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SVP
Joined: 21 Jan 2007
Posts: 2351
Location: New York City

If J is divisible by 12 and 10, is J divisible by 24? The
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22 Apr 2007, 22:32
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. == Message from the GMAT Club Team == THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION. This discussion does not meet community quality standards. It has been retired. If you would like to discuss this question please repost it in the respective forum. Thank you! To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative  Verbal Please note  we may remove posts that do not follow our posting guidelines. Thank you.



VP
Joined: 08 Jun 2005
Posts: 1059

Re: factors
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22 Apr 2007, 22:45
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 !



SVP
Joined: 21 Jan 2007
Posts: 2351
Location: New York City

Re: factors
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22 Apr 2007, 23:13
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: 116

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: 693

Re: factors
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23 Apr 2007, 00:58
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.



SVP
Joined: 21 Jan 2007
Posts: 2351
Location: New York City

Re: factors
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13 May 2007, 09:51
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. == Message from the GMAT Club Team == THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION. This discussion does not meet community quality standards. It has been retired. If you would like to discuss this question please repost it in the respective forum. Thank you! To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative  Verbal Please note  we may remove posts that do not follow our posting guidelines. Thank you.



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Joined: 09 Sep 2013
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Re: If J is divisible by 12 and 10, is J divisible by 24? The
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21 Oct 2018, 00:04
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Re: If J is divisible by 12 and 10, is J divisible by 24? The
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