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M, N, O, P, Q, R and S are sitting around a circular table facing the centre. Only two people are seated between P and Q when counted from the right of P. Only two people are seated between Q and S when counted from the left of S. Only three people are seated between P and N when counted from the left of N. R is seated to the immediate left of M. How many people are seated between O and Q when counted from the right of Q?
One
Two
Three
Zero
One
Fix the position of P first, then place Q, S, and N using the circular constraints to quickly deduce the remaining seats for R, M, and O.
Fix the position of P first, then place Q, S, and N using the circular constraints to quickly deduce the remaining seats for R, M, and O.
Establish positions of P, Q, S, and N
Assume P is at position 1. P to Q (two to the right) puts Q at position 3. Q to S (two to the left, counting clockwise) puts S at position 5. P to N (three to the left, counting anti-clockwise) puts N at position 5, but S is there, so N must be at position 5 counting clockwise from P, placing N at position 6 (3 to the left of P is 6: 1-0, 7-6, 6-5, 5-4, 4-3, 3-2. Wait, 3 seats from P: 7, 6, 5. So N is at 5).
Finalize positions of R, M, and O
With P=1, Q=3, N=5, S=7, positions 2, 4, 6 are open. R is immediate left of M. R and M must occupy 6 and 7, but 7 is S. So they occupy 4 and 5, or 6 and 7. The only valid spots are 6 and 7 (if 7=M, 6=R) or 2 and 1 (impossible). Placing R=2, M=3? No, Q is 3. Correct placement: P=1, R=6, M=7, Q=3, S=5, N=4, O=2. Counting right from Q(3): 2 is the only person between Q and O.
B: Two is incorrect as only one person (P) sits between O and Q to the right of Q. C: Three is incorrect because only one person sits between them. D: Zero is incorrect because O and Q are not adjacent.
A is correct because when placing the seven people in order (P=1, O=2, Q=3, N=4, S=5, R=6, M=7), moving right from Q(3) leads to P(1) then O(2), resulting in exactly one person (P) between O and Q.
In circular arrangement questions, always start by fixing the person mentioned in the most restrictive constraint, usually the one with fixed relative directions.