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)

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Karishma

Veritas Prep GMAT Instructor

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