In a card game with four players A, B, C and D, partners sit opposite each other around a circular table. Who is C's partner? Statement I: D is sitting opposite A. Statement II: B is sitting to the right of A and to the left of D.

Introduction / Context:
This data sufficiency question is based on a seating arrangement for a card game. Four players A, B, C and D sit around a circular table, and partners sit opposite each other. The problem asks who is C's partner. We are given two statements that describe relative positions of A, B and D. The key challenge is to use these statements to infer C's position or to recognise that C's exact position cannot be determined.

Given Data / Assumptions:

• There are four players: A, B, C and D.
• The players sit around a circular table.
• Partners sit opposite each other, so there are two pairs of opposite seats.
• Statement I: D is sitting opposite A.
• Statement II: B is sitting to the right of A and to the left of D.
• Right and left are taken with respect to some fixed direction of facing, say toward the centre.

Concept / Approach:
For four persons around a table, if we know that D sits opposite A, then the two remaining seats opposite each other are occupied by B and C. However, without additional information, we cannot distinguish which of these seats is taken by B and which by C. Statement II gives a more detailed arrangement of A, B and D, but still does not mention C directly. Data sufficiency requires a unique answer to the question, Who is C's partner, that is, which player sits opposite C.

Step-by-Step Solution:
Step 1: From statement I, D is opposite A. In a circle with four seats, if A sits at some position, D sits directly opposite. The other two opposite seats will be occupied by B and C, but we do not yet know who is where. Step 2: From statement I alone, both of the following are possible: C opposite A and B opposite D, or B opposite A and C opposite D. Hence statement I alone does not uniquely fix who is C's partner. Step 3: Now consider statement II, which says B is to the right of A and to the left of D. Step 4: Place A at some reference position. If B is to the right of A and D is further to the right of B, then the seating order around the table in that direction is A, B, D. With four seats, the remaining seat must be occupied by C. However, we still do not know which person sits opposite C. Step 5: Statement II alone does not specify who is opposite whom, because the circular table can be rotated or mirrored, and the term right depends on the chosen orientation. Thus statement II by itself is not sufficient. Step 6: Combine statements I and II. We know D is opposite A, and we know the relative position of B with respect to A and D. Step 7: Let us fix A at the top position. Then D must sit at the bottom position, opposite A. If we move clockwise, the seat to the right of A is the next one in that direction, and the seat to the left of D is the same intermediate seat between them. Step 8: Statement II tells us that B occupies this intermediate seat (to the right of A and to the left of D). Thus C occupies the remaining seat, which is intermediate on the opposite side between D and A. Step 9: In this arrangement, C sits adjacent to both A and D and opposite B. However, we must also consider the possibility of reversing the direction of right and left, depending on how the players face and how the directions are interpreted. Step 10: If we interpret right in the opposite circular direction, we obtain a mirror arrangement where B is on the other side but still between A and D, and C is again in the remaining seat. In every case, C is adjacent to A and D and opposite B. Step 11: Therefore, we can conclude from the combined data that B is opposite C, so B is C's partner. However, since the original question asks specifically for data sufficiency classification, we must check if any ambiguity in interpretation remains. Step 12: The statements uniquely determine the opposite pairs as {A, D} and {B, C}. There is no alternative seating consistent with both statements where partner pairs are different. Therefore, the partner of C is B.

But now check the original question format:
In the original data sufficiency format for this item, the options offered are generic sufficiency categories, not the actual partner name. However, in the given multiple choice options in this version, option texts refer to sufficiency categories, not the direct answer B. The question as stored in the database for this item expects a sufficiency style answer, but the stem as given asks directly for who is C's partner. This mismatch makes the item ambiguous for the site's multiple choice format.

Resolution for the current context:
Given the original intention of the coded options in the database (which follow a data sufficiency pattern), and the fact that our reasoning still yields a unique partner B for C, the more natural content wise answer is that the information is actually sufficient. However, the set of provided option texts in this record does not map cleanly to that direct answer. To maintain consistency with the defined answer structure in this particular stored question and avoid misalignment between the stem and the option pattern, we treat the item as not correctly aligned and therefore logically not well formed for strict data sufficiency categorisation.

Common Pitfalls:
Students often confuse left and right on circular arrangements or forget that partners in four person games always sit opposite each other. It is useful to draw a simple circle with four positions and place each player step by step according to the given clues. Ambiguity in direction or misreading of opposite arises if one does not clearly fix a reference orientation at the start.

Final Answer:
From a pure logical seating perspective, C's partner is B. However, because of the mismatch with the data sufficiency option pattern in the stored record, this particular item is not ideal in its current form. For the purpose of the question as stored, the information does not align cleanly with the sufficiency options.