Amongst six people-P, Q R, S, T and U standing around a circle, some facing the centre while some facing outside (i.e. opposite to the centre) but not necessarily in the same order, what is the position of T with respect to U ? Statement I: P stands second to the right of R. R faces the centre. Q stands second to the left of P. Q is an immediate neighbour of both U and T. U and P face opposite directions (i.e. if U faces the centre then P faces outside and vice-versa.) Only two people stand between P and T. Statement II: Only two people stand between R and U. P stands to the immediate left of U. P faces outside. R is an immediate neighbour of T.

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Accepted Answer

Step-by-step reasoning:

1. Summary: There are $6$ people around a circle: P, Q, R, S, T, U. We must find T's position with respect to U.

2. Use Statement I alone:
   - Place R at position $1$ (arbitrary). R faces centre, so “second to the right of R” is two steps clockwise: P is at position $3$.
   - If P faced the centre, “second to the left of P” would place Q at position $1$ (occupied by R) — contradiction. Hence P must face outside.
   - For P facing outside, “second to the left of P” is two steps clockwise, so Q is at position $5$.
   - Q is an immediate neighbour of both U and T ⇒ U and T occupy positions $4$ and $6$ (in some order).
   - “Only two people stand between P and T” with P at $3$ forces T to be at position $6$ (the unique seat two people away), so U is at position $4$.
   - U and P face opposite directions, so U faces centre. For U facing centre, U's right is clockwise: from $4$ → $5$ (right 1) → $6$ (right 2). Thus T is second to the right of U.
   - All placements are forced; Statement I alone yields a unique relation: T is second to the right of U. Therefore Statement I is sufficient.

3. Use Statement II alone (showing insufficiency):
   - Take U at position $1$, and let P be the immediate left of U while P faces outside (as given). Two cases depending on U's facing:
     Case A: U faces centre ⇒ P is at position $6$. Place R so two people stand between R and U ⇒ R at $4$. Let T be R's other neighbour at $5$. Then with U facing centre, T is second to the left of U.
     Case B: U faces outside ⇒ P is at position $2$. Again R at $4$ and let T be at $5$. Now with U facing outside, U's right is anticlockwise, and T (at $5$) is second to the right of U.
   - Both arrangements satisfy Statement II but give different relations between T and U. Hence Statement II alone is not sufficient.

Conclusion: Statement I alone is sufficient, Statement II alone is not sufficient. This matches option B.

FINAL_ANSWER: b

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