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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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Difficulty:

  95% (hard)

Question Stats:

33% (01:37) correct 67% (01:57) wrong based on 76 sessions

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

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

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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.
Re: In a recently held cricket tournament in one of the universities   [#permalink] 08 Mar 2018, 01:59
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