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In a recently held cricket tournament in one of the universities

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In a recently held cricket tournament in one of the universities  [#permalink]

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New post 23 Feb 2018, 23:48
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In a recently held cricket tournament in one of the universities in Australia, 'N' teams participated in total. The tournament comprised of various rounds, where each round comprised of one or more 'games'. Each 'game' was always between two teams only, and the rules were designed as such that each 'game' resulted in a Win for one team and Loss for the other team, there were no Draws.
What is the value of 'N'?

(1) In the first round of the tournament, each team played a game with every other team, and no two teams played each other more than once. This way, '28' games in total were played in round 1.

(2) Out of 'N', 4 teams were selected after round 1 for round 2, where '2' games were played in total; and 2 teams were selected from round 2 for round 3, where there was only '1' game played that declared the winner. Thus, tournament was over in 3 rounds. This way, in total, '31' games were played in the entire tournament.
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New post 24 Feb 2018, 02:26
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amanvermagmat wrote:
In a recently held cricket tournament in one of the universities in Australia, 'N' teams participated in total. The tournament comprised of various rounds, where each round comprised of one or more 'games'. Each 'game' was always between two teams only, and the rules were designed as such that each 'game' resulted in a Win for one team and Loss for the other team, there were no Draws.
What is the value of 'N'?

(1) In the first round of the tournament, each team played a game with every other team, and no two teams played each other more than once. This way, '28' games in total were played in round 1.

(2) Out of 'N', 4 teams were selected after round 1 for round 2, where '2' games were played in total; and 2 teams were selected from round 2 for round 3, where there was only '1' game played that declared the winner. Thus, tournament was over in 3 rounds. This way, in total, '31' games were played in the entire tournament.


We're asked to find the number of teams.
Let's see which statements give us relevant information, a Logical approach.

(1) This gives us an equation with one variable: N choose 2 = 28 and is therefore solvable.
Sufficient!

(2) so we know that the first round had 31 - 1 - 2 = 28 games but we don't know how they were distributed amongst the teams.
Therefore we cannot create an equation connecting the number of teams to the number of games in round 1.
Insufficient.

(A) is our answer.
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Re: In a recently held cricket tournament in one of the universities  [#permalink]

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New post 08 Mar 2018, 01:20
Hi, I have a question.

For statement 1: Do we assume that all teams in the tournament participated in Round 1 of the tournament or some teams will skip round 1 as they are directly qualify for the 2nd round. As round 1 could be just qualifier rounds for selected under-dog teams, out of which X teams will be selected and join the other directly qualified teams in Round 2.

Can someone please help? I feel little bit confused. Sorry i may sound silly. But just to get clarified, in case CAT throws me such questions on my D-Day

Thanks.
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New post 08 Mar 2018, 01:59
hellosanthosh2k2 wrote:
Hi, I have a question.

For statement 1: Do we assume that all teams in the tournament participated in Round 1 of the tournament or some teams will skip round 1 as they are directly qualify for the 2nd round. As round 1 could be just qualifier rounds for selected under-dog teams, out of which X teams will be selected and join the other directly qualified teams in Round 2.

Can someone please help? I feel little bit confused. Sorry i may sound silly. But just to get clarified, in case CAT throws me such questions on my D-Day

Thanks.


Hello Santhosh

In statement 1 it is mentioned: "each team played a game with every other team, and no two teams played each other more than once. This way, '28' games in total were played in round 1". I think this should clarify your query. All teams participated and each team played with every other team, just once.
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Re: In a recently held cricket tournament in one of the universities  [#permalink]

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New post 09 Apr 2019, 20:29
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DavidTutorexamPAL wrote:
amanvermagmat wrote:
In a recently held cricket tournament in one of the universities in Australia, 'N' teams participated in total. The tournament comprised of various rounds, where each round comprised of one or more 'games'. Each 'game' was always between two teams only, and the rules were designed as such that each 'game' resulted in a Win for one team and Loss for the other team, there were no Draws.
What is the value of 'N'?

(1) In the first round of the tournament, each team played a game with every other team, and no two teams played each other more than once. This way, '28' games in total were played in round 1.

(2) Out of 'N', 4 teams were selected after round 1 for round 2, where '2' games were played in total; and 2 teams were selected from round 2 for round 3, where there was only '1' game played that declared the winner. Thus, tournament was over in 3 rounds. This way, in total, '31' games were played in the entire tournament.


We're asked to find the number of teams.
Let's see which statements give us relevant information, a Logical approach.

(1) This gives us an equation with one variable: N choose 2 = 28 and is therefore solvable.
Sufficient!

(2) so we know that the first round had 31 - 1 - 2 = 28 games but we don't know how they were distributed amongst the teams.
Therefore we cannot create an equation connecting the number of teams to the number of games in round 1.
Insufficient.

(A) is our answer.



In statement 2 we get to know that in round 1 there were 28 games, isn't that the same as data provided in statement 1 ?
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New post 28 Apr 2019, 16:19
anmolsd1995 wrote:

In statement 2 we get to know that in round 1 there were 28 games, isn't that the same as data provided in statement 1 ?


Hey anmolsd1995,

First, apologies for the delayed response. (In general, please PM me if you wish to make sure I see your reply).

In the given data we are not told the structure of the tournament (all we know is that each 'game' was played between two teams). So while we know from stmt 2 that round 1 contained 28 games, we do not know how many teams played these games. Was it best of 5? One match per every pair of teams? 7 teams with only the top 4 passing onwards? Without information on the structure, we cannot know and therefore (2) is insufficient.
Note that the information provided in (1) hints that this is the solution -- (1) is sufficient precisely because it provides information on the structure of the tournament and so you should, when looking at (2), wonder if it gives the same (or equivalent) information.

Best,
David
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In a recently held cricket tournament in one of the universities   [#permalink] 28 Apr 2019, 16:19
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