Number Properties : Data Sufficiency

Number Properties is an all time favorite with the GMAT test makers. Especially in the DS avtar, number properties questions could be quite potent.

Here is a seemingly innocuous question from Number Properties presented as a DS question.

Question

Is ab positive?
(1) (a+b)^2 < (a-b)^2
(2) a = b

It is an “Is” question. So, the answer has to be a definite YES or a definite NO. It cannot be a MAYBE.

Let us evaluate statement 1.
a^2 + b^2 + 2ab < a^2 + b^2 - 2ab
Simplifying we get, 4ab < 0 or ab < 0.
So, we can convincingly answer that ab is not positive. So, statement 1 is sufficient to answer the question.

The correct answer is either A or D.

Now let us evaluate the statement 2. This is actually the statement that could trick you.

a = b.
So, either both a and b or positive or both a and b are negative. In either case ab is positive.
We will certainly be “tempted” to decide that statement 2 is also sufficient.
The catch is that, both a and b could be 0. In that case ab = 0, which is not positive.
As we are not able to conclude if ab is positive or not with statement 2, it is not sufficient.

So, choice A is the correct answer.