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PSAT abstract inequality question.

  1. Oct 1, 2011 #1

    ElijahRockers

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    Gold Member

    p<q, r<s, and r<q.

    Which of the following statements must be true?

    I. p<s
    II. s<q
    III. r<p

    The correct answer could be either one statement, a combination of statements, or none of the statements. Came accross this question while helping some highschool students prepare for their SATs and I'm embarassed to say it stumped me.
     
  2. jcsd
  3. Oct 1, 2011 #2

    Mentallic

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    Try drawing an unlabelled number line, and place 4 points on the line. For the first, p<s, let's assume that p>s. Since for the first two criteria p<q and r<s, this means that the only way the order can fit is if it's r,s,p,q, and since the last criteria r<q holds as well, that means we've found a scenario where p is not less than s, so I. is not necessarily true.
     
  4. Oct 1, 2011 #3

    ElijahRockers

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    Yea, I pretty much came to the conclusion that none of the three statements are necessarily true.
     
  5. Oct 1, 2011 #4

    Mentallic

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    Yep, precisely.
     
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