joyseychow wrote:If x is an integer and sqrt(x) * x - x = a , 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
[spoiler]IMO is C. If I simplify equation sqrt(x) * x - x = a -----> x[sqrt(x) -1]=a, then am I right to say that
x=a or [sqrt(x) -1]=a. Hence shouldn't a be an integer since a=x??? I'm confuse...
OA is E.[/spoiler]
We have an integer x, such that x √x - x = a.
Take example-numbers with the intent of denying a statement in all the "must be true" kind of questions on GMAT.
I. We do not assign terms like even/odd with the irrationals, x = 2, 3, 5... leave a as a complex irrational, so NO.
II. It is certain that x is a non-negative integer, otherwise GMAT would not have put that under '√'. When x =1, a = 0; sufficient reason to deny II.
III. An irrational is not an integer, see I, and deny III.
All denied
[spoiler]
E[/spoiler]