Six boxes — A, B, C, D, E and F — are kept one above another in a stack, but not necessarily in the same order. How many boxes are kept above box D?

Statement I: Only two boxes are kept below box E. Only one box is kept between box E and box B. Box C is kept immediately above box B. Box D is kept above box F but below box A.
Statement II: Box C is kept four boxes above box F. Box C and box A are kept adjacent to each other. More than two boxes are kept between box A and box E. Box B is kept below box D.

The question below consists of two statements numbered I and II given below it. You have to decide whether the data provided in the statement is sufficient to answer the question.

The correct answer is: Data given in statement II alone is sufficient to answer.

Let's analyze the problem step-by-step to determine the sufficiency of the statements. We have six boxes: A, B, C, D, E, and F kept one above another in a stack (positions 1 to 6 from bottom to top, or 6 to 1 from top to bottom).

Analyzing Statement I:
1. "Only two boxes are kept below box E." This means E is at the 3rd position from the bottom (Position 3). Let's denote positions from 6 (top) to 1 (bottom):
Position 6:
Position 5:
Position 4:
Position 3: E
Position 2:
Position 1:
2. "Only one box is kept between box E and box B." Since E is at Position 3, B can be at Position 5 or Position 1.
- Case 1: B is at Position 5.
- Case 2: B is at Position 1.
3. "Box C is kept immediately above box B."
- In Case 1 (B is at Position 5), C must be immediately above B (Position 6).
- In Case 2 (B is at Position 1), C must be immediately above B (Position 2).
Let's represent the configurations:
Case 1:
6: C
5: B
4:
3: E
2:
1:
Case 2:
6:
5:
4:
3: E
2: C
1: B
4. "Box D is kept above box F but below box A." This means the relative order is A ... D ... F.
- In Case 1, we have three empty slots: 4, 2, and 1. Placing A, D, F in these slots gives: A at 4, D at 2, and F at 1. This is a complete arrangement: C (6), B (5), A (4), E (3), D (2), F (1). In this case, 4 boxes (C, B, A, E) are above D.
- In Case 2, we have three empty slots: 6, 5, and 4. Placing A, D, F in these slots gives: A at 6, D at 5, and F at 4. This is a complete arrangement: A (6), D (5), F (4), E (3), C (2), B (1). In this case, 1 box (A) is above D.
Since Statement I gives two different possible positions for D, we cannot uniquely determine how many boxes are kept above D. Thus, Statement I alone is not sufficient.

Analyzing Statement II:
1. "Box C is kept four boxes above box F." This means there are three boxes between C and F (i.e., C is at position x and F is at position x - 4). The possible positions for (C, F) are:
- Case A: C at 6, F at 2
- Case B: C at 5, F at 1
2. "Box C and box A are kept adjacent to each other."
- In Case A (C at 6), A must be at 5.
- In Case B (C at 5), A can be at 6 or 4.
3. "More than two boxes are kept between box A and box E."
- Let's test Case A (C at 6, A at 5, F at 2):
We need more than 2 boxes (i.e., at least 3 boxes) between A (5) and E. The positions between 5 and E must be 4, 3 (if E is at 1) or similar. Let's see: if E is at 1, there are three boxes (4, 3, 2) between A (5) and E (1). Since F is already at 2, E must be at 1. So, E is at 1.
Let's check the slots for Case A: 6 (C), 5 (A), 4 (empty), 3 (empty), 2 (F), 1 (E). The remaining boxes to place are B and D in slots 4 and 3. The next clue says "Box B is kept below box D." So D must be at 4 and B must be at 3. This gives the unique stack: C (6), A (5), D (4), B (3), F (2), E (1). Let's verify the condition: "More than two boxes are kept between box A and box E": A is at 5, E is at 1. The boxes between them are at positions 4, 3, and 2 (D, B, and F). There are exactly 3 boxes, which is "more than two". All conditions are satisfied. Here, the boxes above D (4) are A and C (2 boxes).
- Let's test Case B (C at 5, F at 1):
Subcase B1: A is at 6.
We need more than 2 boxes between A (6) and E. This means E can only be at 2 or 1. But F is at 1, so E must be at 2. The positions between A (6) and E (2) are 5, 4, 3 (three positions), which satisfies the condition. The slots are: 6 (A), 5 (C), 4 (empty), 3 (empty), 2 (E), 1 (F). The remaining boxes B and D must go to 4 and 3. Since B is below D, D is at 4 and B is at 3. This gives: A (6), C (5), D (4), B (3), E (2), F (1). However, let's re-verify the conditions. This also gives a valid arrangement where D is at 4 (2 boxes above D).
Subcase B2: A is at 4.
We need more than 2 boxes between A (4) and E. The only way to have at least 3 boxes between 4 and E is if E is at a position separated by at least 3 slots, which is impossible in a 6-box stack when A is at 4.
Wait, let's check if there is a unique answer for the number of boxes above D in all valid configurations under Statement II:
- In Case A: Stack is C (6), A (5), D (4), B (3), F (2), E (1). The number of boxes above D is 2 (C and A).
- In Case B1: Stack is A (6), C (5), D (4), B (3), E (2), F (1). The number of boxes above D is 2 (A and C).
In both valid cases, box D is positioned at index 4 (from the bottom), meaning there are exactly 2 boxes kept above box D (positions 5 and 6). Therefore, Statement II alone provides a unique and sufficient answer to the question.