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QUESTION: 1

Each of the 10 persons namely A, Q, R, Z, M, N, P, B, K and L are wearing a shirt. The colour of each shirt is one out of blue, green and red. There are ten chairs placed in a row. The chairs are consecutively numbered 1, 2, 3, 4...9 and 10 from left to right in that order. These ten persons have to sit on the chairs such that there is only one person in each chair. The number of persons wearing a green and a blue shirt is 2 and 3 respectively.

Additional Information:

1. No two persons wearing blue shirts sit on consecutively numbered chairs.

2. Among the persons wearing red shirts, exactly three persons always are sitting together while the remaining two never.

3. A person wearing a blue shirt and a person wearing a green shirt never is sitting on consecutively numbered chairs.

4. A person wearing a green shirt cannot sit on chairs numbered 2 or 9.

5. Persons wearing red shirts are not sitting at extreme ends.

The following table provides information about the six different seating arrangements namely I, II, III, IV, V and VI of the ten persons done by Mr. Crazy. He observed that out of all the seating arrangements done by him, there is one arrangement that is not consistent with the information stated under "Additional Information".

Q. Which of the following persons is wearing a blue shirt?

Solution:

Let the people who wear a blue, red and green shirt be denoted by b, r and g respectively. Restrictions on the seating arrangement:

1. Two b’s must not be together.

2. Three r’s must be together.

3. A ‘b’ and a ‘g’ must not be together.

4. A ‘g’ cannot sit on a chair numbered 2 or 9.

**Case I:** A person wearing a green shirt is sitting on chair numbered 1. It is only possible if another person wearing a green shirt sits on chair numbered 2, but this violates restriction number 4. Hence, this is also not possible.

**Case II: **A person wearing a blue shirt sits on chair numbered 1. The six seating arrangements that are possible are as follows.

Now, we see that the cases 4, 5 and 6 are just obtained by reversing the cases 1, 2 and 3 respectively. It can be concluded that in any possible seating arrangement, the chairs numbered 1 and 10 are always occupied by people wearing blue shirts. It is given that the number of people wearing a blue shirt is 3. Looking at the table given in the question, we observe that in each of the six arrangements two out of the three different people i.e. A, B and N always sit on chairs numbered 1 and 10.

Hence it can be concluded that the people who wear a blue shirt are A, B and N From the given table the person wearing a blue shirt can never sit on chairs numbered 2, 4, 7 and 9. So, (in arrangement I), A, B and N sitting on chairs numbered 1, 7 and 10 is inconsistent. Also, the people wearing red shirts sit on chairs numbered 2 and 9 and in all the possible arrangements five different people namely P, Q, M, Z and R are sitting on chairs numbered either 2 or 9. Therefore, P, Q, M, Z and R are wearing red shirts and K and L are wearing green shirts. A, B and N are wearing blue shirts. Hence, N is the answer.

QUESTION: 2

Each of the 10 persons namely A, Q, R, Z, M, N, P, B, K and L are wearing a shirt. The colour of each shirt is one out of blue, green and red. There are ten chairs placed in a row. The chairs are consecutively numbered 1, 2, 3, 4...9 and 10 from left to right in that order. These ten persons have to sit on the chairs such that there is only one person in each chair. The number of persons wearing a green and a blue shirt is 2 and 3 respectively.

Additional Information:

1. No two persons wearing blue shirts sit on consecutively numbered chairs.

2. Among the persons wearing red shirts, exactly three persons always are sitting together while the remaining two never.

3. A person wearing a blue shirt and a person wearing a green shirt never is sitting on consecutively numbered chairs.

4. A person wearing a green shirt cannot sit on chairs numbered 2 or 9.

5. Persons wearing red shirts are not sitting at extreme ends.

The following table provides information about the six different seating arrangements namely I, II, III, IV, V and VI of the ten persons done by Mr. Crazy. He observed that out of all the seating arrangements done by him, there is one arrangement that is not consistent with the information stated under "Additional Information".

Q. Which of the following is not a permissible group of four persons such that the number of persons wearing a red, a green and a blue shirt is 2, 1 and 1 respectively?

Solution:

Let the people who wear a blue, red and green shirt be denoted by b, r and g respectively. Restrictions on the seating arrangement:

1. Two b’s must not be together.

2. Three r’s must be together.

3. A ‘b’ and a ‘g’ must not be together.

4. A ‘g’ cannot sit on a chair numbered 2 or 9.

**Case I: **A person wearing a green shirt is sitting on chair numbered 1. It is only possible if another person wearing a green shirt sits on chair numbered 2, but this violates restriction number 4. Hence, this is also not possible.

