
Ratio problem.
Ok, here is the problem.
Let A,B and C be three points in a plane such that AB:BC = 3:5. Which of the following can be the ratio AB:AC ?
I : 1:2
II : 1:3
III : 3:8
Your choices for the answer are:
(A) I only
(B) II only
(C) III only
(D) I and III only
(E) I, II and III
I tried it and my answer was (C). But unfortunately that's not the correct answer. So, someone please help me with this.

Because the ratio of AB to BC is 3 to 5, we can take our unit of measurement to such that AB is 3 and BC is 5. Let C be some other point in the plane and let "x" be the distance from A to C. C can lie anywhere on the circle of radius 5 with center B. That circle crosses the line through A and B twice and those mark the shortest and longest possible distance from B to C. When the circle crosses the line on the other side of B from A, the distance from B to C is 5 3= 2 and when it crosses the line on the other side of A from B, the distance from B to C is 5+ 3= 8. The ratio of AB to AC must be between 3/8 and 3/2.

HallsofIvy:
Ok, I understood that the ratio must lie between 3/8 and 3/2. So, your choice is (E) ? Because all the three given ratios lies between 3/8 and 3/2.
But according to the book (BARRON'S SAT) from where I took this question, the answer is (D). I don't know how they got this. Or whether I'm doing some mistake in the middle.

Hello, el33t!
is possible.
The three points can be placed like this:
Code:
o C
* *
6 * *
* * 5
* *
* *
A o * * * o B
3
is possible.
The three points can be placed like this:
Code:
:      8      :
ooo
A  3  B   5   C
But is not possible.
Code:
:       9       : ?
ooo
A  3  B   5   C

Thanks both of you for your answers. Doubt cleared.