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.