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Divisibility and Prime Factoring

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Divisibility and Prime Factoring

by jerryragland » Mon May 10, 2010 6:05 pm
Source: MGMAT

If j is divisible by 12 and 10, is j divisible by 24?



Ans: [spoiler]CANNOT BE DETERMINED

Please explain. The explanation make sense but I could not generalize it and I have seen this specific problem types before and I always get it wrong.[/spoiler]
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by mchaubey » Mon May 10, 2010 6:41 pm
yes divisible by 12 and 10 thus 12 and 2*5 or 24 and 5
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by jerryragland » Mon May 10, 2010 6:55 pm
mchaubey wrote:yes divisible by 12 and 10 thus 12 and 2*5 or 24 and 5
No it's not.
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by debmalya_dutta » Mon May 10, 2010 7:29 pm
it is not necessarily divisible by 24
example being 60 which is divisible by 12 and by 10

j is always a multiple of 60 though because LCM of 12 & 10 is 60
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by liferocks » Mon May 10, 2010 7:42 pm
Here the thing to notice is the number which is divisible by both a and b has to be divisible by its LCM

in this case 12 and 10 has LCM of 60..so all the numbers divisible by 12 and 10 is a multiple of 60 ie 60,120,180...clearly all of these are not divisible by 24(60,180)..but some are(120)..so we cannot tell for sure whether the number under discussion is a multiple of 24
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by sanju09 » Tue May 11, 2010 3:25 am
jerryragland wrote:Source: MGMAT

If j is divisible by 12 and 10, is j divisible by 24?



Ans: [spoiler]CANNOT BE DETERMINED

Please explain. The explanation make sense but I could not generalize it and I have seen this specific problem types before and I always get it wrong.[/spoiler]
Which variety of GMAT question is this? PS or DS? It's neither I guess. But liferocks' explanation is perfect!
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by jerryragland » Tue May 11, 2010 4:52 am
sanju09 wrote:
jerryragland wrote:Source: MGMAT

If j is divisible by 12 and 10, is j divisible by 24?



Ans: [spoiler]CANNOT BE DETERMINED

Please explain. The explanation make sense but I could not generalize it and I have seen this specific problem types before and I always get it wrong.[/spoiler]
Which variety of GMAT question is this? PS or DS? It's neither I guess. But liferocks' explanation is perfect!
You are right.. it's neither.. just a plain question
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