GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 05 Jul 2020, 21:59

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

The Least Common multiple of 2^6-1 and 2^9-1 is

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

Hide Tags

Find Similar Topics 
Manager
Manager
avatar
Joined: 07 Sep 2010
Posts: 245
The Least Common multiple of 2^6-1 and 2^9-1 is  [#permalink]

Show Tags

New post Updated on: 08 Jul 2014, 01:35
2
16
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

45% (02:51) correct 55% (02:37) wrong based on 148 sessions

HideShow timer Statistics

The Least Common multiple of 2^6-1 and 2^9-1 is:

A. \(2^{12}+27*2^9-217\)

B. \(2^{12} +63*2^3-1\)

C. \(2^{12}+5^{29}-1\)

D. \(2^{12}+9*2^8 -1\)

E. None of these.

Originally posted by imhimanshu on 21 May 2013, 07:23.
Last edited by Bunuel on 08 Jul 2014, 01:35, edited 3 times in total.
Renamed the topic and edited the question.
Most Helpful Expert Reply
Veritas Prep GMAT Instructor
User avatar
V
Joined: 16 Oct 2010
Posts: 10633
Location: Pune, India
Re: The Least Common multiple of 2^6-1 and 2^9-1 is  [#permalink]

Show Tags

New post 21 May 2013, 20:18
4
5
imhimanshu wrote:
Question

The Least Common multiple of \(2^6-1\) and \(2^9-1\) is

a) 2^12+27*2^9-217
b) 2^ 12 +63*2^3-1
c) 2^12+5^29-1
d) 2^12+9*2^8 -1
e) None of these.

Hi Experts,
I would like to know what is the best approach to solve such questions.

Help will be appreciated.

Thanks
H


Responding to a pm:

The best approach in my opinion is what Zarrolou has suggested above.

LCM * GCF = Product of the numbers = \((2^6-1)*(2^9-1) = (2^3 - 1)(2^3 + 1) * (2^3 - 1)(2^6 + 1 + 2^3)\)

Notice that the only common factor between them is \((2^3 - 1)\) so this must be the GCF. Hence LCM will be the rest of the product.

\(LCM = (2^3 + 1) * (2^3 - 1)(2^6 + 1 + 2^3) = (2^6 - 1)(2^6 + 1 + 2^3)\)

Now how do you get it in the format in the options? Almost all options have \(2^{12}\) and 1 so retain those two and club everything else together.

\(LCM = 2^{12} - 1 + (2^6 + 2^9 - 2^6 - 2^3) = 2^{12} - 1 + 2^3(2^6 - 1) = 2^{12} - 1 + 2^3*63\)

Answer (B)

Note that option 'none of these' makes it more complicated since you cannot try some more esoteric methods e.g. last digit etc. GMAT doesn't give you this option. Also, GMAT doesn't expect you to know a^3 - b^3 = (a-b)(a^2 + ab + b^2). Of course, you should be able to arrive at the LHS, given the RHS.
Hence, there are very few CAT questions which will actually be GMAT relevant. If you are practicing for GMAT, try to stick to a GMAT source, especially if you have limited time.
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Most Helpful Community Reply
Director
Director
User avatar
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 991
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
GMAT ToolKit User
Re: The Least Common multiple of 2^6-1 and 2^9-1 is  [#permalink]

Show Tags

New post 21 May 2013, 09:35
8
1
2
Factoralization (refer herefor the formulas)

\(2^6-1=(2^3+1)(2^3-1)=9*7=3*3*7\)

\(2^9-1=(2^3-1)(2^6+2^3+1)=7*73\)

\(LCM=9*7*73=(2^3+1)(2^3-1)(2^6+2^3+1)=(2^6-1)(2^6+2^3+1)=2^{12}+2^3(2^6-1)-1\)

b) \(2^ {12} +63*2^3-1\)
General Discussion
Manager
Manager
User avatar
Status: *Lost and found*
Joined: 25 Feb 2013
Posts: 110
Location: India
Concentration: General Management, Technology
GMAT 1: 640 Q42 V37
GPA: 3.5
WE: Web Development (Computer Software)
GMAT ToolKit User
Re: The Least Common multiple of 2^6-1 and 2^9-1 is  [#permalink]

Show Tags

New post 21 May 2013, 08:33
imhimanshu wrote:
Question

The Least Common multiple of \(2^6-1\) and \(2^9-1\) is

a) 2^12+27*2^9-217
b) 2^ 12 +63*2^3-1
c) 2^12+5^29-1
d) 2^12+9*2^8 -1
e) None of these.

