Points $A, B, C$, and $D$ lie along a line, in that order. If $A B: A C=1: 5$, and $B C: C D=2: 1$, then the ratio $A B: C D$ is equal to
(A) $1: 1$
(B) $1: 2$
(C) $1: 3$
(D) $2: 5$
(E) $3: 5$

Part B: Each correct answer is worth 6.
Suppose that $A B=x$ for some $x>0$.

Since $A B: A C=1: 5$, then $A C=5 x$.

This means that $B C=A C-A B=5 x-x=4 x$.

Since $B C: C D=2: 1$ and $B C=4 x$, then $C D=2 x$.

![](https://cdn.mathpix.com/cropped/2024_04_20_33a8a6559d675f59baa2g-003.jpg?height=103&width=539&top_left_y=420&top_left_x=847)

Therefore, $A B: C D=x: 2 x=1: 2$.

ANSWER: (B)