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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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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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95% (hard)

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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B
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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


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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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