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19 Jun 2025, 22:46
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Read the data given below carefully and answer the questions that follow. Seven persons Paul, Queen, Rax, Sam, Tom, Unif and Vali are sitting in a row. Rax and Sam sit next to each other. There must be exactly four persons between Queen and Vali. Sam sits to the immediate right of Queen.
1. If Paul and Tom are separated exactly by two persons, then who sits to the immediate left of Vali?
(A) Paul
(B) Tom
(C) Unif
(D) Rax
2. If Queen is not sitting at either extreme of the row, then who among the following has as many persons to his left as he has to his right?
(A) Sam
(B) Unif
(C) Rax
(D) Vali
(A) Sam
(B) Unif
(C) Rax
(D) Vali
3. If Queen sits at one extreme, then who is at the other extreme?
(A) Paul
(B) Tom
(C) Vali
(D) Cannot be determined
(A) Paul
(B) Tom
(C) Vali
(D) Cannot be determined
4. Tom sits to the right of Queen, and Paul is separated from Tom by exactly three persons. Then, who is sitting to the immediate left of Vali?
(A) Unif
(B) Paul
(C) Tom
(D) Rax
(A) Unif
(B) Paul
(C) Tom
(D) Rax
5. In how many different ways can the seven persons sit in a row?
(A) 3
(B) 2
(C) 10
(D) 12
(A) 3
(B) 2
(C) 10
(D) 12
23 Jun 2025, 03:56
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Official Answer:
Let us write down the conditions given in short form and then represent them pictorially. Also, let us treat the left of the persons sitting as “left” and their right as ”right” for interpreting the conditions.
Rax and Sam sit next to each other --> RS or SR.
There are exactly 4 persons between Queen and Vali --> Q ― ― ― ― V or V ― ― ― ― Q.
Sam sits to the immediate right of Queen --> SQ.
Now let us analyse the data/conditions that we are given and then put the three conditions together. Let us number the seats from our left to right as Seat 1 to Seat 7. Since S is to the right of Q and since R and S have to be next to each other, R can come only to the immediate right of S. Thus, R, S and Q, will be in the order RSQ. Since there are four persons between Q and V, Q can be placed in seats 1, 2, 6 or 7. But if Q is in Seat 1or 2, then there are no seats for R and S. Hence, there are only two seats available for Q. Let us fix the positions of R, S and V in each of these two positions of Q and write them down. The directions Left and Right are as shown below.
These are the only two arrangements possible for the four persons V, R, S and Q. The other three persons Paul, Tom and Unif can sit in the three vacant seats in any order, as no information is given about them. Now let us look at each of the questions.
1. Paul and Tom are separated by exactly two persons. Arrangement Ι is the only one possible as in Arrangement ΙΙ, Paul and Tom cannot have exactly two persons between them. So, we have the arrangement as follows: T/P, V, U, P/T, R, S, Q So, Unif must be sitting to the immediate left of Vali.
Choice (C)
2. If Queen is not at the extreme right, then only Arrangement ΙΙ above is possible. The person who has as many persons on his left as on his right can only be the person who is sitting in the middle seat, i.e. seat 4. In this arrangement, Rax is sitting in seat 4.
Choice (C)
3. “Queen sits at one extreme” means that we should look at arrangement Ι. In this arrangement, any one out of the three persons Paul, Tom and Unif can be in seat 1, i.e. extreme right.
Choice (D)
4. If Tom and Paul are separated by exactly three persons, then only Arrangement ΙΙ is possible. So, Tom and Paul have to be in seats 3 and 7, Since, we are also given that Tom is to the right of Queen, Tom has to be in seat 3 and Paul, in seat 7. So, the arrangement must be as follows: V, U, T, R, S, Q, P The person sitting to the immediate left of Vali is Unif.
Choice (A)
5. We have two possible arrangements – Arrangement Ι and Arrangement ΙΙ that we looked at already. In each arrangement, the remaining three people can sit in the remaining three seats in 6 ways. Thus, a total of 12 ways of seating the seven persons is possible.
Choice (D)
Let us write down the conditions given in short form and then represent them pictorially. Also, let us treat the left of the persons sitting as “left” and their right as ”right” for interpreting the conditions.
Rax and Sam sit next to each other --> RS or SR.
There are exactly 4 persons between Queen and Vali --> Q ― ― ― ― V or V ― ― ― ― Q.
Sam sits to the immediate right of Queen --> SQ.
Now let us analyse the data/conditions that we are given and then put the three conditions together. Let us number the seats from our left to right as Seat 1 to Seat 7. Since S is to the right of Q and since R and S have to be next to each other, R can come only to the immediate right of S. Thus, R, S and Q, will be in the order RSQ. Since there are four persons between Q and V, Q can be placed in seats 1, 2, 6 or 7. But if Q is in Seat 1or 2, then there are no seats for R and S. Hence, there are only two seats available for Q. Let us fix the positions of R, S and V in each of these two positions of Q and write them down. The directions Left and Right are as shown below.
These are the only two arrangements possible for the four persons V, R, S and Q. The other three persons Paul, Tom and Unif can sit in the three vacant seats in any order, as no information is given about them. Now let us look at each of the questions.
1. Paul and Tom are separated by exactly two persons. Arrangement Ι is the only one possible as in Arrangement ΙΙ, Paul and Tom cannot have exactly two persons between them. So, we have the arrangement as follows: T/P, V, U, P/T, R, S, Q So, Unif must be sitting to the immediate left of Vali.
Choice (C)
2. If Queen is not at the extreme right, then only Arrangement ΙΙ above is possible. The person who has as many persons on his left as on his right can only be the person who is sitting in the middle seat, i.e. seat 4. In this arrangement, Rax is sitting in seat 4.
Choice (C)
3. “Queen sits at one extreme” means that we should look at arrangement Ι. In this arrangement, any one out of the three persons Paul, Tom and Unif can be in seat 1, i.e. extreme right.
Choice (D)
4. If Tom and Paul are separated by exactly three persons, then only Arrangement ΙΙ is possible. So, Tom and Paul have to be in seats 3 and 7, Since, we are also given that Tom is to the right of Queen, Tom has to be in seat 3 and Paul, in seat 7. So, the arrangement must be as follows: V, U, T, R, S, Q, P The person sitting to the immediate left of Vali is Unif.
Choice (A)
5. We have two possible arrangements – Arrangement Ι and Arrangement ΙΙ that we looked at already. In each arrangement, the remaining three people can sit in the remaining three seats in 6 ways. Thus, a total of 12 ways of seating the seven persons is possible.
Choice (D)
Moderator:
