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

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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.

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 !

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 !

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.