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

 It is currently 26 Mar 2015, 18:02

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If J is divisible by 12 and 10, is J divisible by 24? The

 Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
CEO
Joined: 21 Jan 2007
Posts: 2766
Location: New York City
Followers: 9

Kudos [?]: 331 [0], given: 4

If J is divisible by 12 and 10, is J divisible by 24? The [#permalink]  22 Apr 2007, 21:32
If J is divisible by 12 and 10, is J divisible by 24?

The official ManhattanGMAT answer: cannot be determined.

"If J is divisible by 12 and by 10, its prime factors are 2, 2, 3 and 5. Therefore, any integer that can be constructed as a produt of any of these integers is also a factor of J.

24= 2 x 2 x 2 x 3. There are only two 2's in the prime box; therefore, 24 is not necessarily a factor"

my question is, is this an error?

12 and 10 yields factors of 2,2,3,5,2. There are THREE 2s. Hence 24 is a factor.
 Kaplan Promo Code Knewton GMAT Discount Codes Veritas Prep GMAT Discount Codes
VP
Joined: 08 Jun 2005
Posts: 1147
Followers: 6

Kudos [?]: 126 [0], given: 0

Re: factors [#permalink]  22 Apr 2007, 21:45
bmwhype2 wrote:
If J is divisible by 12 and 10, is J divisible by 24?

The official ManhattanGMAT answer: cannot be determined.

"If J is divisible by 12 and by 10, its prime factors are 2, 2, 3 and 5. Therefore, any integer that can be constructed as a produt of any of these integers is also a factor of J.

24= 2 x 2 x 2 x 3. There are only two 2's in the prime box; therefore, 24 is not necessarily a factor"

my question is, is this an error?

12 and 10 yields factors of 2,2,3,5,2. There are THREE 2s. Hence 24 is a factor.

I don't think its a mistake

you have to look at 10 & 12 separately 10 = 2*5 and 12 = 3*2*2
together they have 2,2,2,3,5 but one of the 2 is repetitive number.

for example:

60 = 5*2*2*3

60/12 = 5

60/10 = 6

but 60/24 = 2.5 - all because the of the mutual 2 !

CEO
Joined: 21 Jan 2007
Posts: 2766
Location: New York City
Followers: 9

Kudos [?]: 331 [0], given: 4

Re: factors [#permalink]  22 Apr 2007, 22:13
KillerSquirrel wrote:
bmwhype2 wrote:
If J is divisible by 12 and 10, is J divisible by 24?

The official ManhattanGMAT answer: cannot be determined.

"If J is divisible by 12 and by 10, its prime factors are 2, 2, 3 and 5. Therefore, any integer that can be constructed as a produt of any of these integers is also a factor of J.

24= 2 x 2 x 2 x 3. There are only two 2's in the prime box; therefore, 24 is not necessarily a factor"

my question is, is this an error?

12 and 10 yields factors of 2,2,3,5,2. There are THREE 2s. Hence 24 is a factor.

I don't think its a mistake

you have to look at 10 & 12 separately 10 = 2*5 and 12 = 3*2*2
together they have 2,2,2,3,5 but one of the 2 is repetitive number.

for example:

60 = 5*2*2*3

60/12 = 5

60/10 = 6

but 60/24 = 2.5 - all because the of the mutual 2 !

thanks, i really appreciate the explanation.
Manager
Joined: 11 Nov 2006
Posts: 144
Followers: 1

Kudos [?]: 1 [0], given: 0

[#permalink]  22 Apr 2007, 22:13
If X is div by 12 then: X / (2^2 * 3) is an integer
If X is div by 10 then: X / (2 * 5) is an integer

The conclusion you can make is that X can be divided by 2^2 * 3 * 5 and still be an integer. If you factorize the number 24 = 2^3 * 3 you will notice the presence of 2^3 , so based on the conclusion drawn before you can not establish that X will be also divisible by 24.
Director
Joined: 29 Aug 2005
Posts: 879
Followers: 7

Kudos [?]: 190 [0], given: 7

Re: factors [#permalink]  22 Apr 2007, 23:58
bmwhype2 wrote:
If J is divisible by 12 and 10, is J divisible by 24?

12 = 2^2*3
10 =2*5

Smallest positive common multuple of these two numbers is 2^2*3*5=60
So, J can be 60, 120 and so on...

If J=60 ===> J/24 IS NOT integer
IF J=120 ===> J/24 = 5 - i.e. IS integer
Therefore, the answer is Yes and NO - i.e. can not be determined.
CEO
Joined: 21 Jan 2007
Posts: 2766
Location: New York City
Followers: 9

Kudos [?]: 331 [0], given: 4

Re: factors [#permalink]  13 May 2007, 08:51
botirvoy wrote:
bmwhype2 wrote:
If J is divisible by 12 and 10, is J divisible by 24?

12 = 2^2*3
10 =2*5

Smallest positive common multuple of these two numbers is 2^2*3*5=60
So, J can be 60, 120 and so on...

If J=60 ===> J/24 IS NOT integer
IF J=120 ===> J/24 = 5 - i.e. IS integer
Therefore, the answer is Yes and NO - i.e. can not be determined.

thanks. much easier to understand now.
Re: factors   [#permalink] 13 May 2007, 08:51
Similar topics Replies Last post
Similar
Topics:
4 Is J divisible by 24? 3 29 Aug 2012, 01:26
16 If j and k are positive integers, j - 2 is divisible by 4 11 17 Apr 2011, 10:43
7 Is the positive integer j divisible by a greater number of 8 03 Feb 2008, 13:51
If J is divisible by 12 and 10, is j divisible by 24 7 29 Sep 2007, 20:30
If j and k are positive integers, j 2 is divisible by 4 4 27 Sep 2005, 03:15
Display posts from previous: Sort by

# If J is divisible by 12 and 10, is J divisible by 24? The

 Question banks Downloads My Bookmarks Reviews Important topics

 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®.