**Team Formation Questions for CAT**

Download important CAT Team Formation Questions with Solutions PDF based on previously asked questions in CAT exam. Practice Team Formation Questions with Solutions for CAT exam.

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**Instructions**

Answer the following questions based on the information given below:

In a sports event, six teams (A, B, C, D, E and F) are competing against each other Matches are scheduled in two stages. Each team plays three matches in Stage â€“ I and two matches in Stage â€“ II. No team plays against the same team more than once in the event. No ties are permitted in any of the matches. The observations after the completion of Stage â€“ I and Stage â€“ II are as given below.

**Stage-I:**

â€¢ One team won all the three matches.

â€¢ Two teams lost all the matches.

â€¢ D lost to A but won against C and F.

â€¢ E lost to B but won against C and F.

â€¢ B lost at least one match.

â€¢ F did not play against the top team of Stage-I.

**Stage-II:**

â€¢ The leader of Stage-I lost the next two matches

â€¢ Of the two teams at the bottom after Stage-I, one team won both matches, while the other lost both matches.

â€¢ One more team lost both matches in Stage-II.

**Question 1:Â **The two teams that defeated the leader of Stage-I are:

a)Â B & F

b)Â E & F

c)Â B & D

d)Â E & D

e)Â F & D

**Question 2:Â **The only team(s) that won both matches in Stage-II is (are):

a)Â B

b)Â E & F

c)Â A, E & F

d)Â B, E & F

e)Â B & F

**Question 3:Â **The teams that won exactly two matches in the event are:

a)Â A, D & F

b)Â D & E

c)Â E & F

d)Â D, E & F

e)Â D & F

**Question 4:Â **The team(s) with the most wins in the event is (are):

a)Â A

b)Â A & C

c)Â F

d)Â E

e)Â B & E

**Instructions**

K, L, M, N, P, Q, R, S, U and W are the only ten members in a department. There is a proposal to form a team from within the members of the department, subject to the following conditions:

- Â A team must include exactly one among P,R and S.
- Â A team must include either M or Q, but not both.
- Â If a team includes K, then it must also include L, and vice versa.
- Â If a team includes one among S, U and W, then it should also include the other two.
- Â L and N cannot be members of the same team.
- Â L and U cannot be members of the same team.

The size of a team is defined as the number of members in the team.

**Question 5:Â **What could be the size of a team that includes K?

a)Â 2 or 3

b)Â 2 or 4

c)Â 3 or 4

d)Â Only 2

e)Â Only 4

**Question 6:Â **In how many ways a team can be constituted so that the team includes N?

a)Â 2

b)Â 3

c)Â 4

d)Â 5

e)Â 6

**Question 7:Â **What would be the size of the largest possible team?

a)Â 8

b)Â 7

c)Â 6

d)Â 5

e)Â cannot be determined

**Question 8:Â **Who can be a member of a team of size 5?

a)Â K

b)Â L

c)Â M

d)Â P

e)Â R

**Question 9:Â **Who cannot be a member of a team of size 3?

a)Â L

b)Â M

c)Â N

d)Â P

e)Â Q

**Question 10:Â **What would be the size of the largest possible team?

[CAT 2006]

a)Â 8

b)Â 7

c)Â 6

d)Â 5

e)Â Cannot be determined

**Question 11:Â **Who can be a member of a team of size 5?

[CAT 2006]

a)Â K

b)Â L

c)Â M

d)Â P

e)Â R

**Question 12:Â **Who cannot be a member of a team of size 3?

[CAT 2006]

a)Â L

b)Â M

c)Â N

d)Â P

e)Â Q

**Question 13:Â **In how many ways a team can be constituted so that the team includes N?

[CAT 2006]

a)Â 2

b)Â 3

c)Â 4

d)Â 5

e)Â 6

**Question 14:Â **What could be the size of a team that includes K?

[CAT 2006]

a)Â 2 or 3

b)Â 2 or 4

c)Â 3 or 4

d)Â Only 2

e)Â Only 4

**Answers & Solutions:**

**1)Â AnswerÂ (B)**

There are a total of $^6 C_2$ matches => 15 matches. The first 9 matches are held in the first stage and remaining 6 in the second stage.

