Math problem: is there something wrong?

akacharlie

Hi,
maybe somebody can help me with that one, that was given to me at a gmat prep course. My guess is that none of the answers are correct, maybe I am wrong but at least I'd like to know why:

In a sports league, ten team are divided into two divisions, with five teams playing in each division. If each team much play each other team in its own division exactly three times, and each team not in its division exactly once, how many games will be scheduled for the entire league?

A) 40
B) 55
C) 80
D) 145
E) 265

I personnaly found 85, as well as some other student of the course. One student found 145 (D) but I think some of the games were counted twice.

This is how I have proceeded:

1) count the number of games within one division:

let say that we have teams

A : plays 3 games vs each of B, C, D, E = 12
B : plays 3 games vs each of C, D, E since 3games vs A has already been counted = 9
C : plays 3 games vs D and E (games vs A and B have been counted) = 6
D : plays 3 games vs E = 3
E : has already played 3 games against each other team

total for one division = 12 + 9 + 6 + 3 = 30

=> total for 2 division in terms of intra games = 30 x 2 = 60

2) now lets count inter division games :
each team plays each other exactly once

A plays 5 game as wel as B, C, D, E = 25
We don't need to x2 because the other teams games are counted in those games

Tot = 60 + 25 = 85

Thanks for your help guys

gabriel