Introduction / Context:
This is a circular arrangement and data sufficiency problem. Five people L, M, N, O and P are standing in a circle facing the centre. We need to identify who is standing to the right of L, using the given statements about which people stand next to each other and on which side. The core concepts here are circular seating, 'right of' in a circle, and checking whether a set of statements is enough to uniquely determine the answer.
Given Data / Assumptions:
- People: L, M, N, O, P.
- They are standing in a circle, facing the centre.
- Question: Who is standing immediately to the right of L?
- Statement 1: Next to L are P and M. (So L has P on one side and M on the other, but we do not yet know which is on the right and which is on the left.)
- Statement 2: O is standing to the right of P.
- Statement 3: O is standing to the left of N.
- All face the centre, so 'right' means the neighbour on the clockwise side when we look at them from above, using the common convention in such problems.
Concept / Approach:
We must check the sufficiency of statements. A statement (or combination of statements) is sufficient if it leads to a unique answer for who is to the right of L, without any ambiguity. We should test: Statement 1 alone, Statement 2 alone, and then Statements 1 and 2 together. Statement 3 is additional information but, given the options, the critical test is whether Statements 1 and 2 together can fix the person to L's right.
Step-by-Step Solution:
Step 1: Use Statement 1 alone: 'Next to L are P and M.' This tells us L's two neighbours are P and M, but does not specify which one is on the right side. So L could have P on the right and M on the left, or M on the right and P on the left. Hence, Statement 1 alone is not sufficient.
Step 2: Use Statement 2 alone: 'O is standing to the right of P.' This gives information only about P and O. It does not involve L at all, so we cannot know who stands to the right of L. Therefore, Statement 2 alone is also not sufficient.
Step 3: Combine Statement 1 and Statement 2. From Statement 1, we know L is between P and M. From Statement 2, O is to the right of P. Because they form a circle facing the centre, consistent arrangements that satisfy both statements can be constructed. When all valid arrangements satisfying both Statement 1 and Statement 2 are examined, L always has the same person to the right.
Step 4: In all consistent arrangements, P ends up on the right side of L and M on the left side of L. Hence, combining Statement 1 and Statement 2 uniquely fixes that P is to the right of L.
Step 5: Statement 3, 'O is standing to the left of N', further restricts positions of O and N but does not change the fact already determined from Statements 1 and 2: P is to the right of L. Thus, Statements 1 and 2 are already sufficient.
Verification / Alternative check:
Try constructing different circular orders satisfying Statement 1 and Statement 2. You will see that although the entire circle can be rotated, the relative positions force P to be on L's right in every valid arrangement.
Because the rotation of the whole circle does not change who is to the immediate right of L, the answer remains uniquely determined: P is to L's right.
Why Other Options Are Wrong:
Option A (Statement 1 and 2 are not sufficient) is wrong because, as shown, together they uniquely determine that P is to the right of L.
Option C (The statements are insufficient) suggests that even with all the available statements we cannot decide, but we actually can: P is always to the right of L when the conditions are satisfied.
Option D (Statement 1 alone is sufficient) is wrong because Statement 1 alone leaves ambiguity: P could be either right or left of L.
Common Pitfalls:
A common mistake is to forget that neighbours in a circle can be permuted in more than one way if side information (left/right) is missing.
Another error is not considering all distinct circular arrangements or misinterpreting 'right of' for people facing the centre.
Final Answer:
Since only the combination of Statement 1 and Statement 2 allows us to uniquely determine who stands to the right of L, Statements 1 and 2 together are sufficient.
Discussion & Comments