From the information given, we can conclude that the following matches were held in first stage:

Stage 1: D-A (A won), D-C (D won), D-F (D won), E-B (B won), E-C (E won), E-F (E won)

One team won all matches. As B, C, D E and F have lost at least one match each, A won all three matches. As A, B, D, E have won at least one match, C and F lost both matches.

From the matches already deduced, we can see that A needs to play 2 more matches, B two more matches and C and F one match each. As C and F lose all matches in stage 1, they cannot play against each other. F did not play against the leader i.e. A. Hence, the remaining matches are A-B (A won), A-C (A won), B-F (B won).

Thus, the stage 1 matches are

Stage 1: D-A (A won), D-C (D won), D-F (D won), E-B (B won), E-C (E won), E-F (E won), A-B (A won), A-C (A won), B-F (B won)

Thus Stage 2 matches are D-B, D-E, E-A, F-A, B-C and C-F (all matches – stage 1 matches)

As A lost both matches, F and E must have won the match vs A. As F won against A, F won both its matches and C lost both its matches. One more team lost both its matches. As B, E and F have won at least one match and A and C have been discussed previously, D must have lost both matches. Hence, stage 2 results are:

Stage 2: D-B (B won), D-E (E won), E-A (E won), F-A (F won), B-C (B won) and C-F (F won)

Hence, the two teams that won against stage 1 leader A are E and F.

**2)Â AnswerÂ (D)**

There are a total of $^6 C_2$ matches => 15 matches. The first 9 matches are held in the first stage and remaining 6 in the second stage.

From the information given, we can conclude that the following matches were held in first stage:

Stage 1: D-A (A won), D-C (D won), D-F (D won), E-B (B won), E-C (E won), E-F (E won)

One team won all matches. As B, C, D E and F have lost at least one match each, A won all three matches. As A, B, D, E have won at least one match, C and F lost both matches.

From the matches already deduced, we can see that A needs to play 2 more matches, B two more matches and C and F one match each. As C and F lose all matches in stage 1, they cannot play against each other. F did not play against the leader i.e. A. Hence, the remaining matches are A-B (A won), A-C (A won), B-F (B won).

Thus, the stage 1 matches are

Stage 1: D-A (A won), D-C (D won), D-F (D won), E-B (B won), E-C (E won), E-F (E won), A-B (A won), A-C (A won), B-F (B won)

Thus Stage 2 matches are D-B, D-E, E-A, F-A, B-C and C-F (all matches – stage 1 matches)

As A lost both matches, F and E must have won the match vs A. As F won against A, F won both its matches and C lost both its matches. One more team lost both its matches. As B, E and F have won at least one match and A and C have been discussed previously, D must have lost both matches. Hence, stage 2 results are:

Stage 2: D-B (B won), D-E (E won), E-A (E won), F-A (F won), B-C (B won) and C-F (F won)

Hence, the teams that won both of their stage 2 matches are B, E and F.

**3)Â AnswerÂ (E)**

There are a total of $^6 C_2$ matches => 15 matches. The first 9 matches are held in the first stage and remaining 6 in the second stage.

From the information given, we can conclude that the following matches were held in first stage:

Stage 1: D-A (A won), D-C (D won), D-F (D won), E-B (B won), E-C (E won), E-F (E won)

One team won all matches. As B, C, D E and F have lost at least one match each, A won all three matches. As A, B, D, E have won at least one match, C and F lost both matches.

From the matches already deduced, we can see that A needs to play 2 more matches, B two more matches and C and F one match each. As C and F lose all matches in stage 1, they cannot play against each other. F did not play against the leader i.e. A. Hence, the remaining matches are A-B (A won), A-C (A won), B-F (B won).

Thus, the stage 1 matches are

Stage 1: D-A (A won), D-C (D won), D-F (D won), E-B (B won), E-C (E won), E-F (E won), A-B (A won), A-C (A won), B-F (B won)

Thus Stage 2 matches are D-B, D-E, E-A, F-A, B-C and C-F (all matches – stage 1 matches)

As A lost both matches, F and E must have won the match vs A. As F won against A, F won both its matches and C lost both its matches. One more team lost both its matches. As B, E and F have won at least one match and A and C have been discussed previously, D must have lost both matches. Hence, stage 2 results are:

Stage 2: D-B (B won), D-E (E won), E-A (E won), F-A (F won), B-C (B won) and C-F (F won)

Hence, the wins by each team are A (3), B(4), C(0), D(2), E(4), F(2). Hence, D and F won exactly 2 matches.

