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

It is currently 22 Oct 2018, 03:45

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 9600 are not divisible by 12?

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

Hide Tags

Director
Director
User avatar
D
Joined: 12 Feb 2015
Posts: 515
Premium Member CAT Tests
How many factors of 9600 are not divisible by 12?  [#permalink]

Show Tags

New post 05 Jun 2018, 22:41
1
19
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

51% (02:10) correct 49% (02:31) wrong based on 200 sessions

HideShow timer Statistics

How many factors of 9600 are not divisible by 12?

A) 48
B) 30
C) 24
D) 20
E) 42

_________________

"Please hit :thumbup: +1 Kudos if you like this post" :student_man:

_________________
Manish :geek:

"Only I can change my life. No one can do it for me"

Most Helpful Community Reply
Director
Director
User avatar
P
Status: Learning stage
Joined: 01 Oct 2017
Posts: 906
WE: Supply Chain Management (Energy and Utilities)
Premium Member
How many factors of 9600 are not divisible by 12?  [#permalink]

Show Tags

New post Updated on: 08 Jun 2018, 18:48
6
3
CAMANISHPARMAR wrote:
How many factors of 9600 are not divisible by 12?

A) 48
B) 30
C) 24
D) 20
E) 42


Let's write 9600 in prime factorization form, 9600=\(2^7\)*\(5^2\)*\(3^1\)

Hence the no of factors of 9600=(7+1)(2+1)(1+1)=8*3*2=48

The no factors of 9600 not divisible by 12=Total of no factors of 9600- Total no of factors of 9600 which are divisible by 12

Now we can write, 9600=\(2^7\)*\(5^2\)*\(3^1\)=\(2^2\)*3(\(2^5\)*\(5^2\))=12(\(2^5\)*\(5^2\))

Since 12(\(2^5\)*\(5^2\)) is multiple of 12, hence the no of factors which are divisible by 12 =(5+1)(2+1)=6*3=18

Therefore,the no factors of 9600 not divisible by 12=48-18=30

Answer option(B)
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine


Originally posted by PKN on 05 Jun 2018, 23:16.
Last edited by PKN on 08 Jun 2018, 18:48, edited 1 time in total.
General Discussion
Director
Director
User avatar
D
Joined: 12 Feb 2015
Posts: 515
Premium Member CAT Tests
Re: How many factors of 9600 are not divisible by 12?  [#permalink]

Show Tags

New post 07 Jun 2018, 04:32
9600 could be written as 12 * 800
Now 10 is a factor of 800, so is 20, so is 400, including many others.
10, 20 and 400 are not divisible by 12 but (12*10), (12*20) and (12*400) are divisible by 12 because we are multiplying and dividing my 12. Hence every factor of 800 is also a factor of 9600 and is divisible by 12 if we are multiplying each factor of 800 by 12.

To find the number of factors of 800 is a straightforward application of number of factors formula:-
(p+1)(q+1)(r+1)... [where p,q,r are exponents of each prime factor]

Therefore 800 can be written as \(2^5∗5^2\)
Therefore the number of factors of 800 are (5+1)(2+1) = 6*3 = 18 factors.

Therefore the no. of factors of 9600 which are divisible by 12 are 18 factors in total.

But the question stem asks us how many factors of 9600 are NOT divisible by 12?

Therefore we will have to deduct all the factors of 9600 which are divisible by 12 from all the factors of 9600 to get all the factors of 9600 which are NOT divisible by 12.

9600 can be written as \(2^7∗3*5^2\)
Therefore the number of factors of 9600 are (7+1)(1+1)(2+1) = 8*2*3 = 48 factors.

