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

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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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?

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 ­

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.