MGMAT-Num Properties: 0 as a multiple

[Genie]

Hi,
I bought the whole set of books from MGMAT, and I must say they are very thorough and comprehensive.
During my study of the Math Number Properties, I figured that at some of the places, 0 was not considered a multiple while at other places, 0 was considered as a multiple (both in case of divisibility rule problems). Is there a specific pattern that we should follow or is one preferred over the other? Should we consider 0 as a multiple of not?

Genie

[gmatkid]

Hi,
I bought the whole set of books from MGMAT, and I must say they are very thorough and comprehensive.
During my study of the Math Number Properties, I figured that at some of the places, 0 was not considered a multiple while at other places, 0 was considered as a multiple (both in case of divisibility rule problems). Is there a specific pattern that we should follow or is one preferred over the other? Should we consider 0 as a multiple of not?

Genie

Hi Genie,

Good question! I had to do some research online, and here's the answer:

Zero IS a multiple of every integer (0 = 0 x any integer). However, the reason you sometimes include 0 as a multiple for GMAT questions and sometimes don't is because the question will probably specify the TYPE of multiple(s) they're looking for.

For example, if the question says "positive multiples of 3", then you would NOT include 0 as a multiple because, while 0 is a multiple of 3, it is not POSITIVE (0 is neither positive nor negative). But if the question said "even multiples of 3", then you WOULD include 0 because 0 is considered even and it is a multiple of 3 (3 x 0 = 0).

However, be careful NOT to include 0 when you're finding the Least Common Multiple (LCM) of two integers. This is because LCM is defined as the lowest POSITIVE integer that is a multiple of both integers.

Hope this helps...I certainly learned a lot!

[RonPurewal]

this has been addressed here (see last post)