# Math Help - Ratio problem.

1. ## 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

(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.

2. 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.

3. 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.

4. Hello, el33t!

Let $A,B,C$ be three points in a plane such that: . $AB:BC \:=\: 3:5$

Which of the following can be the ratio $AB:AC$ ?

. . $\text{(I) }\;1\!:\!2 \qquad \text{(II) }\;1\!:\!3 \qquad \text{(III) }\;3\!:\!8$

The answer choices are:

. . $\begin{array}{ccc}(A) & \text{I only} \\
(B) & \text{II only} \\ (C) & \text{III only} \\ (D)& \text{ I and III only} & \Leftarrow \\
(E) & \text{I, II and III} \end{array}$

$\text{(I)}\;1\!:\!2$ is possible.

The three points can be placed like this:

Code:
                        o C
* *
6   *   *
*     * 5
*       *
*         *
A o  *  *  *  o B
3

$\text{(III)}\:3\!:\!5$ is possible.

The three points can be placed like this:

Code:
      : - - - - - 8 - - - - - :
o---------o-------------o
A  - 3 -  B  - - 5 - -  C

But $\text{(II)}\:1\!:\!3$ is not possible.

Code:
      : - - - - - - 9 - - - - - - : ?
o---------o-------------o
A  - 3 -  B  - - 5 - -  C

5. Thanks both of you for your answers. Doubt cleared.