Confuse with Number Properties problems! Help!!!

[samnguyenfl]

Hi, I just started to study for GMAT and using Manhattan GMAT 4th edition and already get confuse by some of the questions and answers in the book. So if anyone could help I would be really appreciated. Thanks.
Here is the problem:
On the very 1st problem of the problem set it said: If a is divided by 7 or by 18, an integer results. Is a/42 an integer? and the answer that the book provide is Yes because prime factor of 7 and 18 are: 2,3,3,7. Therefore, any integer that can be constructed as a product of any of these prime factors is also a factor of a. And prime factors of 42 are: 2,3,7.

Now, on problem number 5 the question asked: If j is divisible by 12, and by 10, is j divisible by 24? The answer that the book give to this problem is Cannot Be Determine because Primes of 10 and 12 are: 2,2,3,5 and primes of 24 are: 2,2,2,3. And since there are only two 2's in the prime box of 10&12 while 24 has three 2's therefore, 24 is not necessarily a factor of j.

I got confused because the 2 question pretty much asking the same thing but give 2 different answers: and on the first question prime factors of 42 are 2,3,7 while prime factor of 7 and 18 are 2,3,3,7 witch mean there is only one 3 in the prime box of 42 while there is two 3's in the prime box of 7&18. And if we base on answer to question 5 then the answer for question 1 should also be Cannot be Determined isn't?

Thanks.

[CurtisVincentBorns]

On the first problem you only need one 3 to make 42 you do not need two. So from the prime factors of 7 and 18: 2,3,3,7 you have a 2, a 3, and a 7 that you need. 2x3x7= 42

On the second problem you need three 2's to make 24. From the prime factors of 10 and 12 you have: 2,2,3,5. You need to make sure that you don't count an extra 2 because the same 2 that could be used to make 10 could also be used to make that 12. With that being said the only prime factors that you know for sure are 2,2,3,5. Thus you do not know for certain if that third 2 is in the prime factors for j and you do not know if 24 is a factor.

[tim]

thanks; let us know if there are any further questions on this one..