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.
Four of the following five are alike in a certain way and hence form a group. Which of the following does not belong to that group?
Correct Answer :
Box E
Solution :
The correct option is Box E.
Step 1: Understand the given positions and constraints
There are 9 shelves numbered 1 (bottommost) to 9 (topmost).
1. Box C is placed at a shelf number which is a multiple of 3. So, C can be at 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 (G is immediately above E), but G is not placed just below Box C.
5. Box D is placed somewhere below Box E.
6. More than two boxes (i.e. at least 3 boxes) are placed between Box M and Box B.
7. Box F is placed somewhere above Box M.
Step 2: Determine the positions of C, H, and L
Case 1: If C is at shelf 9:
Three boxes between C and H means H is at shelf 5.
Below H (shelf 5), there are 4 boxes (shelves 1 to 4). So, above L there must be 4 boxes, which means L is at shelf 5. But H is already at shelf 5, so Case 1 is invalid.
Case 2: If C is at shelf 6:
Three boxes between C and H means H could be at shelf 2.
Below H (shelf 2), there is 1 box. So, above L there must be 1 box, placing L at shelf 8.
Case 3: If C is at shelf 3:
Three boxes between C and H means H is at shelf 7.
Below H (shelf 7), there are 6 boxes. So, above L there must be 6 boxes, placing L at shelf 3. But C is already at shelf 3, so Case 3 is invalid.
Thus, Case 2 is the only valid arrangement for C, H, and L:
Shelf 8 = L
Shelf 6 = C
Shelf 2 = H
Step 3: Place the remaining boxes
Currently available shelves: 9, 7, 5, 4, 3, 1.
Since Box G is placed just above Box E, they must occupy consecutive empty shelves (G, E).
Possible consecutive pairs of empty shelves are (5, 4) or (4, 3).
Note: G cannot be placed just below C (shelf 6), so G cannot be at shelf 5. Therefore, G and E must be at shelves 4 and 3 respectively.
So, Shelf 4 = G, Shelf 3 = E.
Since Box D is placed below Box E (shelf 3), Box D must be at shelf 1.
So, Shelf 1 = D.
Now, the remaining empty shelves are 9, 7, and 5 for boxes F, M, and B.
We know Box F is placed above Box M, and more than 2 boxes are placed between M and B.
With empty shelves at 9, 7, 5, the gap between shelf 9 and shelf 5 is 3 boxes (shelves 6, 7, 8 are between 5 and 9).
Thus, the two boxes with more than 2 boxes between them must be at shelf 9 and shelf 5.
Since Box F is above M, F can be at shelf 9 or 7. If B is at shelf 9, then M is at shelf 5, and F is at shelf 7 (F is above M).
If B is at shelf 5, then M is at shelf 9, but F must be above M, which would be impossible since 9 is the top shelf.
Therefore:
Shelf 9 = B
Shelf 7 = F
Shelf 5 = M
Final Arrangement from Top (9) to Bottom (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
Step 4: Find the odd one out
Let's check the shelf numbers for each given box:
1. Box E is at shelf 3 (odd shelf number)
2. Box H is at shelf 2 (even shelf number)
3. Box L is at shelf 8 (even shelf number)
4. Box C is at shelf 6 (even shelf number)
5. Box G is at shelf 4 (even shelf number)
All boxes except Box E are placed on even-numbered shelves. Thus, Box E does not belong to the group.
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