**Case II: **A person wearing a blue shirt sits on chair numbered 1. The six seating arrangements that are possible are as follows.

Now, we see that the cases 4, 5 and 6 are just obtained by reversing the cases 1, 2 and 3 respectively. It can be concluded that in any possible seating arrangement, the chairs numbered 1 and 10 are always occupied by people wearing blue shirts. It is given that the number of people wearing a blue shirt is 3. Looking at the table given in the question, we observe that in each of the six arrangements two out of the three different people i.e. A, B and N always sit on chairs numbered 1 and 10.

Hence it can be concluded that the people who wear a blue shirt are A, B and N From the given table the person wearing a blue shirt can never sit on chairs numbered 2, 4, 7 and 9. So, (in arrangement I), A, B and N sitting on chairs numbered 1, 7 and 10 is inconsistent. Also, the people wearing red shirts sit on chairs numbered 2 and 9 and in all the possible arrangements five different people namely P, Q, M, Z and R are sitting on chairs numbered either 2 or 9. Therefore, P, Q, M, Z and R are wearing red shirts and K and L are wearing green shirts.

Option (1): A (Blue), P (Red), R (Red) and L (Green): Permissible

Option (2): N (Blue), Q (Red), K (Green) and Z (Red): Permissible

Option (3): K (Green), A (Blue), N (Blue) and Z (Red): Not Permissible

Option (4): B (Blue), L (Green), M (Red) and Q (Red): Permissible.

QUESTION: 3

These questions are based on the following information. P, Q, R, S and T sit around a table. P sits two seats to the left of R and Q sits two seats to the right of R.

Q. If S sits in between Q and R, who sits to the immediate right of P?

Solution:

P sits two seats to the left of R, and Q sits two seats to the right of R. We can represent this information in the diagram below.

If S sits between Q and R, then the arrangement is as follows.

As can be seen from the diagram, T is to the immediate right of P. Choice (a)

QUESTION: 4

Each of the 10 persons namely A, Q, R, Z, M, N, P, B, K and L are wearing a shirt. The colour of each shirt is one out of blue, green and red. There are ten chairs placed in a row. The chairs are consecutively numbered 1, 2, 3, 4...9 and 10 from left to right in that order. These ten persons have to sit on the chairs such that there is only one person in each chair. The number of persons wearing a green and a blue shirt is 2 and 3 respectively.

Additional Information:

1. No two persons wearing blue shirts sit on consecutively numbered chairs.

2. Among the persons wearing red shirts, exactly three persons always are sitting together while the remaining two never.

3. A person wearing a blue shirt and a person wearing a green shirt never is sitting on consecutively numbered chairs.

4. A person wearing a green shirt cannot sit on chairs numbered 2 or 9.

5. Persons wearing red shirts are not sitting at extreme ends.

The following table provides information about the six different seating arrangements namely I, II, III, IV, V and VI of the ten persons done by Mr. Crazy. He observed that out of all the seating arrangements done by him, there is one arrangement that is not consistent with the information stated under "Additional Information".

Q. Which of the following persons is wearing a green shirt?

Solution:

Let the people who wear a blue, red and green shirt be denoted by b, r and g respectively. Restrictions on the seating arrangement:

1. Two b’s must not be together.

2. Three r’s must be together.

3. A ‘b’ and a ‘g’ must not be together.

4. A ‘g’ cannot sit on a chair numbered 2 or 9.

**Case I: **A person wearing a green shirt is sitting on chair numbered 1. It is only possible if another person wearing a green shirt sits on chair numbered 2, but this violates restriction number 4. Hence, this is also not possible.

**Case II: **A person wearing a blue shirt sits on chair numbered 1. The six seating arrangements that are possible are as follows.

Now, we see that the cases 4, 5 and 6 are just obtained by reversing the cases 1, 2 and 3 respectively. It can be concluded that in any possible seating arrangement, the chairs numbered 1 and 10 are always occupied by people wearing blue shirts. It is given that the number of people wearing a blue shirt is 3. Looking at the table given in the question, we observe that in each of the six arrangements two out of the three different people i.e. A, B and N always sit on chairs numbered 1 and 10.

