what is the prime box approch?

by **yamini** Tue Sep 25, 2007 1:03 pm

I did not find any information regarding this prime box in the 2006 manhatton GMAT books.

by **RonPurewal** Mon Oct 01, 2007 5:40 am

I haven't seen the 2006 books (I was just hired on recently, and so I've only seen the 2007 books), but, if the prime box is in there, it should be in the Number Properties volume.

The 'prime box' is a box in which you list all the prime factors known to be contained in a given number.
For a known number, this is a cinch: just list all the prime factors of the number. for instance, the prime box for the number 24 would contain 2, 2, 2, 3 (because 24 = 2 x 2 x 2 x 3).
The real value in the prime box comes in when it's used for an UNKNOWN. For instance, let's say that X is a common multiple of both 14 and 21. Since X is a multiple of each of these numbers, then X must contain all of the prime factors of both numbers. Therefore, the prime box for X contains:
a 2 and a 7 (because of 14), and
a 3 and a 7 (because of 21).
Therefore, the prime box for X contains at least a 2, a 3, and a 7. (Notice that it doesn't have to contain two 7's, although it certainly could.)

That's the basics.