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# If J is divisible by 12 and 10, is j divisible by 24

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CEO
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If J is divisible by 12 and 10, is j divisible by 24 [#permalink]  29 Sep 2007, 20:30
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If J is divisible by 12 and 10, is j divisible by 24?
Director
Joined: 03 May 2007
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Re: PS ManhattanGMAT page 17 #5 [#permalink]  29 Sep 2007, 20:41
bmwhype2 wrote:
If J is divisible by 12 and 10, is j divisible by 24?

E. could be or could not be. if j = 60, then no. if j = 120 or its multiple, yes.
CEO
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Re: PS ManhattanGMAT page 17 #5 [#permalink]  29 Sep 2007, 21:05
Fistail wrote:
bmwhype2 wrote:
If J is divisible by 12 and 10, is j divisible by 24?

E. could be or could not be. if j = 60, then no. if j = 120 or its multiple, yes.

let's break it down

j is divisible by 12: prime factors are 2,2,3
j is divisible by 10: prime factors are 2,5
therefore, the factors of j are: 2,2,2,3,5

is J divisible by 24?
factors of 24: 2,2,2,3

therefore 24 is a prime factor of j

the prime factors match up. i see it from your approach and my approach. pls advise. thanks
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Re: PS ManhattanGMAT page 17 #5 [#permalink]  29 Sep 2007, 21:41
bmwhype2 wrote:
Fistail wrote:
bmwhype2 wrote:
If J is divisible by 12 and 10, is j divisible by 24?

E. could be or could not be. if j = 60, then no. if j = 120 or its multiple, yes.

let's break it down

j is divisible by 12: prime factors are 2,2,3
j is divisible by 10: prime factors are 2,5
therefore, the factors of j are: 2,2,2,3,5
is J divisible by 24?
factors of 24: 2,2,2,3

therefore 24 is a prime factor of j

the prime factors match up. i see it from your approach and my approach. pls advise. thanks

you do not know the red part. you can only say that factors of j are: 2, 2, 3, and 5 not 2, 2, 2, 3, and 5.

if we know 2, 2, 2, 3, and 5 were factors of j, most of gmatters' life would be much easier and most them join Goldman Sacs, Blackstone Group, and Citigroup private equity.

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Re: PS ManhattanGMAT page 17 #5 [#permalink]  29 Sep 2007, 21:43
bmwhype2 wrote:
Fistail wrote:
bmwhype2 wrote:
If J is divisible by 12 and 10, is j divisible by 24?

E. could be or could not be. if j = 60, then no. if j = 120 or its multiple, yes.

let's break it down

j is divisible by 12: prime factors are 2,2,3
j is divisible by 10: prime factors are 2,5
therefore, the factors of j are: 2,2,2,3,5

is J divisible by 24?
factors of 24: 2,2,2,3

therefore 24 is a prime factor of j

the prime factors match up. i see it from your approach and my approach. pls advise. thanks

When you are trying to get the factors of J , you need to include all the factors in the bigger number (which is 12 and hence 2 2 and 3) and the only the ones in the smaller one which are not already accommodated in the bigger number. So that leaves only 5 with us. So the factors of J at the minimum would be 2 2 3 5.
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Kudos [?]: 349 [0], given: 4

Re: PS ManhattanGMAT page 17 #5 [#permalink]  30 Sep 2007, 15:10
carpeD wrote:
bmwhype2 wrote:
Fistail wrote:
bmwhype2 wrote:
If J is divisible by 12 and 10, is j divisible by 24?

E. could be or could not be. if j = 60, then no. if j = 120 or its multiple, yes.

let's break it down

j is divisible by 12: prime factors are 2,2,3
j is divisible by 10: prime factors are 2,5
therefore, the factors of j are: 2,2,2,3,5

is J divisible by 24?
factors of 24: 2,2,2,3

therefore 24 is a prime factor of j

the prime factors match up. i see it from your approach and my approach. pls advise. thanks

When you are trying to get the factors of J , you need to include all the factors in the bigger number (which is 12 and hence 2 2 and 3) and the only the ones in the smaller one which are not already accommodated in the bigger number. So that leaves only 5 with us. So the factors of J at the minimum would be 2 2 3 5.

Thanks.
What does this concept fall under?
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LCM of 12 and 10 = 60. So J is a multiple of 60. If J = 60, then J is not divisible by 24. If J = 240, then J is divisible by 4.

If this is a DS statement, then the answer is insufficient.
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ywilfred wrote:
LCM of 12 and 10 = 60. So J is a multiple of 60. If J = 60, then J is not divisible by 24. If J = 240, then J is divisible by 24.

If this is a DS statement, then the answer is insufficient.

thanks. your post of multiples clarified it tremendously.
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