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

It is currently 24 Jul 2014, 04:13

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 represents the largest 4 digit number

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
Manager
Manager
User avatar
Status: Starting Work
Affiliations: Chartered Engineer
Joined: 20 Jun 2010
Posts: 198
Location: United Arab Emirates
Concentration: General Management, Leadership
Schools: INSEAD - Class of 2013
WE: Business Development (Energy and Utilities)
Followers: 7

Kudos [?]: 27 [1] , given: 19

Which of the following represents the largest 4 digit number [#permalink] New post 06 Jun 2011, 02:14
1
This post received
KUDOS
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

53% (02:45) correct 47% (03:02) wrong based on 32 sessions
Which of the following represents the largest 4 digit number that can be added to 7249 in order to make the derived number divisible by each of 12, 14, 21, 33 & 54.

A. 9123
B. 9383
C. 8727
D. 1067
E. None Of The Above
[Reveal] Spoiler: OA
3 KUDOS received
Math Forum Moderator
avatar
Joined: 20 Dec 2010
Posts: 2049
Followers: 125

Kudos [?]: 875 [3] , given: 376

GMAT Tests User
Re: LCM & HCF [#permalink] New post 06 Jun 2011, 02:27
3
This post received
KUDOS
mattapraveen wrote:
Which of the following represents the largest 4 digit number that can be added to 7249 in order to make the derived number divisible by each of 12, 14,21, 33 & 54.

A.9123
B.9383
C.8727
D.1067
E.None Of The Above


Find the LCM of the given numbers.
12= 2*2*3
14= 2*7
21= 3*7
33= 3*11
54= 3*2*3*3

Max powers of all prime numbers:
2=2
3=3
7=1
11=1

LCM=2^2*3^3*7^1*11^1=8316

8316-7249=1067. Thus, if we add 1067 to 7249, the number will be divisible by all the given numbers.
However, 1067 is not the GREATEST 4-digit number to satisfy the condition.

Next number that will be divisible is:
1067+8316=9383

Thus, adding 9383 to 7249 will give us a number that will be divisible by all the given numbers PLUS 9383 is the greatest 4-digit number that satisfies this condition.

Ans: "B"
_________________

~fluke

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
User avatar
Status: Don't worry about finding inspiration. It eventually come >>>>>>>
Joined: 31 May 2011
Posts: 23
Location: Î Ñ D Ï Â
Followers: 0

Kudos [?]: 7 [0], given: 2

Re: LCM & HCF [#permalink] New post 06 Jun 2011, 03:24
here,
LCM of 12,14,21.33 and 54 comes to be 8316.
Now subtract 7249 from 8316 we get 1067 but 1067 is n0t the greatest 4 digit number so add 1067 to 8316 we get 9383. thus "B" is the correct option.
Manager
Manager
User avatar
Status: Starting Work
Affiliations: Chartered Engineer
Joined: 20 Jun 2010
Posts: 198
Location: United Arab Emirates
Concentration: General Management, Leadership
Schools: INSEAD - Class of 2013
WE: Business Development (Energy and Utilities)
Followers: 7

Kudos [?]: 27 [0], given: 19

Re: LCM & HCF [#permalink] New post 06 Jun 2011, 03:24
fluke wrote:
mattapraveen wrote:
Which of the following represents the largest 4 digit number that can be added to 7249 in order to make the derived number divisible by each of 12, 14,21, 33 & 54.

A.9123
B.9383
C.8727
D.1067
E.None Of The Above


Find the LCM of the given numbers.
12= 2*2*3
14= 2*7
21= 3*7
33= 3*11
54= 3*2*3*3

Max powers of all prime numbers:
2=2
3=3
7=1
11=1

LCM=2^2*3^3*7^1*11^1=8316

8316-7249=1067. Thus, if we add 1067 to 7249, the number will be divisible by all the given numbers.
However, 1067 is not the GREATEST 4-digit number to satisfy the condition.

Next number that will be divisible is:
1067+8316=9383

Thus, adding 9383 to 7249 will give us a number that will be divisible by all the given numbers PLUS 9383 is the greatest 4-digit number that satisfies this condition.

Ans: "B"


Bulls Eye and in No time.
SVP
SVP
avatar
Joined: 16 Nov 2010
Posts: 1692
Location: United States (IN)
Concentration: Strategy, Technology
Followers: 30

Kudos [?]: 275 [0], given: 36

GMAT Tests User Premium Member Reviews Badge
Re: LCM & HCF [#permalink] New post 06 Jun 2011, 04:05
Let us do the prime factorization of the numbers and get the LCM

12 = 2^ * 3
14 = 2 * 7
21 = 7*3
33 = 3 * 11
54 = 3^3 * 2

So LCM = 3^3 * 11 * 7 * 2^2

= 27 * 77 * 4

= 8316

Now the lowest number to satisfy thus would be = 8316 - 7249 = 1067

But we need to check other options also, so let us add 8316 once again to 1067.

= 8316 + 1067 = 9383

Answer - B
_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
avatar
Joined: 08 Sep 2010
Posts: 172
Followers: 0

Kudos [?]: 14 [0], given: 18

GMAT Tests User
Re: LCM & HCF [#permalink] New post 11 Jun 2011, 14:26
good one...nice explanation
_________________

My will shall shape the future. Whether I fail or succeed shall be no man's doing but my own.

If you like my explanations award kudos.

SVP
SVP
User avatar
Joined: 06 Sep 2013
Posts: 1629
Location: United States
Concentration: Finance
GMAT 1: 710 Q48 V39
WE: Corporate Finance (Investment Banking)
Followers: 10

Kudos [?]: 132 [0], given: 254

GMAT ToolKit User
Re: LCM & HCF [#permalink] New post 12 Nov 2013, 11:53
mattapraveen wrote:
Which of the following represents the largest 4 digit number that can be added to 7249 in order to make the derived number divisible by each of 12, 14,21, 33 & 54.

A.9123
B.9383
C.8727
D.1067
E.None Of The Above


Trying to find a simple approach for this one.
Let's see if this works

So we need it to be divisible by 12, 14, 21, 33 and 54. Note that these numbers have several primes in common. What is the largest prime that we have among all these. 11.

OK so we need to find out if the sum will be divisible by 11. First we can tell that 7249 is divisible by 11 because 7+4-2-9=0 which is a multiple of 11.
So we need another multiple of 11, so that the sum of both also throws a multiple of 11. Let's strat with the greatest number cause that's what wer are being asked.
9383 = 17-6 = 11. It is of course a multiple of 11 so option (B) then is the correct answer

Throw me some freaking Kudos!!
Cheers
J :)
Re: LCM & HCF   [#permalink] 12 Nov 2013, 11:53
    Similar topics Author Replies Last post
Similar
Topics:
11 Experts publish their posts in the topic Which of the following is the largest? mau5 5 25 Nov 2013, 01:02
4 Experts publish their posts in the topic Which of the following quantities is the largest? mrinal2100 4 14 Jun 2011, 09:22
2^10= 1024. Which is the largest of the following numbers? kevincan 2 12 Jul 2006, 15:42
The largest number amongst the following that will perfectly jlui4477 6 25 Feb 2006, 10:47
The largest number amongst the following that will perfectly cool_jonny009 10 11 Nov 2005, 20:48
Display posts from previous: Sort by

Which of the following represents the largest 4 digit number

  Question banks Downloads My Bookmarks Reviews Important topics  


cron

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®.