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OG 13 Problem

This topic has 1 member reply
oquiella Master | Next Rank: 500 Posts Default Avatar
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OG 13 Problem

Post Tue Dec 22, 2015 3:08 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    If K is an integer and 2
    A. One
    B. Two
    C. Three
    D. Four
    E. Five

    Answer: A


    Why please explain your reasoning

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    Top Member

    Post Tue Dec 22, 2015 10:47 pm
    Quote:
    If K is an integer and 2 < k < 7, for how many different values of k is there a triangle with sides of lengths 2,7, and k?

    A. One
    B. Two
    C. Three
    D. Four
    E. Five
    For three line segments to work as a triangle, the lengths of any two of the segments have to add up to a sum greater than the length of the third. Otherwise two sides will not be long enough to connect with each other and with the ends of the third side.

    The integers k such that 2 < k < 7 are 3, 4, 5 and 6.

    See how many of those could form a triangle with sides 2, 7, and k.

    If the lengths of the three segments were 2, 7 and 3, the segments 2 and 3 long would not be long enough to connect with each other and with the ends of the segment 7 long to form a triangle.

    2 + 4 < 7 Doesn't work.

    2 + 5 = 7 The only way to connect all the ends is to put them together flat. That's not a triangle.

    2 + 6 > 7 -- 7 + 2 > 6 -- 7 + 6 > 2 That works.

    So only K = 6 works and the correct answer is A.

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