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False proof way to solve number property questions like

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False proof way to solve number property questions like [#permalink]  09 Jan 2013, 20:42
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Question Stats:

50% (01:25) correct 50% (00:34) wrong based on 12 sessions
What is the false proof way of solving questions like, 'If j is divisible by 12 and 10, is j divisible by 24?'
(a) Yes
(b) No
(c) Cannot be determined

How I happened to solve this question is:
2,2,3 are factors of 12.
2,5 are factors of 10.

Since 24 is 8*3 which can be formed from above factors of 12 and 10(as per factor foundation rule), j is divisible by 24.

But, the answer is 'Cannot be determined', since he rightly shows that if j=60 then 60 is not divisible by 24, where as it is divisible by 12, 10.
Thus, can anyone show me a false proof procedure(without falling into any traps as above), to solve the above type of questions?
[Reveal] Spoiler: OA

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Re: False proof way to solve number property questions like [#permalink]  09 Jan 2013, 21:05
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As j is divisible by 12 &10, you will need to find the LCM(12,10) and check if 24 is factor of that LCM.

In this case LCM(12,10) = 60 and 24 is not factor of 60 -> Hence j is not always divisible by 24. (Hence answer -> cannot be determined)

Lets take another example, say K is divisible by 30 & 8 -> LCM(30,8)=120 -> 24 is factor of 120 -> Hence K is always divisible by 24.
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Re: False proof way to solve number property questions like [#permalink]  09 Jan 2013, 21:13
PraPon wrote:
As j is divisible by 12 &10, you will need to find the LCM(12,10) and check if 24 is factor of that LCM.

In this case LCM(12,10) = 60 and 24 is not factor of 60 -> Hence j is not always divisible by 24. (Hence answer -> cannot be determined)

Lets take another example, say K is divisible by 30 & 8 -> LCM(30,8)=120 -> 24 is factor of 120 -> Hence K is always divisible by 24.

Solid answer. Something I was looking for. Kudos!
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Re: False proof way to solve number property questions like   [#permalink] 09 Jan 2013, 21:13
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