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chess

Expert replies
by shashank.ism » Tue Feb 09, 2010 7:15 am
N girls and 2N boys played a chess tournament. Every player played every other player exactly once. The boys won 7/5 times as many matches as the girls (and there were no draws). Then which among the following is definitely false? (Assume 1 point for a win and 0 for a loss)

a Boys pocketed prime number of points against girls
b Girls always won twice or more matches than boys won against them
c The sum of the scores of top 3 individual players was not between 25 and 33
d The sum of the scores of top 3 individual players was 69
e none of these
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Source: — Problem Solving |

by harsh.champ » Tue Feb 09, 2010 2:21 pm
shashank.ism wrote:N girls and 2N boys played a chess tournament. Every player played every other player exactly once. The boys won 7/5 times as many matches as the girls (and there were no draws). Then which among the following is definitely false? (Assume 1 point for a win and 0 for a loss)

a Boys pocketed prime number of points against girls
b Girls always won twice or more matches than boys won against them
c The sum of the scores of top 3 individual players was not between 25 and 33
d The sum of the scores of top 3 individual players was 69
e none of these
total no. of matches = (3N) C 2 . [total no. of points = 3N C 2]
let the girls have won x matches. (x points )
the boys have won 7/5 x matches. (7/5 x points)

By logic, b is definitely false.
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