Linear Seating Arrangement Questions and Answers

Answer: C

There are 6 arrangements.

Four people can sit in 4! = 24 ways. Treat P and R as a block to count the arrangements where they are adjacent: 3! × 2 = 12. So 24 - 12 = 12 arrangements keep P and R apart.

In any arrangement, S is either to the right of Q or to the left, and swapping S and Q turns one case into the other without affecting whether P and R are adjacent. So exactly half of the 12 have S to the right of Q, giving 6.

12 forgets the condition on S and Q, and 8 is not a possible count. 2 is the count if S must sit immediately to the right of Q, which the question does not require.

Answer: B

The line, from left to right, is W T S Q P V R.

T is fourth to the left of V, W is just left of T, and Q is third to the right of W. Put T in place p: then W is p − 1, Q is p + 2 and V is p + 4. W needs p of at least 2, and V must not be at the end, so p + 4 is at most 6. Only p = 2 works: W 1, T 2, Q 4, V 6.

Places 3, 5 and 7 remain for P, R and S. R is not next to Q, so R is not in 3 or 5 and must be 7. S is not next to V, so S is not 5 or 7 and must be 3. That leaves P in 5.

The extreme ends are therefore W and R (WR). P and S sit in the middle of the line, at places 5 and 3, so WP, PS and SR all name at least one person who is not at an end.

Answer: D

The Board keyed Data insufficient, which follows if 'between' is read as anywhere between Father and Wife.

Four members are to the left of the Son, so the Son is 5th. Three are to the right of the Mother, so the Mother is 3rd. The Son sits between Father and Wife, so one of them is 6th (the only seat right of the Son) and the other is in 1, 2 or 4. The Grand daughter is not in between any of the members, so she is at an end; 6th is taken, so she is 1st.

Seats 1 to 6: Grand daughter, ?, Mother, ?, Son, ?

Father or Wife is 6th, and the other of the two shares seats 2 and 4 with the Grand son. Both orders fit the statements, so the Grand son can be 2nd or 4th. Only if 'between' meant immediately beside the Son would seat 4 go to Father or Wife and the Grand son be 2nd, an extra condition the question does not state.

Answer: D

B is second from left.

Number the seats 1 to 5 from the left. E is at the left end, seat 1 (IV), and C is second from the right, seat 4 (V). D sits next to C but not next to E, so D is in seat 3 or 5, and A sits next to C (VII), so A is in the other of seats 3 and 5.

A must also sit next to B and to the right of B (I, VI). If A were in seat 5, B would have to be in seat 4, which C holds, so A is in seat 3, D in seat 5, and B in seat 2.

The arrangement is E, B, A, C, D, so B is second from the left. The extreme left is E, the extreme right is D, and second from the right is C.

Answer: B

The seat next to D is occupied by A.

C is next to neither A nor D, so C's only possible neighbour is B, and C must sit at one end with B beside it: C, B, _, _. A must be next to B, giving C, B, A, D.

D is at the other end, with A as the only neighbour. B sits next to C and A, not D, so 'B' and 'B and A' are wrong, and the arrangement is fully determined.

The arrangement could also be written D, A, B, C from the other end; it is the same seating, so D's only neighbour is still A.

Answer: C

R and T sit between P and E.

Number the five seats 1 to 5 from left to right. P is on the extreme left (seat 1), and E is second from the extreme right (seat 4).

T sits next to E, so T is in seat 3 or 5. T also sits next to R; if T were in seat 5, R would have to be in seat 4, which is E's. So T is in seat 3, R is in seat 2, and S takes seat 5:

P, R, T, E, S

The people between P and E are R and T. S is at the right end, so the options with S are wrong.

Answer: C

Correct answer: Taud is in between Paul and Jack

Paul takes one of the two middle houses, and Harry stands immediately left of Larry with at least one house further to their left. Mike lives between Paul and Larry, which seats Harry, Larry, Mike and Paul in houses 2 to 5. Because Harry is immediately left of Larry, Harry would lie between Taud and Larry whenever Taud is further left - the question rules that out, so Taud is to Larry’s right. At least one boy lives right of Robert, so Robert is not in house 8, and Jack must stay clear of Siman. The row reads:

1 Jack · 2 Harry · 3 Larry · 4 Mike · 5 Paul · 6 Siman · 7 Robert · 8 Taud

Checking the statements: Robert is in house 7, not the left end; Robert does stand between Siman and Taud; and Siman, Robert and Taud - three boys - live to Paul’s right. But Taud is at the far right of the row and Jack at the far left, with Paul between them, so Taud is not between Paul and Jack. That is the statement which is not correct.

Answer: B

A is at middle position, so arrangement will be like this at this stage

Now it is told that that there is no person to the right of E, it means E is at the extreme right of the line ⇒ E is at the position 7. It is also told that D is at extreme corner of row and adjacent to B. Since one end is already occupied by E so D will be at position 1 and B will be at position 2. So our arrangement will be like:

Again, it is told that there is only one person between E and F and it is also told that B and C are opposite side of A. Since B is on the left side of A, so C will be on the right side of A. Since there is only one person between E and F so position 6 will be occupied by C and F at 5. Now only one position is remaining so that will be lled by G.

Hence, position of G is between A and B.

Answer: B

Correct answer: X

S and Z occupy the two middle places, third and fourth, and A and P the two ends. R must sit to A’s left, which is only possible if A is at the far end - so P is first, R fifth and A sixth, leaving X second. The person to P’s right is therefore X.

Answer: A

Correct answer: None

All seven face north, so right means east. W sits five places to T’s right and not at an end, so T is first and W sixth; Y is exactly in the middle and U three places to Y’s right. Z must be three places from X and not beside Y, which fixes the rest. From left to right the row reads T, Z, V, Y, X, W, U.

Seating them alphabetically from right to left would put Z first, Y second, X third and so on to T at the far right. Comparing that with the row above, not one of the seven keeps the place they already hold, so the answer is none.