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In a cricket championship, there were 120 matches played. Every two te

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Bunuel
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In a cricket championship, there were 120 matches played. Every two te [#permalink] New post   12 Mar 2021, 03:15
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A
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25% (medium)

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78% (01:44) correct 22% (02:02) wrong based on 67 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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Re: In a cricket championship, there were 120 matches played. Every two te [#permalink] New post   24 Mar 2021, 06:28
Bunuel wrote:
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


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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Re: In a cricket championship, there were 120 matches played. Every two te [#permalink] New post   28 Mar 2021, 09:13
120 = (x^2 - x)/2 Alternative approach
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Re: In a cricket championship, there were 120 matches played. Every two te [#permalink] New post   30 Mar 2021, 07:10
Expert Reply
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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Re: In a cricket championship, there were 120 matches played. Every two te [#permalink] New post   27 Apr 2022, 04:27
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Re: In a cricket championship, there were 120 matches played. Every two te [#permalink]
27 Apr 2022, 04:27
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