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# Ask for help to explain question 32 in TSA 2008

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1. Ask for help to explain question 32 in TSA 2008
I really dont understand the exact meaning of the question 32 in TSA 2008 paper:
A betball tournament is divided into two stages. In the first stage, the teams are divided into equal groups within which each team plays every team once. In the second stage, the winners of each group take part in a knockout competition which starts with four quarter finals.
Which of the following could be the number of teams starting the tournament?
A 8
B 20
C 44
D 50
E 72

I want to know how the winners of each group are produced? You see, if 20 teams totally, 10 teams each group, we can also have 4 winners from each group.
Can someone tell me why the answer is E? or what is the exact process of the tournament?
2. Re: Ask for help to explain question 32 in TSA 2008
(Original post by dearmj)
I really dont understand the exact meaning of the question 32 in TSA 2008 paper:
A betball tournament is divided into two stages. In the first stage, the teams are divided into equal groups within which each team plays every team once. In the second stage, the winners of each group take part in a knockout competition which starts with four quarter finals.
Which of the following could be the number of teams starting the tournament?
A 8
B 20
C 44
D 50
E 72

I want to know how the winners of each group are produced? You see, if 20 teams totally, 10 teams each group, we can also have 4 winners from each group.
Can someone tell me why the answer is E? or what is the exact process of the tournament?
I assume it's implying that only one team goes through from each group. If that's the case then only E can be correct as it's the only one which can support exactly eight groups with more than one team in each. But yes, there's definitely information missing from the question.

EDIT: To be clearer:
There are four quarter finals so eight teams must go through to the second stage. If we assume that only one team goes through from each group, there must be eight groups, and the question says these groups are equal. Therefore the original number of teams must divide by 8, leaving us A and E. If it was A, there wouldn't be a first stage as all the teams would go through and no matches would have to be played, therefore it must be E.
Last edited by lp386; 17-04-2012 at 14:15.
3. Re: Ask for help to explain question 32 in TSA 2008
4 quarter finals => 8 teams.
The 8 teams all had their own group "the winners of each group take part....". So each of the 8 teams has a group of the same size, so it has to be a multiple of 8. This leaves 8 or 72, but it can't be 8 since they did actually have a group stage (if it was 8 each group would be of size 1, and therefore not actually have any matches), leaving only 72.

I would work backwards, as above, rather than doing "if 20, then...". But yes, I see the issue you have, "the winners of each group" is taken to mean 1 winner from each group, it is ambiguous but otherwise you would have more than 1 possible answer so you have to interpret it as 1 from each group.
4. Re: Ask for help to explain question 32 in TSA 2008
(Original post by dearmj)
I really dont understand the exact meaning of the question 32 in TSA 2008 paper:
A betball tournament is divided into two stages. In the first stage, the teams are divided into equal groups within which each team plays every team once. In the second stage, the winners of each group take part in a knockout competition which starts with four quarter finals.
Which of the following could be the number of teams starting the tournament?
A 8
B 20
C 44
D 50
E 72

I want to know how the winners of each group are produced? You see, if 20 teams totally, 10 teams each group, we can also have 4 winners from each group.
Can someone tell me why the answer is E? or what is the exact process of the tournament?
Only the winners of each groups goes to the Quarter Finals. There are 4 Quarter Finals, hence 8 teams in the Quarter Finals. 8 winners means there are 8 groups. So the number of teams must be a multiple of 8.

It can't be A because then they would have played no group games. So it must be the only other multiple of 8 which is E, 72 teams.
5. Re: Ask for help to explain question 32 in TSA 2008
(Original post by lp386)
I assume it's implying that only one team goes through from each group. If that's the case then only E can be correct as it's the only one which can support exactly eight groups with more than one team in each. But yes, there's definitely information missing from the question.

EDIT: To be clearer:
There are four quarter finals so eight teams must go through to the second stage. If we assume that only one team goes through from each group, there must be eight groups, and the question says these groups are equal. Therefore the original number of teams must divide by 8, leaving us A and E. If it was A, there wouldn't be a first stage as all the teams would go through and no matches would have to be played, therefore it must be E.
Thanks a lot, it really help.

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Last updated: April 17, 2012
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