I guess even without picking any numbers we can solve for this question.
Given y and x are both negative. Also the questions is a must be true type. Hence if we can prove even one case wherein the inequality fails we can eliminate the option.
(A)x/y> xy -- Both L.H.S and R.H.S will become +ve since x, y both are -ve. Also since x is farther away from -1 than y, it means x/y will be a always lesser than xy. Eliminated.
(B) y/x> x + y -- L.H.S is always +ve and R.H.S is always -ve. This is the correct option.
(C)y/x> xy -- L.H.S and R.H.S is +ve. However y/x will be always less than xy.
(D)y/x< x + y -- L.H.S is always +ve and R.H.S is always -ve. Eliminated.
(E)y/x>x/y -- Since x is farther away from -1 and y y/x will be always less than x/y. Both L.H.S and R.H.S is +ve.
Answer B.
"The will-to-do achieves the deed, when the mind that wills is strong indeed"
