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Math Help - Ratio problem.

  1. #1
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    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.
    Last edited by el33t; August 14th 2010 at 04:31 AM.
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  2. #2
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    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.
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  3. #3
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    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.
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  4. #4
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    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} \\<br />
(B) & \text{II only} \\ (C) & \text{III only} \\ (D)& \text{ I and III only} & \Leftarrow \\<br />
(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
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  5. #5
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    Thanks both of you for your answers. Doubt cleared.
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