Question 54
In a game of Riemannian ball two teams face each other; at every moment, each team fields $k \gt 1$ players. At the end of each play a point is awarded to one of the two teams; moreover, each team may make an arbitrary number of substitutions before the next play begins. Alice and Barbara are members of the Geodesics team. At the end of today's game, Alice observes that, while she was on the field, the Geodesics won 7 more plays than they lost. When Barbara was on the field, on the other hand, they lost 2 more plays than they won. Each of the other Geodesics players took part in as many winning plays as losing ones. What is the value of $k$?
(A) 3
(B) 5
(C) 6
(D) 9
(E) The data are not sufficient to determine it.
(A) 3
(B) 5
(C) 6
(D) 9
(E) The data are not sufficient to determine it.