gcd of a, b, and 3a+23b 1. a = 4 2. gcd(a, b,

  post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| 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®.