Directions (22-24): Each of the questions below, consist of a question and three statements numbered I, II and III. You have to decide whether the data provided in the statements are sufficient to answer the question. Read the three statements and Give answer

Statement I: K sits second to the right of B. Two persons sit between K and P. Only one person sits between B and T.
Statement II: N is the only person sits to the right of P. The number of persons sits between K and N is one more than the number of persons sits between D and T.
Statement III: F sits adjacent to D who sits fourth to the right of C.

Correct Answer: If the data in all three statements I, II and III together are necessary to answer the question.

To determine if the statements are sufficient to answer the question regarding the linear seating arrangement (such as determining the total number of persons or the exact position of a person), we analyze the statements step-by-step:

Step 1: Analyze Statement I
1. K sits second to the right of B. This gives the relative position: B _ K.
2. Two persons sit between K and P. This leads to two cases:
Case A: B _ K _ _ P
Case B: P _ _ B _ K
3. Only one person sits between B and T. This means T is second to the left or second to the right of B.
Since K is already second to the right of B, T must be second to the left of B:
For Case A: T _ B _ K _ _ P
For Case B: P _ T B _ K
Since we cannot determine a unique arrangement or the total number of positions, Statement I alone is not sufficient.

Step 2: Analyze Statement II
1. N is the only person who sits to the right of P, which means P is second from the right end and N is at the extreme right end (... P N).
2. The number of persons sitting between K and N is one more than the number of persons between D and T.
Statement II alone does not provide the positions of B, K, T, or C, and is therefore not sufficient.

Step 3: Analyze Statement III
1. F sits adjacent to D, and D sits fourth to the right of C.
This gives the relation: C _ _ _ D, with F being adjacent to D (either F C _ _ _ D, C _ _ F D, or C _ _ _ D F).
Statement III alone provides no connection to B, K, P, T, or N, and is therefore not sufficient.

Step 4: Combine Statements I, II, and III
1. From Statement I and II, using Case A: T _ B _ K _ _ P N.
Here, the number of persons sitting between K and N is 3 (namely the two vacant positions and P).
2. According to Statement II, the number of persons between D and T must be:
3 - 1 = 2 persons.
Since D must be 2 places away from T, D can be placed relative to T. Since T is near the left, D must be to the right of T, placing D in the vacant seat between B and K: T _ B D K _ _ P N.
3. Now, incorporating Statement III: D sits fourth to the right of C. This means C is 4 places to the left of D. Since D is in position 4 (with T at 1, B at 3), C can be uniquely positioned to the left of T.
4. Also, F sits adjacent to D, which helps place F uniquely.
Only by combining all three statements can we fix the relative and absolute positions of all individuals (C, F, T, B, D, K, P, and N) and determine the complete arrangement. Therefore, all three statements are necessary.