Hi All,

We're told that a basketball team plays games only against the other five teams in its league and always in the following order: Croton, Darby, Englewood, Fiennes, and Garvin and the team’s FINAL game of the season is against Fiennes. We're asked which of the following answers COULD be the number of games in the team’s schedule.

To start, you should notice that the question asks for what COULD be the total number of games. This means that there are multiple answers to this question, so we have to keep working until we find one of those solutions among the 5 answer choices. There are a couple of different ways to approach this question, but you find the 'brute force' approach to be fastest/easiest.

The team begins with Croton (C) and ends with Fiennes (F), so it's possible that the team played: C, D, E, F = 4 games. That answer isn't among the choices, though, so the team has to continue playing games...

After playing C, D, E and F, the team then plays G.... and then continues on....

C, D, E and F. This is a total of 9 games. That answer isn't among the choices either, so the team keep playing.... You should note that the next 'cycle' of games will add another 5 games to the total, and then another 5 games and another 5 games, etc.

Thus, the total number of games played COULD be 4, 9, 14, 19, 24, 29, etc. (a positive integer that ends in a 4 or a 9). There's only one answer that matches.

Final Answer:

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Rich

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