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# If X is divisible by 2,6,9,12,15,30, is X divisible by 8?

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If X is divisible by 2,6,9,12,15,30, is X divisible by 8? [#permalink]

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12 Dec 2012, 12:28
If X is divisible by 2,6,9,12,15,30, is X divisible by 8?

The easiest method to arriving at an answer?
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Re: If X is divisible by 2,6,9,12,15,30, is X divisible by 8? [#permalink]

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12 Dec 2012, 22:39
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laythesmack23 wrote:
If X is divisible by 2,6,9,12,15,30, is X divisible by 8?

The easiest method to arriving at an answer?

Findout factors and derive unique combination of it. But that should be done only for very complicated numbers. For small numbers u can just observe:

For the given question.. we have 8 => 2^3
None of the given choices can give u a multiple of 2^3. So ans is No.

To find out how to use it, If the question has asked 18 then? factors, 18 = 2 * 3^3
We have 2 which gives 2^1 and 9 which gives 3^3. Hence Ans would have been Yes.
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Re: If X is divisible by 2,6,9,12,15,30, is X divisible by 8? [#permalink]

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13 Dec 2012, 10:54
I didnt get the point

We can see a multiple of 8 too!

12 = 4 X 3
2 is already there. so we do have 2^3 right?

Vips0000 wrote:
laythesmack23 wrote:
If X is divisible by 2,6,9,12,15,30, is X divisible by 8?

The easiest method to arriving at an answer?

Findout factors and derive unique combination of it. But that should be done only for very complicated numbers. For small numbers u can just observe:

For the given question.. we have 8 => 2^3
None of the given choices can give u a multiple of 2^3. So ans is No.

To find out how to use it, If the question has asked 18 then? factors, 18 = 2 * 3^3
We have 2 which gives 2^1 and 9 which gives 3^3. Hence Ans would have been Yes.
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Re: If X is divisible by 2,6,9,12,15,30, is X divisible by 8? [#permalink]

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13 Dec 2012, 18:10
ambitiousgal wrote:
I didnt get the point

We can see a multiple of 8 too!

12 = 4 X 3
2 is already there. so we do have 2^3 right?

No..
12 = 2^2 * 3^1
2 = 2^1
in both 2 and 12 there is one common 2.
When u need to find out if a number A is divisible by number B, you need to be able to ascertain that all the factors of B are in A.
So if a number X is divisible by 12 and 2, you know that X has atleast 2^2 and 3^1 (For it to be divisible) it can guarantee that X will be divisible by 2, 4, 6, 12. Beyond this, this information can not give anything else.
eg. consider that X =12. It is divisible by 12 and 2 but not by 8.
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Re: If X is divisible by 2,6,9,12,15,30, is X divisible by 8? [#permalink]

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19 Feb 2013, 23:14
I'll say NO.
Take for ex 180. It is divisible by all 2,6,9,12,15,30.......... but not divisible by 8.
So, as 2,6,9,12,15,30 does not have a multiple of 8, there LCM is not divisible by 8
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Re: If X is divisible by 2,6,9,12,15,30, is X divisible by 8? [#permalink]

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20 Feb 2013, 19:38
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Expert's post
somalwar wrote:
I'll say NO.
Take for ex 180. It is divisible by all 2,6,9,12,15,30.......... but not divisible by 8.
So, as 2,6,9,12,15,30 does not have a multiple of 8, there LCM is not divisible by 8

Technically, it is incorrect to say 'No'.
The answer to the question is 'Cannot say/May be'

Looking at the factors, we do not see any which has an 8 in it so we cannot say that X must have 8 as a factor.
But, there is nothing to say that it is not divisible by 8 in addition to all the factors given above.

i.e. X can be 180 (as you pointed out) and X can also be 360 (in which case it is divisible by 8)
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If X is divisible by 2,6,9,12,15,30, is X divisible by 8? [#permalink]

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22 Jul 2014, 18:31
If X is divisible by 2,6,9,12,15,30, is X divisible by 8?

.
.
2=2
6=3*2
9=3*3
12=3*2*2
15=3*5
30=2*3*5

The least possible value of X is X=2*2*3*3*5 (Not divisible by 8).
However, a greater value of X could be X=2*2*2*3*3*5 (divisible by 8)
If X is divisible by 2,6,9,12,15,30, is X divisible by 8?   [#permalink] 22 Jul 2014, 18:31
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