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Bunuel
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Teams A and B play in a basketball tournament. The first team to win 18 Nov 2020, 01:11
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Question Stats:

44% (02:33) correct 56% (02:11) wrong based on 110 sessions

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Teams A and B play in a basketball tournament. The first team to win two games in a row or a total of four games wins the tournament. What is the number of ways the tournament can occur?

(A) 13
(B) 14
(C) 15
(D) 16
(E) 17


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Bunuel
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Teams A and B play in a basketball tournament. The first team to win 18 Nov 2020, 01:14
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Bunuel
Teams A and B play in a basketball tournament. The first team to win two games in a row or a total of four games wins the tournament. What is the number of ways the tournament can occur?

(A) 13
(B) 14
(C) 15
(D) 16
(E) 17


Are You Up For the Challenge: 700 Level Questions
Show more

Similar questions:
https://gmatclub.com/forum/teams-a-and- ... 39630.html
https://gmatclub.com/forum/teams-a-and- ... 39631.html
https://gmatclub.com/forum/teams-a-and- ... 39633.html
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abhik1502
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Teams A and B play in a basketball tournament. The first team to win 25 Nov 2020, 07:07
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Pls suggest the solution
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Fdambro294
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Teams A and B play in a basketball tournament. The first team to win 25 Nov 2020, 10:18
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I’d love to see an algebraic Solution.

Since the numbers were reasonable, I “brute forced” the problem and luckily caught on to a pattern.

Rules:

win 2 in a row it is over

win 4 total it is over.


Start with the easiest scenario: 2 games

A - A
or
B - B


They could also play 3 games:

A - B - B
or
B - A - A


We can also have them play 4 games:

A - B - A - A
or
B - A - B - B


Since once we get 2 wins in a row the tournament ends, we can do 2 ways each for:

5 games
A - B - A - B - B
or
B - A - B - A - A


And 6 games
A - B - A - B - A - A
or
B - A - B - A - B - B


The tricky part is realizing there is 4 ways for the tournament to be played for 7 total games

Option 1: no team wins 2 in a row and the team who wins 1st ends up as the 4th win

A - B - A - B - A - B - A
or
B - A - B - A - B - A - B


Option 2: the team that wins 2nd, goes on to win the last 2 games for a total of 4

A - B - A - B -A - B - B
or
B - A - B - A - B - A - A


There are 14 ways the tournament can be played.

(B)

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Teams A and B play in a basketball tournament. The first team to win 25 Nov 2020, 21:17
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Fdambro294
I’d love to see an algebraic Solution.

Since the numbers were reasonable, I “brute forced” the problem and luckily caught on to a pattern.

Rules:

win 2 in a row it is over

win 4 total it is over.


Start with the easiest scenario: 2 games

A - A
or
B - B


They could also play 3 games:

A - B - B
or
B - A - A


We can also have them play 4 games:

A - B - A - A
or
B - A - B - B


Since once we get 2 wins in a row the tournament ends, we can do 2 ways each for:

5 games
A - B - A - B - B
or
B - A - B - A - A


And 6 games
A - B - A - B - A - A
or
B - A - B - A - B - B


The tricky part is realizing there is 4 ways for the tournament to be played for 7 total games

Option 1: no team wins 2 in a row and the team who wins 1st ends up as the 4th win

A - B - A - B - A - B - A
or
B - A - B - A - B - A - B


Option 2: the team that wins 2nd, goes on to win the last 2 games for a total of 4

A - B - A - B -A - B - B
or
B - A - B - A - B - A - A


There are 14 ways the tournament can be played.

(B)

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I followed the same approach but missed the last part about 7 games and got 12 as the answer. Now I know why.
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Regor60
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Teams A and B play in a basketball tournament. The first team to win 12 Mar 2023, 06:20
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Bunuel
Teams A and B play in a basketball tournament. The first team to win two games in a row or a total of four games wins the tournament. What is the number of ways the tournament can occur?

(A) 13
(B) 14
(C) 15
(D) 16
(E) 17


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If time is a consideration, since a given pattern of winning is available to each team means an even number of total ways, the answer choices can be reduced to just two

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Teams A and B play in a basketball tournament. The first team to win 21 May 2024, 12:15
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