Hi Experts,
I would like to know what is the best approach to solve such questions.

Help will be appreciated.

Thanks
H



I feel [B] is the answer. I am not sure my way is the shortest (coz i did have to go thru a lot of calculation), but it is a way nonetheless :)

From the above, one can find that the HCF of the numbers \(2^6-1\) and \(2^9-1\) is 7. By the rule,
LCM*HCF = Product of two numbers
=> LCM = Product of two numbers /7

7 can be expressed as \(2^3 -1\). By checking all the answer choices one can see that only [B] i.e. \(2^ 12 +63*2^3-1\),
also written as, \(2^ 12 +(2^6 - 1)2^3-1 = 2^ 12 +2^9 -2^3 -1\), results the product of numbers i.e. \(2^15 - 2^6 - 2^9 + 1.\)

Hope my answer is accurate! Would certainly appreciate a shorter way on this! :)

Regards,
Arpan

**edited to correct typo
SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1706
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: The Least Common multiple of 2^6-1 and 2^9-1 is  [#permalink]

Show Tags

New post 08 Jul 2014, 01:05
Bunuel, kindly update the OA in expanded / Mathematical form.
The un-formatted options tend to confuse :)
Thanks
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 64951
Re: The Least Common multiple of 2^6-1 and 2^9-1 is  [#permalink]

Show Tags

New post 08 Jul 2014, 01:36
Manager
Manager
User avatar
B
Joined: 30 Jan 2020
Posts: 53
Location: India
Schools: ISB, S P Jain Global
Re: The Least Common multiple of 2^6-1 and 2^9-1 is  [#permalink]

Show Tags

New post 30 Mar 2020, 05:28
The Least Common multiple of 2^6-1 and 2^9-1 is:

The following steps will help to solve the sum very easily-:

First, lets get the units digit values of 2^6-1 and 2^9-1
1.Units digit of 2^6-1 is 3
2.Units digit of 2^9-1 is 1

Consider every option here with respect to taking the units digit of the value.
A. - 5 (Eliminated as the required values are not multiples of 3 and 1)
B. - 3
C. - 0 (Eliminated as the required values are odd numbers, i.e. 3 and 1)
D.- 9

We are left with option B and D

LCM of 3 and 1 is option B., i.e. 3( which is its unit digit)


Official Answer- Option B.


Thanks.

Regards,
Raunak Damle!

Cheers!
CEO
CEO
User avatar
V
Joined: 03 Jun 2019
Posts: 3182
Location: India
GMAT 1: 690 Q50 V34
WE: Engineering (Transportation)
Premium Member Reviews Badge CAT Tests
The Least Common multiple of 2^6-1 and 2^9-1 is  [#permalink]

Show Tags

New post 30 Mar 2020, 09:38
imhimanshu wrote:
The Least Common multiple of 2^6-1 and 2^9-1 is:

A. \(2^{12}+27*2^9-217\)

B. \(2^{12} +63*2^3-1\)

C. \(2^{12}+5^{29}-1\)

D. \(2^{12}+9*2^8 -1\)

E. None of these.


The Least Common multiple of 2^6-1 and 2^9-1 is:

\(2^6 -1 = (2^3+1)(2^3-1) \)
\(2^9 -1 = (2^3 -1)(2^6 + 2^3 + 1) \)

\(LCM (2^6 -1,2^9 -1) = (2^3+1)(2^9-1) = 2^{12} +2^9 -2^3 -1 = 2^{12} + 64*2^3 - 2^3 - 1 = 2^{12} +63*2^3 - 1\)

IMO B
_________________
Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com
GMAT Club Bot
The Least Common multiple of 2^6-1 and 2^9-1 is   [#permalink] 30 Mar 2020, 09:38

The Least Common multiple of 2^6-1 and 2^9-1 is

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





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