If x and y are positive integers such that x < y and z=x/y, which of the following must be true?
I. z<(x − 1)/y
II. z<(x − 1)/(y − 1)
III. z>(x + 1)/(y + 1)
Answers:
A) I only	B) I and II	C) II and III	D) II only	E) None of these
x &lt; y --&gt; Let x = 2 and y = 3 --&gt; z = 2/3   I. z&lt;(x − 1)/y --&gt; 2/3 &lt; 1/3 --&gt; False   II. z&lt;(x − 1)/(y − 1) --&gt; 2/3 &lt; 1/2 --&gt; False   III. z&gt;(x + 1)/(y + 1) --&gt; 2/3 &gt; 3/4 --&gt; False   Answer: None of these
<result>E</result>
If x and y are positive integers such that x < y and z=x/y, which of the following must be true?
I. z<(x − 1)/y
II. z<(x − 1)/(y − 1)
III. z>(x + 1)/(y + 1)