Carcass wrote:

If B is the midpoint of line segment AD and C is the midpoint of line segment BD, what is the value of \(\frac{AB}{AC}\) ?

(A) \(\frac{3}{4}\)

(B) \(\frac{2}{3}\)

(C) \(\frac{1}{2}\)

(D) \(\frac{1}{3}\)

(E) \(\frac{1}{4}\)

Let AD be 10 i.e AB = 5 and BD = 5 (AD = AB + BD as B is mid point)

Now C is midpoint for BD, BD = BC + CD.

As per our values BD = 5 then BC = 2.5 and CD = 2.5

\(\frac{AB}{AC}\)

=> \(\frac{5}{5 + 2.5}\) ( Note : AC = AB + BC )

=> \(\frac{5}{7.5}\)

=> \(\frac{1}{1.5}\)

=> \(\frac{1}{(3/2)}\)

=> 2/3.

Ans B