If a, b, c and d are positive integers and a/b < c/d, which of the following must be true?
I. (a+c)/(b+d) < c/d
II. (a+c)/(b+d) < a/b
III. (a+c)/(b+d) = a/b +c/d Choose the correct answer:	A) None	B) I only	C) II only	D) I and II	E) I and III
If a, b, c and d are positive integers and a/b &lt; c/d, which of the following must be true?   Since the numbers are positive we can safely cross-multiply. So, we are given that ad&lt;bcad&lt;bc.   I. a+cb+d&lt;cda+cb+d&lt;cd = ad+cd&lt;bc+cd   ad+cd&lt;bc+cd= cdcd cancels out: ad&lt;bc. This is given to be true.   II. a+cb+d&lt;aba+cb+d&lt;ab = ab+bc&lt;ab+adab+bc&lt;ab+ad= ab   ab cancels out: bc&lt;ad bc&lt;ad. Opposite what is given, thus this option is not true.   III. a+cb+d=ab+cda+cb+d=ab+cd. From I we already know that a+cb+d&lt;cda+cb+d&lt;cd, thus when we add a positive value (abab) to (cdcd)we make the right hand side even bigger.Thus a+cb+d=ab+cda+cb+d=ab+cd cannot be true.   Answer: I only.
<result>B</result>
If a, b, c and d are positive integers and a/b < c/d, which of the following must be true?
I. (a+c)/(b+d) < c/d
II. (a+c)/(b+d) < a/b
III. (a+c)/(b+d) = a/b +c/d