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by shankar.ashwin » Mon Nov 07, 2011 11:42 pm
A tennis tournament is conducted in which 100 girls participate. Each of them plays an opponent and the winner is progressed to the next round. If in any round there are odd number of participants, the girl with highest ranking gets a wild card and is automatically progressed to the next round. This is repeated until there is a clear winner of the tournament. How many matches are held in the tournament? (Assume no two girls have the same ranking and no match ends in a tie)

A) 50
B) 97
C) 99
D) 100
E) 200
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by rijul007 » Tue Nov 08, 2011 12:58 am
No of girls ----- No of matches ----- Wild card

100------------50----------------------0
50-------------25----------------------0
25-------------12----------------------1
13-------------6-----------------------1
7--------------3-----------------------1
4--------------2-----------------------0
2--------------1------------------------


Total no of matches = 50+25+12+6+3+2+1 = 99

Option C
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by neelgandham » Tue Nov 08, 2011 1:12 am
A step by step explanation for the benefit of the Quant-haters :-)

The total number of girls who participated in the tournament is 100

First Round - 50 Girls play 50 Opponents in 50 matches leaving 50 winners
Number of matches played in the first round = 50
Number of players who progressed to the next round = 50

Second Round - 25 Girls play 25 Opponents in 25 matches leaving 25 winners
Number of matches played in the first round = 25
Number of players who progress to the next round = 25

Third Round - 12 Girls play 12 Opponents in 12 matches leaving 12+1 winners (As the number of participants is odd - 25,the girl with highest ranking gets a wild card and is automatically progressed to the next round)
Number of matches played in the first round = 12
Number of players who progress to the next round = 13

Fourth Round - 6 Girls play 6 Opponents in 6 matches leaving 6+1 winners (As the number of participants is odd - 13,the girl with highest ranking gets a wild card and is automatically progressed to the next round)
Number of matches played in the first round = 6
Number of players who progress to the next round = 7

Fifth Round - 3 Girls play 3 Opponents in 3 matches leaving 3+1 winners (As the number of participants is odd - 13,the girl with highest ranking gets a wild card and is automatically progressed to the next round)
Number of matches played in the first round = 3
Number of players who progress to the next round = 4

Sixth Round - 2 Girls play 2 Opponents in 2 matches leaving 2 winners
Number of matches played in the first round = 2
Number of players who progress to the next round = 2

Seventh Round - 1 Girl plays 1 Opponent in 1 match leaving 1 winner
Number of matches played in the first round = 1
Number of players who progress to the next round = 1

Total number of matches played in the tournament = 1 + 2 + 3 + 6 + 12 + 25 + 50 = 99

IMO C
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by shankar.ashwin » Tue Nov 08, 2011 2:10 am
The OA is 99

Not sure if this is helpful, but there's a pattern here.

2 people - 1 match
3 people - 2 matches
4 people - 3 matches
5 people - 4 matches.

100 people - 99 matches.
'N' people - (N-1) matches.
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by satishchandra » Tue Nov 08, 2011 3:39 am
shankar.ashwin wrote: If in any round there are odd number of participants
Odd number in every group can not be maintained.
In first round 100 members (Not an odd number)
In last round 2 members (Not an odd number)
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by shankar.ashwin » Tue Nov 08, 2011 3:52 am
Sir, don't quite get your question.
satishchandra wrote:
shankar.ashwin wrote: If in any round there are odd number of participants
Odd number in every group can not be maintained.
In first round 100 members (Not an odd number)
In last round 2 members (Not an odd number)
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by user123321 » Tue Nov 08, 2011 4:06 am
50+25+12+6+3+2+1 = 99

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by satishchandra » Tue Nov 08, 2011 5:15 am
shankar.ashwin wrote:A tennis tournament is conducted in which 100 girls participate. Each of them plays an opponent and the winner is progressed to the next round. If in any round there are odd number of participants, the girl with highest ranking gets a wild card and is automatically progressed to the next round. This is repeated until there is a clear winner of the tournament. How many matches are held in the tournament? (Assume no two girls have the same ranking and no match ends in a tie)

A) 50
B) 97
C) 99
D) 100
E) 200
As per the question,
The condition is that Every round has odd number of participants.
However, first and last rounds do not contain odd number of participants.
In first round 100 members (Not an odd number)
In last round 2 members (Not an odd number)
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by shankar.ashwin » Tue Nov 08, 2011 5:19 am
I think it clearly states ''If in any round" and not "In every round"
satishchandra wrote:
shankar.ashwin wrote:A tennis tournament is conducted in which 100 girls participate. Each of them plays an opponent and the winner is progressed to the next round. If in any round there are odd number of participants, the girl with highest ranking gets a wild card and is automatically progressed to the next round. This is repeated until there is a clear winner of the tournament. How many matches are held in the tournament? (Assume no two girls have the same ranking and no match ends in a tie)

A) 50
B) 97
C) 99
D) 100
E) 200
As per the question,
The condition is that Every round has odd number of participants.
However, first and last rounds do not contain odd number of participants.
In first round 100 members (Not an odd number)
In last round 2 members (Not an odd number)
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