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Math Help - logic problem

  1. #1
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    logic problem

    There are 4 boys , P,Q,R,S. If P is taller than R and Q is taller than S and P is shorter than Q and R is shorter than S, then if we arranged the boys in order of height from smallest to largest, only one of the statement is true:

    a)R is shorter than S who is shorter than P who is shorter than Q
    b)R is shorter than S who is shorter than Q who is shorter than P
    c)R is shorter than P who is shorter than Q who is shorter than S
    d)there is not enough information to tell
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  2. #2
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    Quote Originally Posted by kl050196 View Post
    There are 4 boys , P,Q,R,S. If P is taller than R and Q is taller than S and P is shorter than Q and R is shorter than S, then if we arranged the boys in order of height from smallest to largest, only one of the statement is true:

    a)R is shorter than S who is shorter than P who is shorter than Q
    b)R is shorter than S who is shorter than Q who is shorter than P
    c)R is shorter than P who is shorter than Q who is shorter than S
    d)there is not enough information to tell
    You are given the following relationships:

    . . . . .P > R
    . . . . .Q > S
    . . . . .P < Q
    . . . . .R < S

    Since Q > P and P > R, then Q > P > R. Since S > R and P > R, and since Q > P > R, then you have three of four that are greater than R. So which must be the least?

    Since Q > P > R and Q > S > R, then Q is shown as being greater than three of four. Which much be the greatest?

    Is there any way to tell which of P and S is the greater?
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