Hi VJesus12,

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: B

GMAT assassins aren't born, they're made,
Rich

VJesus12 wrote: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 choice B. (Notice that if 5n + 4 = 24, then n = 4.)

Answer: B

VJesus12 wrote: ↑

Sun Oct 15, 2017 5:33 pm

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

The OA is B.

Is there a short way to get the correct answer?

We are assuming that the first game must be played against Croton; otherwise each of the given numbers is a possible number of games (for instance, if the first game is played against Darby; then the 18th game will be against Fiennes).

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 choice B. (Notice that if 5n + 4 = 24, then n = 4.)

Answer: B