Number Properties: Chapter 1 # 5

by **Khalid** Fri Nov 21, 2008 2:40 pm

I am tripping on this one. Think the answer is wrong. Thanks for yoru help

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

12 = 2x2x3
10 = 2x5

24= 2x2x2x3

Between 12 and 10, I have 3 2's and a 3

So shouldn't the answer be Yes.

Or am I wrong in counting the extra 2.

Thanks

by **Caveman** Sun Nov 23, 2008 5:30 am

The smallest number which will satisfy this is LCM of 12 and 10 which is 60. Clearly not divisible by 24. This is because factors of 12 have two 2's and 10 has only single. But for 24 we need three 2's. Hence we need an additional 2.

Using this, 60 x 2 = 120, which is not divisible by 24.

by **Joey Z.** Fri Dec 05, 2008 9:16 pm

"Between 12 and 10, I have 3 2's and a 3"

Here you got it wrong, you are double-counting the 2 that is a factor of BOTH 12 and 10.

To be divisible by 24, a number has to be divisible by 8 and 3. The 3 here is guaranteed because j is divisible by 12, which equals 4*3. That j is divisible by 10 doesn't help in this question, because it only reveals further that j is divisible by 5, NOTHING ELSE.

If, however, it is given that j is divisible by 12 and 16 (or 40, or 56, etc.), then the answer would be yes.

by **JonathanSchneider** Sun Dec 07, 2008 12:05 pm

Khalid, a lot of people get tripped up on this. It's the GMAT's favorite divisibility trick.
Nice work Joey and Caveman on the explanation!