Quant Exam > Quant Questions > In a chess tournament every person played one...
Start Learning for Free
In a chess tournament every person played one game with every other person in the group. The total number of games that men played between themselves exceeded those played by men with women by 18. If there were 4 women in the tournament, in all how many games were played in the tournament?
- a)114
- b)66
- c)78
- d)120
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
In a chess tournament every person played one game with every other pe...
MC2 - MC1 wC1 = 18, where M and W are the number of men and women respectively.
Most Upvoted Answer
In a chess tournament every person played one game with every other pe...
Problem Analysis:
We are given that every person played one game with every other person in the group. We need to find the total number of games played in the tournament when the total number of games that men played between themselves exceeded those played by men with women by 18.
Given:
- Total number of women in the tournament = 4
To find:
- The total number of games played in the tournament
Solution:
Let's assume there are 'n' people in the tournament.
- The number of games played by each person = (n-1)
- Total number of games played in the tournament = nC2 (combination of 'n' people taken 2 at a time)
As per the given condition, the total number of games that men played between themselves exceeded those played by men with women by 18.
Let's assume the number of men in the tournament = 'm'. Then the number of women in the tournament = (n-m).
- Number of games played between men = mC2
- Number of games played between men and women = m*(n-m)
- Given, mC2 - m*(n-m) = 18
Simplifying the above expression, we get:
mC2 - m*n + m^2 + 18 = 0
mC2 = (nC2 - m*n) + 18
Substituting the value of nC2 in terms of 'n':
mC2 = (n*(n-1)/2 - m*n) + 18
2mC2 = n*(n-1) - 2m*n + 36
2mC2 = n*(n-2m+1) + 36
As per the given condition, there are 4 women in the tournament.
Hence, the number of men = n-4
Substituting this value in the above equation, we get:
2(mC2) = (n-4)*(n-2m+5) + 36
We know that the total number of games played in the tournament = nC2
Substituting the value of nC2 in terms of 'n':
2(mC2) = n*(n-1) - 4*(n-4) - 2m*n + 10m + 36
2(mC2) = n^2 - 2mn + 10m - 4
n^2 - 2mn + 10m - 4 - 2(mC2) = 0
We can solve this equation to get the value of 'n'.
n = [2m + sqrt(4m^2 - 40m + 36 + 8mC2)] / 2
n = m + sqrt(m^2 - 10m + 9 + 2mC2)
We know that 'n' is an integer, hence we need to find the value of 'm' such that the above expression gives an integer value for 'n'.
As 'm' increases, the value of 'n' also increases. We can try different values of 'm' to find the smallest possible value of 'm' that gives an integer value for 'n'.
Trying different values of 'm', we get:
- For m = 10, n = 20
- For m = 11, n =
We are given that every person played one game with every other person in the group. We need to find the total number of games played in the tournament when the total number of games that men played between themselves exceeded those played by men with women by 18.
Given:
- Total number of women in the tournament = 4
To find:
- The total number of games played in the tournament
Solution:
Let's assume there are 'n' people in the tournament.
- The number of games played by each person = (n-1)
- Total number of games played in the tournament = nC2 (combination of 'n' people taken 2 at a time)
As per the given condition, the total number of games that men played between themselves exceeded those played by men with women by 18.
Let's assume the number of men in the tournament = 'm'. Then the number of women in the tournament = (n-m).
- Number of games played between men = mC2
- Number of games played between men and women = m*(n-m)
- Given, mC2 - m*(n-m) = 18
Simplifying the above expression, we get:
mC2 - m*n + m^2 + 18 = 0
mC2 = (nC2 - m*n) + 18
Substituting the value of nC2 in terms of 'n':
mC2 = (n*(n-1)/2 - m*n) + 18
2mC2 = n*(n-1) - 2m*n + 36
2mC2 = n*(n-2m+1) + 36
As per the given condition, there are 4 women in the tournament.