All the factors of 9600 which are NOT divisible by 12 = 48 factors - 18 factors = 30 factors [hence the correct answer is (B)]
_________________

"Please hit :thumbup: +1 Kudos if you like this post" :student_man:

_________________
Manish :geek:

"Only I can change my life. No one can do it for me"

Intern
Intern
avatar
B
Joined: 02 May 2018
Posts: 7
Re: How many factors of 9600 are not divisible by 12?  [#permalink]

Show Tags

New post 07 Jun 2018, 05:41
can someone please explain how the get factors of 9600 divisible by 12
Director
Director
User avatar
D
Joined: 12 Feb 2015
Posts: 515
Premium Member CAT Tests
Re: How many factors of 9600 are not divisible by 12?  [#permalink]

Show Tags

New post 07 Jun 2018, 05:48
1
Meghakothari98 wrote:
can someone please explain how the get factors of 9600 divisible by 12


To find the number of factors of 9600 that are divisible by 12 is a straightforward application of number of factors formula & some LOGIC:-
(p+1)(q+1)(r+1)... [where p,q,r are exponents of each prime factor]

9600 could be written as 12 * 800
Now 10 is a factor of 800, so is 20, so is 400, including many others.
10, 20 and 400 are not divisible by 12 but (12*10), (12*20) and (12*400) are divisible by 12 because we are multiplying and dividing my 12. Hence every factor of 800 is also a factor of 9600 and is divisible by 12 if we are multiplying each factor of 800 by 12.

To find the number of factors of 800 is a straightforward application of number of factors formula:-
(p+1)(q+1)(r+1)... [where p,q,r are exponents of each prime factor]

Therefore 800 can be written as \(2^5∗5^2\)
Therefore the number of factors of 800 are (5+1)(2+1) = 6*3 = 18 factors.

All the factors of 800 are also the factors of 9600 that are divisible by 12 because as per our LOGIC we are multiplying each factor of 800 by 12. Therefore the no. of factors of 9600 that are divisible by 12 is also 18 factors.

Please revert in case if you need more clarification!!
_________________

"Please hit :thumbup: +1 Kudos if you like this post" :student_man:

_________________
Manish :geek:

"Only I can change my life. No one can do it for me"

Director
Director
User avatar
D
Joined: 12 Feb 2015
Posts: 515
Premium Member CAT Tests
Re: How many factors of 9600 are not divisible by 12?  [#permalink]

Show Tags

New post 07 Jun 2018, 05:51
Meghakothari98 wrote:
can someone please explain how the get factors of 9600 divisible by 12


For practice:-

https://gmatclub.com/forum/how-many-fac ... 66709.html

https://gmatclub.com/forum/how-many-fac ... 67283.html
_________________

"Please hit :thumbup: +1 Kudos if you like this post" :student_man:

_________________
Manish :geek:

"Only I can change my life. No one can do it for me"

Director
Director
User avatar
D
Joined: 12 Feb 2015
Posts: 515
Premium Member CAT Tests
Re: How many factors of 9600 are not divisible by 12?  [#permalink]

Show Tags

New post 07 Jun 2018, 05:54
Meghakothari98 wrote:
can someone please explain how the get factors of 9600 divisible by 12


Another method just to lay a strong foundation on how to use the formula using another logic but not advisable to use it in GMAT as this method is time consuming:-

https://gmatclub.com/forum/how-many-fac ... l#p2072897
_________________

"Please hit :thumbup: +1 Kudos if you like this post" :student_man:

_________________
Manish :geek:

"Only I can change my life. No one can do it for me"

Target Test Prep Representative
User avatar
P
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3907
Location: United States (CA)
Re: How many factors of 9600 are not divisible by 12?  [#permalink]

Show Tags

New post 07 Jun 2018, 17:07
CAMANISHPARMAR wrote:
How many factors of 9600 are not divisible by 12?

A) 48
B) 30
C) 24
D) 20
E) 42


Let’s first determine the total number of factors of 9600. We express 9600 as a product of primes. We add 1 to each prime’s exponent, and then find the product of those numbers.

9600 = 96 x 100 = 16 x 6 x 5^2 x 2^2 = 2^4 x 2 x 3 x 5^2 x 2^2 = 2^7 x 3 x 5^2

So the total number of factors of 9600 is (7 + 1)(1 + 1)(2 + 1) = 48.