Hence it can be concluded that the people who wear a blue shirt are A, B and N From the given table the person wearing a blue shirt can never sit on chairs numbered 2, 4, 7 and 9. So, (in arrangement I), A, B and N sitting on chairs numbered 1, 7 and 10 is inconsistent. Also, the people wearing red shirts sit on chairs numbered 2 and 9 and in all the possible arrangements five different people namely P, Q, M, Z and R are sitting on chairs numbered either 2 or 9. Therefore, P, Q, M, Z and R are wearing red shirts and K and L are wearing green shirts. K and L are wearing green shirts. Hence, K is the answer.

QUESTION: 5

1. No two persons wearing blue shirts sit on consecutively numbered chairs.

2. Among the persons wearing red shirts, exactly three persons always are sitting together while the remaining two never.

3. A person wearing a blue shirt and a person wearing a green shirt never is sitting on consecutively numbered chairs.

4. A person wearing a green shirt cannot sit on chairs numbered 2 or 9.

5. Persons wearing red shirts are not sitting at extreme ends.

Q. Which of the arrangements done by Mr. Crazy is not consistent with the information stated under "Additional Information"?

Solution:

1. Two b’s must not be together.

2. Three r’s must be together.

3. A ‘b’ and a ‘g’ must not be together.

4. A ‘g’ cannot sit on a chair numbered 2 or 9.

**Case I: **A person wearing a green shirt is sitting on chair numbered 1. It is only possible if another person wearing a green shirt sits on chair numbered 2, but this violates restriction number 4. Hence, this is also not possible.

**Case II: **A person wearing a blue shirt sits on chair numbered 1. The six seating arrangements that are possible are as follows.

Now, we see that the cases 4, 5 and 6 are just obtained by reversing the cases 1, 2 and 3 respectively. It can be concluded that in any possible seating arrangement, the chairs numbered 1 and 10 are always occupied by people wearing blue shirts. It is given that the number of people wearing a blue shirt is 3. Looking at the table given in the question, we observe that in each of the six arrangements two out of the three different people i.e. A, B and N always sit on chairs numbered 1 and 10.

Hence it can be concluded that the people who wear a blue shirt are A, B and N From the given table the person wearing a blue shirt can never sit on chairs numbered 2, 4, 7 and 9. So, (in arrangement I), A, B and N sitting on chairs numbered 1, 7 and 10 is inconsistent. Also, the people wearing red shirts sit on chairs numbered 2 and 9 and in all the possible arrangements five different people namely P, Q, M, Z and R are sitting on chairs numbered either 2 or 9. Therefore, P, Q, M, Z and R are wearing red shirts and K and L are wearing green shirts. (a) I arrangement is not consistent.

QUESTION: 6

These questions are based on the following information. P, Q, R, S and T sit around a table. P sits two seats to the left of R and Q sits two seats to the right of R.

Q. Which of the following cannot be the correct seating arrangement of the five persons in either the clockwise direction or the anti-clockwise direction?

Solution:

P sits two seats to the left of R, and Q sits two seats to the right of R. We can represent this information in the diagram below.

We will take each choice and see whether it fits in the arrangement that we represented through a diagram in the analysis of the data (the same diagram is reproduced below).

We can see that the arrangement given in choice (a) is not possible and hence the answer choice is (a).

QUESTION: 7

These questions are based on the following information. P, Q, R, S and T sit around a table. P sits two seats to the left of R and Q sits two seats to the right of R.

Q. If S is not sitting next to Q, who is sitting between Q and S?

Solution:

P sits two seats to the left of R, and Q sits two seats to the right of R. We can represent this information in the diagram below.

If S is not next to Q, then the seating arrangement is fixed as follows.

Now P is between Q and S. Choice (b)

QUESTION: 8

Q. If a new person U joins the group such that the initial conditions for the seating arrangement should be observed and also a new condition that U does not sit next to R be satisfied, then which of the following statements is true?

Solution:

P sits two seats to the left of R, and Q sits two seats to the right of R. We can represent this information in the diagram below.

On the basis of the diagram that we drew, we find that to accommodate U we have to create a new slot between P and Q.

Hence, choice (c) is the correct answer. Choice (c)

QUESTION: 9

Q. If a new person U joins the group such that the initial conditions for the seating arrangement should be observed and also a new condition that U does not sit next to P, S or T be satisfied, then who will be the neighbours of P (one on either side)?

Solution:

P sits two seats to the left of R, and Q sits two seats to the right of R. We can represent this information in the diagram below.

We create a new slot for the sixth person. But since U will not sit next to P, S or T, he will have to sit between R and Q. The arrangement will then look as follows:

As we can see from the diagram, the neighbours of P will be T and S.

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