We can either try to apply some number sense or simply test some values.

I have a feeling the latter might be faster.

If |a/b| and |x/y| are reciprocals, AND (a/b)(x/y) < 0, then it could be the case that: a = 1, b = 1, x = 1 and y = -1

Now check out the choices....

A. $(1)(1) < 0$ NOT TRUE

B. $\frac{1}{1} (\frac{1}{-1}) < -1$ NOT TRUE

C. $\frac{1}{1} < 1$ NOT TRUE

D. $\frac{1}{1} = \frac{-(-1)}{1}$ TRUE!

E. $\frac{-1}{1} > \frac{1}{1}$ NOT TRUE

Answer: D

Cheers,
Brent