Linear Seating Arrangement Questions and Answers

Answer: D

The statement that is not true is K is in the farthest East.

Build the order from West to East. A is West of P, and T is between them: A, T, P. K is West of both T and A, and East of B: B, K, A. Combining:

West: B, K, A, T, P :East

So P is farthest East, T is West of P, and B is West of A and K, all true. K is second from the West end, not the farthest East.

Answer: C

Vibha is sitting at the south end. People facing east have north on their left and south on their right, so the south end is the right-hand end of the row. Ria is second to the left of Sweta, so Sweta cannot be in the first two seats. If Sweta is in seat 4 (counting from the north end) then Ria is in seat 2, and Bhumi must sit next to Sweta with Vibha on Bhumi's far side, which fails because the seats are taken or run out. If Sweta is in seat 5, Bhumi would be in seat 4 and Vibha in seat 3, which is Ria's seat. Only Sweta in seat 3 works: Ria is in seat 1, Bhumi in seat 4, Vibha in seat 5, and Arun in seat 2. The row from north to south is Ria, Arun, Sweta, Bhumi, Vibha, so the south end is Vibha, not Sweta, Bhumi or Arun.

Answer: D

S is sitting to the left of P. All face north, so left is the west side and the line from west to east reads as the order of left to right. R is immediately to the left of U, giving R U. Q is at an extreme end with U as a neighbour, so Q is at the east end: R U Q. Only T is between R and P, so P T R U Q. The remaining person S cannot be between R and P, so S takes the west end: S P T R U Q. The person to the left of P is therefore S, not T, R or U.

Answer: B

Three persons face south. G sits second to the right of H, who faces north and so has east on the right. G is at an extreme end, so H is second from the other end. E is not next to G, so E is at the far end and F is between H and G.

F's two neighbours, H and G, face opposite directions, so G faces south. E faces the same way as G, which is south. H's neighbours E and F face the same way, so F is south too. So E, F and G face south, and H faces north.

Answer: A

Two friends stand between S and Q. Only P is taller than R, so P is tallest and R is second tallest. Only S is shorter than T, so S is shortest and T is second shortest. Q is taller than U, and the two places left are the middle ones, so U is third and Q is fourth.

The row from shortest to tallest is S, T, U, Q, R, P. Between S (first) and Q (fourth) stand T and U, which is two people. One, zero and three do not match this order.

A quick check: from the row S, T, U, Q, R, P read from shortest to tallest, S is shortest and has T only above it among the two lowest places, and P is the only one taller than R, so every given condition holds with this single order.

Answer: C

P is at one of the extreme ends. Facing west, a person's right is north, so P stands immediately north of T. Only N is between K and T, so the order from north to south must be P, T, N, K. Only J is between L and K, so J and L follow K: P, T, N, K, J, L.

P is at the north end, so (C) is true. P is not between L and T, L is at the south extreme end, and the person at T's immediate right is P, not N.

A check on the order P, T, N, K, J, L: N is the only person between T and K, J is the only person between K and L, and P is immediately to the right of T, so every clue is met.

Answer: B

Number the seven places 1 to 7 from the left, which is the west side for people facing north. C is immediately left of E, so C and E are in neighbouring places; G is a neighbour of E and A, so G sits on E's other side with A beyond it, and F is third to the right of E. That gives C, E, G, A, F in a row. D must have four people between itself and E, so D is at the far right end and the remaining boy B sits between F and D. The row is C, E, G, A, F, B, D. The boys between C and D are E, G, A, F and B, which makes 5. The answer is 5, option (B); 2, 4 and 3 count too few of them.

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.