gmatgambler wrote:

If x is a positive number and a=√x∗x−x, which of the following must be true?

I. a is even

II. a is positive

III. a is an integer

A)I only

B)II only

C)III only

D)I and II

E) None of the above

Also, let me point out how we arrive at the numbers that we should try here. Given x is a positive number and \(a =\sqrt{x}*x - x\).

\(\sqrt{x}\) makes us think of perfect squares. We try to put in a perfect square such as 4 and see that all conditions are met.

So now we need to think of the cases when the condition may not be met.

Let's figure out whether a must be positive.

\(\sqrt{x}\) is positive and x is positive but for a to be positive, \(\sqrt{x}*x\) MUST be greater than x. Will \(\sqrt{x}*x\) be less than x in any case? It will be if \(\sqrt{x}\) is less than 1 i.e. a fraction. So this leads us to x = 1/4. We must try this value. When x = 1/4, we see that a is not positive, is not an integer and hence the question of even or odd doesn't arise.

Answer (E)

_________________

Karishma

Veritas Prep GMAT Instructor

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