Here, when we set up a comparison between the two quantities

|xy|-x ? xy

-xy-x. ? xy

…

-1 ? 2y

How can we write |xy| = -xy : this was an explanation from powerprep II

Answer is D

Here, when we set up a comparison between the two quantities

|xy|-x ? xy

-xy-x. ? xy

…

-1 ? 2y

How can we write |xy| = -xy : this was an explanation from powerprep II

Answer is D

|xy| is always going to be negative here, This is as per rules of Abs Value/Modulus so we can say that |xy| equals -xy.

so we have

-xy-x and xy

add xy to both sides

-x and 2xy

both values will always be negative, however we cant say anything about relative greatness of them since y can be just anything. hence D

I used plugging of random numbers:

CASE 1: Let x = 3, y = -0.1

A = |(3)(-0.1)| - 3 = 0.3 - 3 = -2.7

B = (3)(-0.1) = -0.3

Hence, A < B

CASE 2: Let x = 3, y = -4

A = |(3)(-4)| - 3 = 12 - 3 = 9

B = (3)(-4) = - 12

Hence, A > B

Since both cases contradict each other, the correct option should be D, i.e we cannot determine the relationship from the given information.