Six friends A, B, C, D, E, and F are seated around a circular table facing the center. Who is seated second to the left of E?

I. C sits second to the right of D, who sits second to the right of E.

II. B and F sit opposite each other, and E sits between B and D.

Decide which of the following options is correct based on the sufficiency of the statements.

Question

Six friends A, B, C, D, E, and F are seated around a circular table facing the center. Who is seated second to the left of E?

I. C sits second to the right of D, who sits second to the right of E.

II. B and F sit opposite each other, and E sits between B and D.

Decide which of the following options is correct based on the sufficiency of the statements.

Accepted Answer

**Solution:**

1. Analyze Statement I alone:
   - D sits second to the right of E.
   - C sits second to the right of D.

From this, we can place E, then count two seats to the right to place D, and from D, count two seats to the right to place C.
   However, the positions of A, B, and F are unknown, so we cannot definitively determine who sits second to the left of E.
   Therefore, statement I alone is insufficient.

2. Analyze Statement II alone:
   - B and F sit opposite each other.
   - E sits between B and D.

This tells us E's neighbors (B and D) and that B and F are opposite.
   But the exact position of E and others around the table is not fixed, so we cannot conclusively find who is second to the left of E.
   Hence, statement II alone is insufficient.

3. Analyze both statements together:
   - From statement I, D is second to the right of E.
   - From statement II, E sits between B and D, and B and F are opposite.

Using both, we can fix the positions of E, D, B, F, and C around the table.
   Once these are fixed, the position second to the left of E can be identified uniquely.

**Answer:** Both statements I and II together are necessary to answer the question.

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