Number Properties

[ksahaitham]

Hi, I just started preparing for the GMAT exam today and began with Number Properties. While answering the questions for chapter 1, I was faced with a question that i'm not sure about its answer in the book. The question is number (5) which states the folloing:

If J is divisible by 12 and 10, is J divisible be 24?

my answer was yes but the book said it cannot be determind as the prime factors include 2,2,3 and 5 while 24 = 2x2x2x3

my answer was based on the following:

thr prime factors for 12 is: 2,2,3. the prime factors for 10 is: 2,5. So, the prime factors for J is: 2,2,2,3,5 which can construct 24!

Can anyone tell me if my conclusion is right or wrong?

Many Thanks in Advance,

Haitham

[Pradeep]

It is given that the number is divisible by 12 (2,2,3) and 10 (2,5). So the prime factorisation of the given number includes at least two 2s, a 3 and a 5.

A number will be divisible by 24 (2,2,2,3) if prime factorisation of the number includes at least three 2s and a 3; and that is why the answer is "can not be determined".

[Guest]

It is given that the number is divisible by 12 (2,2,3) and 10 (2,5). So the prime factorisation of the given number includes at least two 2s, a 3 and a 5.

A number will be divisible by 24 (2,2,2,3) if prime factorisation of the number includes at least three 2s and a 3; and that is why the answer is "can not be determined".

[Guest]

It is given that the number is divisible by 12 (2,2,3) and 10 (2,5). So the prime factorisation of the given number includes at least two 2s, a 3 and a 5.

A number will be divisible by 24 (2,2,2,3) if prime factorisation of the number includes at least three 2s and a 3; and that is why the answer is "can not be determined".

[ksahaitham]

Thanks a lot Pradeep

it is clear for me know, and number 60 made it clearer

I appreciate your help

[esledge]

Yes, thanks for the nice explanation Pradeep.

Take-away: watch out for overlap between the factors in the prime boxes.

[afvatcha]

Im sorry but I still don't get it. I think I understand the question, essentially what is the prime box for a number divisible by (atleast 10 and 12) and from the prime box can you make 24. After looking at the answer it's obvios that it cannot be determined.

MY QUESTION, if anyone can help me is what are the rules for setting up a mutual prime box when you have two seperate prime boxes?

[ahistegt]

The same question is discussed here as well:
http://www.manhattangmat.com/forums/hol ... t2210.html

[afvatcha]

Thanks for pointing me in the right direction!!!

[JonathanSchneider]

: )