A city is hosting a table tennis tournament for its residents. Each

Question

A city is hosting a table tennis tournament for its residents. Each team has exactly two players, and each player is on exactly one team. In each round, each team plays exactly one other team and either wins or loses. The winning team advances to the next round and the losing team is eliminated. No team or player drops out except by losing a game. The tournament is in progress, and exactly 512 players participated in the first round.

From the available options, select a number of tournament rounds and a number of teams such that after the specified number of rounds there will be the specified number of teams remaining in the tournament. Make only two selections, one in each column.

ID: 100389

Sajjad1994 · Accepted Answer

Official Explanation https://gmatclub.com/forum/download/file.php?mode=view&id=61216 OE.jpg

Apt0810 · Answer

So here initially total number of teams are 512/2= 256

So in round 1 256/2 = 128 matches will be played since after each of these 128 matches the loosing team will be eliminated so remaining would be 128

Subsequently in round 2- 128/2 = 64 matches will be played

in round 3- 64/2 = 32 matches will be played

in round 4- 32/2 = 16 matches will be played

So after round 4, 16 teams will be remaining

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yashikaaggarwal · Answer

We have 512 participants to be paired under a team of two who will play one match with the opposition team and losing team will be eliminated.

512 players = 256 teams (2*256=512)
One team is playing with other then 128teams vs. 128teams (1st round)
128 matches were played in first round.

Now, 128 losing teams are eliminated after first round.
So 128 teams will be divided in pair of 64 teams to play against each other.
64 vs. 64 (2nd round)
Similarly,
32 vs. 32 (3rd round)
16 vs. 16 (4th round)
8 vs. 8 (5th round)... And so on.

Now we have no. 2 4 8 16 32
=> Let say 32 teams were remaining, but 32 are remaining After 3rd round.
So 32 can't be the remaining team.
=> Let say 2 teams were remaining but 2 were remaining after 7th round which is also not an option.
=> Similarly if you put values in other combinations, you will find only 16 teams were remaining after 4th round. (The possible combination)

So the answer is 4th round and 16 teams.

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mrfrantic · Answer

After reading the question stem multiple times, I'm still not getting what we have to calculate as the words are little bit confusing to me. Can anyone please explain?

Arut · Answer

Initial setup:
We start with 512 players.
Each team has 2 players.
So, we begin with 512 ÷ 2 = 256 teams.

How the tournament progresses:
In each round, teams play against each other.
Half of the teams win and advance, while the other half lose and are eliminated.
This means that after each round, the number of teams is cut in half.

Let's follow the progression:
Start: 256 teams
After Round 1: 256 ÷ 2 = 128 teams
After Round 2: 128 ÷ 2 = 64 teams
After Round 3: 64 ÷ 2 = 32 teams
After Round 4: 32 ÷ 2 = 16 teams

Why 4 rounds and 16 teams is the answer:
After 4 rounds, we have exactly 16 teams left.
This matches perfectly with the options given in the question.

Checking other options:
After 2 rounds, we'd have 64 teams (not in the options).
After 8 rounds, we'd have only 1 team left (not in the options).

Verification:
The question asks for a number of rounds and a number of teams that match.
4 rounds and 16 teams is the only pair from the given options that correctly describes a stage in this tournament.
Remember, in each round, half the teams are eliminated. So the number of teams follows a pattern of division by 2: 256, 128, 64, 32, 16, 8, 4, 2, 1. The pair "4 rounds" and "16 teams" is the only one from the options that fits this pattern.

Ans from Perplexity

kanikaa9 · Answer

Once you read 512 and each team has exactly 2 players and each player is in exactly one team.. know that it is related to powers of 2.

Now coming to the question, just list the number of rounds and # of teams in each round. 
Eg: 1st Round - 256 teams
2nd round - 128 teams
3rd - 64 teams
4th - 32 teams
5th - 16 teams
...
8th - 2 teams

The ques asks after the specified round choose how many teams will be remaining,  only 4 and 16 works ... so after 4th round 16 teams remain.
 DON'T make the mistake of choosing 32.

GMATCoachBen · Answer

Bunuel

Suggested question edit: there is a typo "playler".

Thanks!

GMATCoachBen · Answer

Well said, this is a great example of the importance of  always reading carefully and double checking exactly what variable/group/subset/units we are talking about.

We start with 512   players  , but the question asks for the number of   teams.   We must divide by 2 players per team, to convert the units from players to teams.

A lot of people miss this step of dividing 512 by 2, and then they choose 32 here for the number of teams.

Sajjad1994 · Answer

Fixed. Thank you!

Teams remaining	Rounds completed	Statements
		2
		4
		8
		16
		32

A city is hosting a table tennis tournament for its residents. Each

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A city is hosting a table tennis tournament for its residents. Each

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