GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 24 Sep 2018, 10:35

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

How many factors of the number 2^6*3^5*5^4*6^3 are multiples of 360?

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

Hide Tags

Retired Moderator
User avatar
P
Status: The best is yet to come.....
Joined: 10 Mar 2013
Posts: 526
GMAT ToolKit User
How many factors of the number 2^6*3^5*5^4*6^3 are multiples of 360?  [#permalink]

Show Tags

New post 20 Oct 2017, 07:35
2
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

67% (02:18) correct 33% (02:03) wrong based on 39 sessions

HideShow timer Statistics

How many factors of the number \(2^6*3^5*5^4*6^3\) are multiples of 360?

A. 36
B. 108
C. 144
D. 196
E. 288

_________________

Hasan Mahmud

PS Forum Moderator
avatar
D
Joined: 25 Feb 2013
Posts: 1217
Location: India
GPA: 3.82
GMAT ToolKit User Premium Member Reviews Badge
How many factors of the number 2^6*3^5*5^4*6^3 are multiples of 360?  [#permalink]

Show Tags

New post 20 Oct 2017, 07:44
1
2
Mahmud6 wrote:
How many factors of the number \(2^6*3^5*5^4*6^3\) are multiples of 360?

A. 36
B. 1088
C. 144
D. 196
E. 288


\(2^6*3^5*5^4*6^3=2^9*3^8*5^4\)

\(360=2^3*3^2*5\)

all factors of \(2^9*3^8*5^4\) that can be written as multiples of \(360\) will be of the form \(2^3*3^2*5*p\)

therefore \(2^9*3^8*5^4=2^3*3^2*5*p\)

or \(p= 2^6*3^6*5^3\)

Now the number of factors of \(p=(1+6)*(1+6)*(1+3)=196\)

Option D
Board of Directors
User avatar
V
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3672
Premium Member Reviews Badge CAT Tests
How many factors of the number 2^6*3^5*5^4*6^3 are multiples of 360?  [#permalink]

Show Tags

New post 20 Oct 2017, 07:47
To find out the number of multiples of 360, let's first find out its factors and then take them out of the total factors. This will ensure that the remaining factors will always include the factors of 360.

Let's solve now:

360 = 9 * 4 * 10 = \(3^2*2^3*5^1\)

That means let's take two 3s, three 2s and one 5 out of the original number.

\(2^6*3^5*5^4*6^3\)

After taking the required factors out, we are left with : \(2^3*3^3*5^3*6^3\)

As per the formula, \(a^p*b^q*c^r\), we have number of factors = (p+1)(q+1)(r+1), where a,b and c MUST be distinct primes.

Let's prime factorise all and club the common number, I will have the number as \(2^6*3^6*5^4\) [Confused? Just split take 6 = 2*3 and then join 2 with existing 2s and 3 with existing 3s]

Therefore, for our question I can say, number of factors multiple of 360 = (6+1) ( 6+1)(3+1) = 49*4 = 196

Hence, answer must be D.
_________________

My GMAT Story: From V21 to V40
My MBA Journey: My 10 years long MBA Dream
My Secret Hacks: Best way to use GMATClub | Importance of an Error Log!
Verbal Resources: All SC Resources at one place | All CR Resources at one place
Blog: Subscribe to Question of the Day Blog

GMAT Club Inbuilt Error Log Functionality - View More.
New Visa Forum - Ask all your Visa Related Questions - here.

New! Best Reply Functionality on GMAT Club!



Find a bug in the new email templates and get rewarded with 2 weeks of GMATClub Tests for free

GMAT Club Bot
How many factors of the number 2^6*3^5*5^4*6^3 are multiples of 360? &nbs [#permalink] 20 Oct 2017, 07:47
Display posts from previous: Sort by

How many factors of the number 2^6*3^5*5^4*6^3 are multiples of 360?

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

Events & Promotions

PREV
NEXT


Copyright

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