MGMAT Number Properties Book:

by **MGMAT Reader** Thu Jul 31, 2008 11:48 am

Hello Stacey / Ron:

On Page 78: x^3-3x^2.....

The statement B says x=2(z+1)

Put z=0 and the number is just even and yet not divisible by 4.

Now I did read a statement by Stacey that 0 was divisible by 4 in one of the earlier statements. Is it safe to assume then for all future references that if the equation shows divisibility of 0 by any integer just ignore it?

Could you please explain this a bit further? Shouldnt the question be read as: X is an even integer not = 2.

Thanks!

by **esledge** Mon Sep 15, 2008 5:07 pm

Zero is divisible by any non-zero integer. List some multiples to see why this makes sense.

Positive multiples of 4: 4, 8, 12, 16, 20, etc. (adjacent terms differ by 4)
Negative multiples of 4: -4, -8, -12, -16, -20, etc. (adjacent terms differ by 4)

But the difference between -4 and 4 is 8, thus violating the pattern. Zero is a multiple of 4 because it is 4 more than the next lower multiple, and 4 less than the next higher multiple...Same as any other multiple of 4.

Also, 0/4 = 0 = integer, which is the requirement for divisibility.