Eight friends J, K, L, M, P, Q, R and S are sitting around a square table…
2023
Eight friends J, K, L, M, P, Q, R and S are sitting around a square table facing the centre. Some sit at the corners and some at the mid-points of the sides. ‘P’ sits third to the left of ‘R’. ‘P’ sits at one of the corners. ‘K’ sits second to the right of ‘Q’. ‘Q’ does not sit at any of the corners. ‘Q’ is not an immediate neighbour of ‘P’. ‘S’ is an immediate neighbour of ‘J’. ‘S’ does not sit at any of the middle of the sides. Only three persons sit between ‘S’ and ‘L’. Who sits second to the left of ‘M’?
- A.
L
- B.
Q
- C.
S
- D.
P
Attempted by 49 students.
Show answer & explanation
Correct answer: C
Improved solution:
Step-by-step reasoning:
There are 8 seats: 4 corners and 4 mid-sides. Facing the centre, a person's left is the clockwise direction and right is the anticlockwise direction. For clarity, number seats 1 to 8 clockwise.
P is third to the left of R and P is at a corner. To make the third-to-left position a corner, R must be at a mid-side.
Place R at seat 2 (a mid-side). Then P (third to R's left, i.e., three seats clockwise) is at seat 5 (a corner).
Q is not at a corner and is not adjacent to P, so Q must be at seat 8 (a mid-side) rather than the mid-sides adjacent to P.
K sits second to the right of Q. Right is anticlockwise, so counting two seats anticlockwise from seat 8 places K at seat 6 (a mid-side).
S is a corner and only three persons sit between S and L, so S and L occupy opposite corners. Since P occupies one corner (seat 5), S and L must occupy the other opposite corner pair (seats 3 and 7).
J is an immediate neighbour of S. Of the two corner choices for S, if S were at seat 7 both neighbouring seats (6 and 8) are already occupied by K and Q, so J could not be placed. Therefore S is at seat 3 and L is at seat 7, with J occupying seat 4.
The only remaining seat is seat 1, so M is at seat 1.
Final clockwise order starting from seat 1 (M) is: M, R, S, J, P, K, L, Q.
Question: Who sits second to the left of M?
Since left is clockwise, the second person to the left of M (two seats clockwise from M) is the person at seat 3, which is S. Answer: S.