9600 = 12 x 800

To determine how many factors ARE divisible by 12, we can break 800 into primes and determine the total number of factors of 800.

800 = 8 x 100 = 2^3 x 2^2 x 5^2 = 2^5 x 5^2

So 800 has (5 + 1)(2 + 1) = 18

Thus, the number of factors of 9600 that are not divisible by 12 are 48 - 18 = 30.

Answer: B
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Intern
Intern
avatar
B
Joined: 06 Apr 2017
Posts: 7
Re: How many factors of 9600 are not divisible by 12?  [#permalink]

Show Tags

New post 08 Jun 2018, 12:52
PKN wrote:
CAMANISHPARMAR wrote:
How many factors of 9600 are not divisible by 12?

A) 48
B) 30
C) 24
D) 20
E) 42


Let's write 9600 in prime factorization form, 9600=\(2^7\)*\(5^2\)*\(3^1\)

Hence the no of factors of 9600=(7+1)(2+1)(1+1)=8*3*2=48

The no factors of 9600 not divisible by 12=Total of no factors of 9600- Total no of factors of 9600 which are divisible by 12

Now we can write, 9600=\(2^7\)*\(5^2\)*\(3^1\)=\(2^2\)*3(\(2^5\)*\(5^2\))=12(\(2^5\)*\(5^2\))

Since \(2^5\)*\(5^2\) is multiple of 12, hence the no of factors which are divisible by 12 =(5+1)(2+1)=6*3=18

Therefore,the no factors of 9600 not divisible by 12=48-18=30

Answer option(B)



2^5*5^2 is a multiple of 12 ?
Director
Director
User avatar
P
Status: Learning stage
Joined: 01 Oct 2017
Posts: 906
WE: Supply Chain Management (Energy and Utilities)
Premium Member
Re: How many factors of 9600 are not divisible by 12?  [#permalink]

Show Tags

New post 08 Jun 2018, 18:50
avijit02 wrote:
PKN wrote:
CAMANISHPARMAR wrote:
How many factors of 9600 are not divisible by 12?

A) 48
B) 30
C) 24
D) 20
E) 42


Let's write 9600 in prime factorization form, 9600=\(2^7\)*\(5^2\)*\(3^1\)

Hence the no of factors of 9600=(7+1)(2+1)(1+1)=8*3*2=48

The no factors of 9600 not divisible by 12=Total of no factors of 9600- Total no of factors of 9600 which are divisible by 12

Now we can write, 9600=\(2^7\)*\(5^2\)*\(3^1\)=\(2^2\)*3(\(2^5\)*\(5^2\))=12(\(2^5\)*\(5^2\))

Since \(2^5\)*\(5^2\) is multiple of 12, hence the no of factors which are divisible by 12 =(5+1)(2+1)=6*3=18

Therefore,the no factors of 9600 not divisible by 12=48-18=30

Answer option(B)



2^5*5^2 is a multiple of 12 ?


Hi avijit02,

Typo error edited. Thanks
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

Intern
Intern
avatar
B
Joined: 31 May 2018
Posts: 17
Location: United States
Concentration: Finance, Marketing
Re: How many factors of 9600 are not divisible by 12?  [#permalink]

Show Tags

New post 26 Jun 2018, 03:47
Meghakothari98 wrote:
can someone please explain how the get factors of 9600 divisible by 12


9600=2^7*3*5^2
total factors of 9600=(7+1)(1+1)(2+1)=8*2*3=48
since we want to find factors of 12
write 9600 as a multiple of 12
now 9600=(2^2*3)(2^5*5^2)=12(2^5*5^2)
now factors of 9600 divisible by 12=(5+1)(2+1)=6*3=18
now from here we can find factors of 9600 not divisible by 12
=total factors of 9600-factors of 9600 divisible by 12
=48-18=30
GMAT Club Bot
Re: How many factors of 9600 are not divisible by 12? &nbs [#permalink] 26 Jun 2018, 03:47
Display posts from previous: Sort by

How many factors of 9600 are not divisible by 12?

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


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®.