Bunuel wrote:
For all numbers a and b, the operation @ is defined by a@b = a^2 - ab. If xy ≠ 0, then which of the following can be equal to zero?
I. x@y
II. (xy)@y
III. x@(x + y)
A. II only
B. I and II only
C. I and III only
D. II and III only
E. All of the above
Kudos for a correct solution.
a@b = a^2 - ab = a(a-b)
x and y both are not 0.
I. x@y
x@y = x(x - y)
This will be 0 when either x = 0 (not possible as given), or x - y = 0 i.e. x = y (this is possible)
II. (xy)@y
(xy)@y = xy(xy - y) = xy^2(x - 1)
This will be 0 when either x or y is 0 (not possible) or x = 1 (this is possible)
III. x@(x + y)
x@(x + y) = x(x - (x+y)) = -xy
This will be 0 when at least one of x and y is 0 - (both not possible as given)
Hence only (I) and (II) can be 0. Answer (B)
_________________
Karishma
Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >