Directions (76-80) :Study the following information carefully and answer the questions given below:

Nine boxes are placed one above the other. The bottommost shelf is numbered as 1 and just above it is numbered as 2 and so on till the topmost shelf is numbered as 9.

Box C is placed at the position which is a multiple of 3. Three boxes are placed between Box C and Box H. There are as many boxes placed below Box H as above Box L. Box G is placed just above Box E but not placed just below Box C. Box D is placed below Box E. More than two boxes are placed between Box M and Box B. Box F is placed above Box M.

The number of boxes placed between Box D and Box M is half of the number of boxes placed above Box _____.

Correct Option/Answer: Box E

Let us solve the puzzle step-by-step to find the arrangement of the nine boxes placed on shelves numbered 1 to 9 from bottom to top.

Step 1: Analyze the given conditions

1. Box C is placed at a position which is a multiple of 3. So, Box C can be on shelf 3, 6, or 9.
2. Three boxes are placed between Box C and Box H.
3. The number of boxes placed below Box H is equal to the number of boxes placed above Box L.
4. Box G is placed just above Box E (i.e., G is directly above E), but G is not placed just below Box C.
5. Box D is placed below Box E.
6. More than two boxes are placed between Box M and Box B.
7. Box F is placed above Box M.

Step 2: Determine the positions of Box C, Box H, and Box L

Let's consider the possible positions for C:

Case 1: C is on shelf 9
If C = 9, then H must be on shelf 5 (since 3 boxes are between 9 and 5: shelves 8, 7, 6).
If H = 5, the number of boxes below H is 4. Thus, the number of boxes above L must also be 4, which puts L on shelf 5. But H is already on shelf 5, so Case 1 is invalid.

Case 2: C is on shelf 3
If C = 3, then H must be on shelf 7 (since 3 boxes are between 3 and 7: shelves 4, 5, 6).
If H = 7, the number of boxes below H is 6. Thus, the number of boxes above L must be 6, which puts L on shelf 3. But C is already on shelf 3, so Case 2 is invalid.

Case 3: C is on shelf 6
If C = 6, H can be on shelf 2 (since 3 boxes are between 6 and 2: shelves 5, 4, 3).
If H = 2, the number of boxes below H is 1. Thus, the number of boxes above L must be 1, which puts L on shelf 8.

Step 3: Place the remaining boxes

Currently placed:
Shelf 9:
Shelf 8: L
Shelf 7:
Shelf 6: C
Shelf 5:
Shelf 4:
Shelf 3:
Shelf 2: H
Shelf 1:

We know Box G is placed just above Box E (G-E pair), and G is not just below C (so G cannot be on shelf 5).
Also, D is below E. So E cannot be on shelf 1.
Let's test available consecutive slots for G and E:

- If G = 5 and E = 4: Invalid because G cannot be just below C (shelf 6).
- If G = 4 and E = 3: Then D is below E, so D = 1. The remaining empty shelves are 9, 7, 5. The remaining boxes are B, M, F.
Since Box F is above Box M, and more than two boxes are between Box M and Box B:
If B = 9, M = 5, then F = 7 (F is above M). The number of boxes between M (shelf 5) and B (shelf 9) is 3 (shelves 6, 7, 8), which satisfies "more than 2 boxes".

Let's check all conditions for this complete arrangement:

Shelf 9: B
Shelf 8: L
Shelf 7: F
Shelf 6: C
Shelf 5: M
Shelf 4: G
Shelf 3: E
Shelf 2: H
Shelf 1: D

Verification:
1. C is at shelf 6 (multiple of 3) - True.
2. 3 boxes between C (6) and H (2) - True (shelves 5, 4, 3).
3. Boxes below H (1) = Boxes above L (1) - True.
4. G (4) is just above E (3) and G is not just below C (6) - True.
5. D (1) is below E (3) - True.
6. More than 2 boxes between M (5) and B (9) - True (3 boxes: shelves 6, 7, 8).
7. F (7) is above M (5) - True.

Step 4: Answer the specific question

The question asks: "The number of boxes placed between Box D and Box M is half of the number of boxes placed above Box _____."

1. Box D is on shelf 1 and Box M is on shelf 5. The boxes between D and M are on shelves 2, 3, and 4. So, there are 3 boxes placed between Box D and Box M.
2. 3 is half of 6 ($3=\frac{6}{2}$).
3. We need to find which box has 6 boxes placed above it. The box with 6 boxes above it must be placed on shelf 3 (since $9-3=6$).
4. Box E is placed on shelf 3.

Therefore, the number of boxes placed between Box D and Box M is half of the number of boxes placed above Box E.