actleader wrote:

Is the integer m an even number?

(1) |m| = -m

(2) (m)(m - 1)(m + 2) = 0

I'm happy to help with this.

Statement #1 is equivalent to the statement that m =< 0, that m is zero or a negative number. For more explanation of this, see this blog post:

http://magoosh.com/gmat/2012/gmat-math- ... -of-minus/We know from this that m is zero or negative, but not necessarily even or odd, so this statement, alone and by itself, is

not sufficient.

Statement #2: We solve this with the Zero Product Property.

The ZPP says:

If A*B = 0, then A = 0 or B = 0Notice that, in this statement, the word "or" is no garnish, but rather an essential piece of mathematical equipment.

By extension,

If A*B*C = 0, then A = 0 or B = 0 or C = 0.Here, we have:

(m)(m - 1)(m + 2) = 0

===> m = 0 OR (m - 1) = 0 OR (m + 2) = 0

===> m = 0 OR m = +1 or m = -2

From this statement, m could be any of these three, so it could be even or odd. This statement, alone and by itself, is

not sufficient.

Combined statementsWe look at our set from the second statement, m = {0, +1, -2}, and because of the constraint of the first statement, we know m must be zero or negative, so we can keep 0 and -2, but we have to exclude +1. Now we are down to m = {0, -2}. We don't know which one m equals, but since both of them are even, we now definitively know that m is even. Thus, combined, the statements are

sufficient.

Answer =

CDoes all this make sense?

Mike

_________________

Mike McGarry

Magoosh Test Prep