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On the number line, point R has coordinate r

This topic has 1 expert reply and 0 member replies
jjjinapinch Senior | Next Rank: 100 Posts Default Avatar
Joined
24 Jul 2017
Posted:
83 messages

On the number line, point R has coordinate r

Post Mon Aug 07, 2017 9:12 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    On the number line, point R has coordinate r and point T has coordinate t. Is t < 0?

    (1) -1 < r < 0
    (2) The distance between R and T is equal to r²

    Official Guide question
    Answer: C

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    Post Mon Aug 07, 2017 3:58 pm
    Hi jjjinapinch,

    We're told that point R and point T are on a Number Line (as r and t, respectively). We're asked if t < 0. This is a YES/NO question. This question can be solved by TESTing VALUES.

    1) -1 < r < 0

    Fact 1 gives us a range of values for r, but tells us NOTHING about t.
    Fact 1 is INSUFFICIENT

    2) The distance between R and T is equal to r²

    IF.... r=1 and t=2, then the distance between them is 1^2 and the answer to the question is NO.
    IF.... r=2 and t = -2, then the distance between them is 2^2 and the answer to the question is YES.
    Fact 2 is INSUFFICIENT

    Combined, we know that -1 < r < 0 ... so.... 0 < r^2 < 1.
    Since we know that r is a NEGATIVE FRACTION, we can deduce that |r| > (r)^2. Since r is negative, this means that the distance between r and t will ALWAYS limit t to the 'negative side' of the Number Line (in basic terms, t can never get 'far enough away' from r to equal 0 or a positive). Thus, the answer to the question is ALWAYS YES.

    For example, if r = -1/2, then r^2 = +1/4.... so t would have to be either -3/4 or -1/4... and BOTH of those results yields a YES answer.
    Combined, SUFFICIENT

    Final Answer: C

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