JEE Main 2014 · 19 Apr · Shift 1 · Mathematics Q66

← JEE Main 2014 · 19 Apr · Shift 1

MathematicsSingle correct+4 / -1Question 66 of 90

Two women and some men participated in a chess tournament in which every participant played two games with each of the other participants. If the number of games that the men played between them-selves exceeds the number of games that the men played with the women by 66, then the number of men who participated in the tournament lies in the interval :

[8, 9]

[10, 12)

(11, 13]

(14, 17)

Answer and worked solution

Official answer: B

With $m$ men:

games among the men: $2\binom m2=m(m-1)$ ;
games between men and women: $2\times2m=4m$ .

$m(m-1)-4m=66$ gives $m^2-5m-66=0$ , so $m=11$ , which lies in $[10,12)$ .

Topics:Combinations

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JEE Main 2014 · 19 Apr · Shift 1, Mathematics question 66