**4)Â AnswerÂ (E)**

From the information given, we can conclude that the following matches were held in first stage:

Stage 1: D-A (A won), D-C (D won), D-F (D won), E-B (B won), E-C (E won), E-F (E won)

Thus, the stage 1 matches are

Thus Stage 2 matches are D-B, D-E, E-A, F-A, B-C and C-F (all matches – stage 1 matches)

Stage 2: D-B (B won), D-E (E won), E-A (E won), F-A (F won), B-C (B won) and C-F (F won)

Hence, the wins by each team are A(3), B(4), C(0), D(2), E(4), F(2). Hence, most wins are by B and E.

**5)Â AnswerÂ (E)**

A team which has K should have L also.

Since L is there in the team, N and U should not be there in the team. Since U is not there in the team, S and W should not be there in the team.

So, the team will have K, L, one of P and R and one of M or Q.

So, the team size will be 4.

**6)Â AnswerÂ (E)**

Since N is in the team, L and K cannot be in the team.

The team can have one of M and Q. So, 2 ways of selection.

If the team has S, then it should have U and W as well.

If the team has no S, then it should have one of P or R.

So, the number of ways of forming the team is 2*(1+2) = 6 ways

**7)Â AnswerÂ (D)**

Out of P, R and S only 1 can be in the team. If S is there, U and W will also be there. So, P and R should not be in the team for its size to be maximum.

Out of M and Q, only 1 can be there.

If L is there in the team, N and U cannot be in the team.

If L is not there in the team, then K is also not there in the team but N and U can be in the team.

So, the maximum team size is 5 consisting of S, U, W, (M or Q), N.

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**8)Â AnswerÂ (C)**

Out of P, R and S only 1 can be in the team. If S is there, U and W will also be there. So, P and R should not be in the team for its size to be maximum.

Out of M and Q, only 1 can be there.

If L is there in the team, N and U cannot be in the team.

If L is not there in the team, then K is also not there in the team but N and U can be in the team.

So, the maximum team size is 5 consisting of S, U, W, (M or Q), N.

So, M can be a member of team size 5.

**9)Â AnswerÂ (A)**

If L is in the team, the team should include K also. The team should have one among P, R and S and one among M and Q.

So, the team size cannot be 3 if L is in the team.

**10)Â AnswerÂ (D)**

Out of P, R and S only 1 can be in the team. If S is there, U and W will also be there. So, P and R should not be in the team for its size to be maximum.

Out of M and Q, only 1 can be there.

If L is there in the team, N and U cannot be in the team.

If L is not there in the team, then K is also not there in the team but N and U can be in the team.

So, the maximum team size is 5 consisting of S, U, W, (M or Q), N.

**11)Â AnswerÂ (C)**

Out of M and Q, only 1 can be there.

If L is there in the team, N and U cannot be in the team.

If L is not there in the team, then K is also not there in the team but N and U can be in the team.

So, the maximum team size is 5 consisting of S, U, W, (M or Q), N.

So, M can be a member of team size 5.

**12)Â AnswerÂ (A)**

If L is in the team, the team should include K also. The team should have one among P, R and S and one among M and Q.

So, the team size cannot be 3 if L is in the team.

**13)Â AnswerÂ (E)**

Since N is in the team, L and K cannot be in the team.

The team can have one of M and Q. So, 2 ways of selection.

If the team has S, then it should have U and W as well.

If the team has no S, then it should have one of P or R.

So, the number of ways of forming the team is 2*(1+2) = 6 ways

**14)Â AnswerÂ (E)**

A team which has K should have L also.

Since L is there in the team, N and U should not be there in the team. Since U is not there in the team, S and W should not be there in the team.

So, the team will have K, L, one of P and R and one of M or Q.

So, the team size can be 4.

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