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Bunuel
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Given
    • In a cricket championship, there were 120 matches played.
    • Every two teams played one match with each other.

To find
    • The number of teams participating in the championship.

Approach and Working out
For 1 match, 2 teams are needed.
So, total number of matches= total number of ways of selecting 2 teams = nc2 = n(n-1)/2
    • n(n-1)/2 = 120
    • n(n-1) = 240
\(n^2\) - n -240 =0

    • \(n^2\) -16n +15n -240 = 0
    • n(n-16) +15(n-16) = 0
    • (n + 15) (n - 16) = 0
    • n= 16, -15 (We reject –15 as number of matches cannot be negative)
      o n=16

Hence, option D is the correct answer.

Correct Answer: Option D
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Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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