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In a cricket team of 20 players, there are a certain number of wicket-

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In a cricket team of 20 players, there are a certain number of wicket-  [#permalink]

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New post Updated on: 21 Feb 2019, 04:38
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Methodical Ways to Solve Venn Diagrams - Exercise Question #2

2- In a cricket team of 20 players, there are a certain number of wicket-keepers. All of them can either bowl or bat or both. The number of wicket-keepers who can only bat are 3 and the number of wicket keepers who can only bowl is 1. Five players in the team are all-rounders, who can bat as well as bowl, but are not wicket-keepers. If there are atleast 5 players in the team, who can only bat or who can only bowl. Then what is the maximum number of players who can do all three things?

Options

A) 0
B) 1
C) 2
D) 3
E) 4

To read the article: Methodical Ways to Solve Venn Diagrams

To solve question 1: Question 1

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Originally posted by EgmatQuantExpert on 20 Feb 2019, 04:44.
Last edited by EgmatQuantExpert on 21 Feb 2019, 04:38, edited 3 times in total.
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Re: In a cricket team of 20 players, there are a certain number of wicket-  [#permalink]

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New post 20 Feb 2019, 11:25
I am not able to understandIf there are atleast 5 players in the team, who can only bat or who can only bowl
not able to get an exact value which needs to be considered.....



EgmatQuantExpert wrote:
Methodical Ways to Solve Venn Diagrams - Exercise Question #2

2- In a cricket team of 20 players, there are a certain number of wicket-keepers. All of them can either bowl or bat. The number of wicket-keepers who can only bat are 3 and the number of wicket keepers who can only bowl is 1. Five players in the team are all-rounders, who can bat as well as bowl, but are not wicket-keepers. If there are atleast 5 players in the team, who can only bat or who can only bowl. Then what is the maximum number of players who can do all three things?

Options

A) 0
B) 1
C) 2
D) 3
E) 4

To read the article: Methodical Ways to Solve Venn Diagrams

To solve question 1: Question 1

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Re: In a cricket team of 20 players, there are a certain number of wicket-  [#permalink]

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New post 21 Feb 2019, 01:37
Answer is A.

If you need someone to do all 3, he/she must know how to wicket keep. However, it is clearly written that a wicketkeeper can't both bowl and bat.

Therefore, no such person exists.
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Re: In a cricket team of 20 players, there are a certain number of wicket-  [#permalink]

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New post 21 Feb 2019, 03:45
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Re: In a cricket team of 20 players, there are a certain number of wicket-  [#permalink]

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New post 21 Feb 2019, 03:47
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In a cricket team of 20 players, there are a certain number of wicket-  [#permalink]

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New post 25 Feb 2019, 21:20

Solution



Understanding the question


Let us first identify the different sets mentioned in this question,

    • The universal set is the players of the team.
    • Among them,
      o Set A is the people who are batsmen,
      o Set B is the people who are bowlers, and
      o Set C is the people who are wicket-keepers
      o In this question, the number of players who can do neither of the above = 0

Now that we have identified the sets mentioned in the question, let’s understand the information given about them
    • We are told that the total number of players in the team = 20
    • Among them, there are certain number of wicket-keepers and all of them are either batsmen or bowler or both.
      o This implies that there is no player, in the team, who is only a wicket-keeper
      o The number of wicket-keepers who can only bat = 3, and
      o The number of wicket-keepers who can only bowl = 1
    • We are also told that there are atleast 5 players, who can only bat, and atleast 5 players , who can only bowl
    • Five players in the team are all-rounders, who can bat and bowl, but are not wicket-keepers
    • And we need to find out the maximum number of players, who can do all three things.

Draw the Venn Diagram


Now that we have understood all the information that is given to us, let’s represent this information in a two-set venn-diagram.

Image


Let’s find relationships between different entities in the venn diagram using the information given to us

    • In this question, n(U) = n(A or B or C)
    • Thus,
      o n(U) = n(A or B or C) = a + b + c + d + e + f + g = 20
      o We know, c = 0, since there is no player who is only a wicket-keeper
         So, a + b + d + e + f + g = 20 ……… (1)

    • And, we are given that,
      o n(only A and C) = 3, which implies that f = 3
      o n(only B and C) = 3, which implies that e = 1
      o n( only A and B) = 5, which implies that d = 5

    • Substituting these values in equation (1), we get, a + b + g = 20 – 3 – 1 - 5 = 11 ……. (2)
    • We are also given that,
      o n(only A) ≥ 5 => a ≥ 5
      o n(only B) ≥ 5 => b ≥ 5

    • In equation (2), a + b + g = 11, ‘g’ represents the number of the players, who can do all three things
      o For ‘g’ to be maximum, (a + b) must be minimum
      o We know that the minimum value of a and b are 5 each. So, the minimum value of a + b = 5 + 5 = 10
      o Therefore, the maximum value of g = 11 – 10 = 1

Hence, the maximum number of players, in the team, who can do all three things = 1

Image


Hence, the correct answer is option B.

Image

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In a cricket team of 20 players, there are a certain number of wicket-   [#permalink] 25 Feb 2019, 21:20
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