If a, b, c and d are positive integers and a/b < c/d, which of the following must be true?

[BTGmoderatorDC]

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

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


OA B

Source: GMAT Prep

[Scott@TargetTestPrep]

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

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


OA B

Source: GMAT Prep

Let’s analyze inequalities in the given Roman numerals. That is, if we can simplify them to the inequality in the given problem, then they are true. Otherwise, they are not.

I. (a + c)/(b + d) < c/d

d(a + c) < c(b + d)

ad + cd < bc + cd

ad < bc

Dividing both sides by bd, we have:

a/b < c/d

We see that I is true.

II. (a+c)/(b+d) < a/b

b(a + c) < a(b + d)

ab + bc < ab + ad

bc < ad

Dividing both sides by bd, we have:

c/d < a/b

We see that II is not true.

III. (a+c)/(b+d) = a/b + c/d

Notice that this is an equation, not an inequality, and in general, this is not true regardless of whether a/b < c/d.

Answer: B