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.

How many boxes are placed below Box M?

Correct Option: Four

Let us solve the puzzle step-by-step to find the exact arrangement of the nine boxes placed from shelf 1 (bottommost) to shelf 9 (topmost).

Step 1: Determine the positions of C and H

Box C is placed at a position that is a multiple of 3. So, C can be at shelf 3, 6, or 9.

Three boxes are placed between Box C and Box H.

• Case 1: If C is at shelf 9, then H is at shelf 5 (3 boxes between: 8, 7, 6).

• Case 2: If C is at shelf 6, then H can be at shelf 2 (3 boxes between: 5, 4, 3).

• Case 3: If C is at shelf 3, then H can be at shelf 7 (3 boxes between: 4, 5, 6).

Step 2: Place Box L using Box H

There are as many boxes placed below Box H as above Box L.

• In Case 1 (H at 5): 4 boxes below H, so 4 boxes above L ⇒ L is at shelf 5. But H is already at 5, so Case 1 is invalid.

• In Case 2 (H at 2): 1 box below H, so 1 box above L ⇒ L is at shelf 8.

• In Case 3 (H at 7): 6 boxes below H, so 6 boxes above L ⇒ L is at shelf 3. But C is already at 3, so Case 3 is invalid.

Therefore, only Case 2 is valid:

Shelf 8: L

Shelf 6: C

Shelf 2: H

Step 3: Place Box G, Box E, and Box D

• Box G is placed just above Box E (GE pair), but G is not placed just below C (so G cannot be at shelf 5).

• Box D is placed below Box E.

Available vacant positions are shelves 9, 7, 5, 4, 3, 1.

If G is at shelf 4 and E is at shelf 3 (GE pair), then D can be at shelf 1 (since D is below E). This satisfies all conditions for G, E, and D.

Now the arrangement looks like:

Shelf 9: Vacant (F/M/B)

Shelf 8: L

Shelf 7: Vacant (F/M/B)

Shelf 6: C

Shelf 5: Vacant (F/M/B)

Shelf 4: G

Shelf 3: E

Shelf 2: H

Shelf 1: D

Step 4: Place Box F, Box M, and Box B

The remaining empty shelves are 9, 7, and 5.

• Box F is placed above Box M.

• More than two boxes are placed between Box M and Box B.

If B is placed at shelf 9 and M is placed at shelf 5, the number of boxes between M and B is 3 (shelves 6, 7, 8), which is "more than two".

F is then placed at shelf 7, which is above M (shelf 5).

Final Arrangement from top to bottom (Shelf 9 to 1):

Shelf 9: Box B

Shelf 8: Box L

Shelf 7: Box F

Shelf 6: Box C

Shelf 5: Box M

Shelf 4: Box G

Shelf 3: Box E

Shelf 2: Box H

Shelf 1: Box D

Conclusion:

Box M is on shelf 5. The boxes placed below Box M are at shelves 4, 3, 2, and 1, which equals 4 boxes (Box G, Box E, Box H, and Box D).

Therefore, there are Four boxes placed below Box M.