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Bunuel
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In a cricket championship, there were 120 matches played. Every two te 12 Mar 2021, 03:15
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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35% (medium)

Question Stats:

70% (01:40) correct 30% (02:15) wrong based on 84 sessions

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In a cricket championship, there were 120 matches played. Every two teams played one match with each other. The number of teams participating in the championship is


(A) 19
(B) 18
(C) 17
(D) 16
(E) 15
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D
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stne
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In a cricket championship, there were 120 matches played. Every two te 24 Mar 2021, 06:28
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Bunuel
In a cricket championship, there were 120 matches played. Every two teams played one match with each other. The number of teams participating in the championship is


(A) 19
(B) 18
(C) 17
(D) 16
(E) 15
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Basically we are given \(n_{C_2} = 120\)

\(\frac{n!}{2!* (n-2)! } =120\)

\(\frac{n * n-1}{2} =120\)

\(n* ( n-1) =240\)

Solving for \(n \)

\(n= 16\)

Ans-D

Hope it's clear.
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In a cricket championship, there were 120 matches played. Every two te 28 Mar 2021, 09:13
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120 = (x^2 - x)/2 Alternative approach
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In a cricket championship, there were 120 matches played. Every two te 30 Mar 2021, 07:10
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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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In a cricket championship, there were 120 matches played. Every two te 27 Apr 2022, 04:27
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