Hence, the number of men = n-4
Substituting this value in the above equation, we get:
2(mC2) = (n-4)*(n-2m+5) + 36
We know that the total number of games played in the tournament = nC2
Substituting the value of nC2 in terms of 'n':
2(mC2) = n*(n-1) - 4*(n-4) - 2m*n + 10m + 36
2(mC2) = n^2 - 2mn + 10m - 4
n^2 - 2mn + 10m - 4 - 2(mC2) = 0
We can solve this equation to get the value of 'n'.
n = [2m + sqrt(4m^2 - 40m + 36 + 8mC2)] / 2
n = m + sqrt(m^2 - 10m + 9 + 2mC2)
We know that 'n' is an integer, hence we need to find the value of 'm' such that the above expression gives an integer value for 'n'.
As 'm' increases, the value of 'n' also increases. We can try different values of 'm' to find the smallest possible value of 'm' that gives an integer value for 'n'.
Trying different values of 'm', we get:
- For m = 10, n = 20
- For m = 11, n =
|
Explore Courses for Quant exam
|
|
Similar Quant Doubts
In a chess tournament every person played one game with every other person in the group. The total number of games that men played between themselves exceeded those played by men with women by 18. If there were 4 women in the tournament, in all how many games were played in the tournament?a)114b)66c)78d)120Correct answer is option 'D'. Can you explain this answer?
Question Description
In a chess tournament every person played one game with every other person in the group. The total number of games that men played between themselves exceeded those played by men with women by 18. If there were 4 women in the tournament, in all how many games were played in the tournament?a)114b)66c)78d)120Correct answer is option 'D'. Can you explain this answer? for Quant 2025 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about In a chess tournament every person played one game with every other person in the group. The total number of games that men played between themselves exceeded those played by men with women by 18. If there were 4 women in the tournament, in all how many games were played in the tournament?a)114b)66c)78d)120Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a chess tournament every person played one game with every other person in the group. The total number of games that men played between themselves exceeded those played by men with women by 18. If there were 4 women in the tournament, in all how many games were played in the tournament?a)114b)66c)78d)120Correct answer is option 'D'. Can you explain this answer?.
In a chess tournament every person played one game with every other person in the group. The total number of games that men played between themselves exceeded those played by men with women by 18. If there were 4 women in the tournament, in all how many games were played in the tournament?a)114b)66c)78d)120Correct answer is option 'D'. Can you explain this answer? for Quant 2025 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about In a chess tournament every person played one game with every other person in the group. The total number of games that men played between themselves exceeded those played by men with women by 18. If there were 4 women in the tournament, in all how many games were played in the tournament?a)114b)66c)78d)120Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a chess tournament every person played one game with every other person in the group. The total number of games that men played between themselves exceeded those played by men with women by 18. If there were 4 women in the tournament, in all how many games were played in the tournament?a)114b)66c)78d)120Correct answer is option 'D'. Can you explain this answer?.
Solutions for In a chess tournament every person played one game with every other person in the group. The total number of games that men played between themselves exceeded those played by men with women by 18. If there were 4 women in the tournament, in all how many games were played in the tournament?a)114b)66c)78d)120Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Quant.
Download more important topics, notes, lectures and mock test series for Quant Exam by signing up for free.
Here you can find the meaning of In a chess tournament every person played one game with every other person in the group. The total number of games that men played between themselves exceeded those played by men with women by 18. If there were 4 women in the tournament, in all how many games were played in the tournament?a)114b)66c)78d)120Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
In a chess tournament every person played one game with every other person in the group. The total number of games that men played between themselves exceeded those played by men with women by 18. If there were 4 women in the tournament, in all how many games were played in the tournament?a)114b)66c)78d)120Correct answer is option 'D'. Can you explain this answer?, a detailed solution for In a chess tournament every person played one game with every other person in the group. The total number of games that men played between themselves exceeded those played by men with women by 18. If there were 4 women in the tournament, in all how many games were played in the tournament?a)114b)66c)78d)120Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of In a chess tournament every person played one game with every other person in the group. The total number of games that men played between themselves exceeded those played by men with women by 18. If there were 4 women in the tournament, in all how many games were played in the tournament?a)114b)66c)78d)120Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice In a chess tournament every person played one game with every other person in the group. The total number of games that men played between themselves exceeded those played by men with women by 18. If there were 4 women in the tournament, in all how many games were played in the tournament?a)114b)66c)78d)120Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice Quant tests.
|
|
Explore Courses for Quant exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup