SOLUTION: If X, Y are non-zero integers and X/Y < |X/Y| < Y, which of the following must be true? I. X is negative II. Y is positive III. X/Y is negative (A) I only (B) II only (C)

Algebra ->  Inequalities -> SOLUTION: If X, Y are non-zero integers and X/Y < |X/Y| < Y, which of the following must be true? I. X is negative II. Y is positive III. X/Y is negative (A) I only (B) II only (C)      Log On


   

Question 1201950: If X, Y are non-zero integers and X/Y < |X/Y| < Y, which of the following must be true?
I. X is negative
II. Y is positive
III. X/Y is negative
(A) I only
(B) II only
(C) III only
(D) II and III only
(E) I, II and III
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


|X/Y| is non-negative; so if |X/Y| < Y, Y must be positive. So II is true.

If X/Y < |X/Y|, then X/Y must be negative. Then, since Y is positive, X must be negative. So I is true.

And since X must be negative and Y must be positive, X/Y must be negative. So III is true.

ANSWER: (E) I, II, and III must all be true