Problem Solving

If x < y < -1, which of the following must be true?

(A)x/y> xy (B) y/x> x + y (C)y/x> xy (D)y/x< x + y (E)y/x>x/y

Pick numbers and substitute for x and y.
[spoiler](B) y/x> x + y[/spoiler]

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.