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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. If the team’s final game of the season is against Fiennes, which of the following could be the number of games in the team’s schedule?

Re: A basketball team plays games only against the other five teams in its [#permalink]

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12 Dec 2015, 01:53

My answer is B.\ Let "A" as the initial team which have to play against with Croton (C), Darby (D), Englewood (E), Fiennes (F), and Garvin (G); According to the question, we have a column as below Game 1st 2nd 3rd 4th 5th (Or final game) A A A A A C D E G F (fixed) There are 4! ways to arrange a game with A - or 24 ways. -----> B is a correct answer.

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. If the team’s final game of the season is against Fiennes, which of the following could be the number of games in the team’s schedule?

A. 18 B. 24 C. 56 D. 72 E. 81

Matches will continue to happen in cycles of 5

so the total number of matches should be a multiple of 5 +4 form i.e. 5x+4 form

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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. If the team’s final game of the season is against Fiennes, which of the following could be the number of games in the team’s schedule?

A. 18 B. 24 C. 56 D. 72 E. 81

We are given that a team plays the following teams in the following order:

Croton, Darby, Englewood, Fiennes, and Garvin.

Thus, we see that we have a repeating pattern of 5 teams or 5n, in which n is a positive integer.

Since the final game is played against Fiennes, the number of games will have to be equal to 5n + 4.

Of the answer choices, the only number that can equal 5n + 4, in which n is a positive integer, is answer choices B. (Notice that if 5n + 4 = 24, then n = 4.)

Answer: B
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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.