If \(a, b, c\) and \(d\) are positive integers and \(\dfrac{a}{b} < \dfrac{c}{d},\) which of the following must be true?

If \(a, b, c\) and \(d\) are positive integers and \(\dfrac{a}{b} < \dfrac{c}{d},\) which of the following must be true?

I. \(\dfrac{a+c}{b+d} < \dfrac{c}{d}\)

II. \(\dfrac{a+c}{b+d} < \dfrac{a}{b}\)

III. \(\dfrac{a+c}{b+d} = \dfrac{a}{b} + \dfrac{c}{d}\)

A. None
B. I only
C. II only
D. I and II
E. I and III

Answer: B

Source: GMAT Prep