Study the following information carefully and answer the questions given below.
Seven boxes- A, B, C, D, E, F and G are kept one above another in a single stack but not necessarily in the same order.
Only two boxes are kept between box A and box F. Box B is kept two boxes above box F. Only three boxes are kept between box B and box G. The number of boxes kept above box G is one more than the number of boxes kept below box C. Box D is kept two boxes below box C. Box E does not kept below box D.
If all the boxes are arranged in alphabetical order from top to bottom, then how many boxes remain unchanged in their position?
Correct Answer :
Two
Solution :
The correct answer is Two.
Let us determine the correct sequence of the boxes from top to bottom (positions 1 to 7) step-by-step based on the given clues:
1. Box B is kept two boxes above box F:
This means the arrangement must look like: B, _, F.
2. Only two boxes are kept between box A and box F:
This gives us two cases:
- Case A: A is above F. Since B is two boxes above F, A must be above B, leading to the sequence: A, B, _, F.
- Case B: A is below F. The sequence becomes: B, _, F, _, _, A.
3. Only three boxes are kept between box B and box G:
- In Case A (A, B, _, F), G must be below B (since B is near the top). So, G is placed at the 4th position below B, giving: A, B, _, F, _, G (6 boxes).
- In Case B (B, _, F, _, _, A), G is placed at the 4th position below B: B, _, F, _, G, A (6 boxes).
4. Let's test the remaining conditions on Case B (B, _, F, _, G, A):
Since there are 7 boxes, there is one more position to be determined. Let the positions from 1 to 7 be:
Pos 1: _
Pos 2: B
Pos 3: _
Pos 4: F
Pos 5: _
Pos 6: G
Pos 7: A
5. The number of boxes kept above box G is one more than the number of boxes kept below box C:
- From the arrangement, G is at position 6. The number of boxes above G is 5.
- Therefore, the number of boxes below C must be 5 - 1 = 4.
- For C to have exactly 4 boxes below it, C must be placed at position 3.
6. Box D is kept two boxes below box C:
- Since C is at position 3, D must be at position 5 (3 + 2 = 5).
- Now, the remaining empty position is 1, which must be occupied by E.
7. Verify the remaining condition: "Box E is not kept below box D":
- E is at position 1 and D is at position 5. Since E is above D, this condition is satisfied.
The final arrangement from top to bottom is:
1. E
2. B
3. C
4. F
5. D
6. G
7. A
Now, let's compare this arrangement with the alphabetical order (A to G) from top to bottom:
Original Position vs. Alphabetical Position:
Position 1: E vs. A (Changed)
Position 2: B vs. B (Unchanged)
Position 3: C vs. C (Unchanged)
Position 4: F vs. D (Changed)
Position 5: D vs. E (Changed)
Position 6: G vs. F (Changed)
Position 7: A vs. G (Changed)
Therefore, only two boxes (B and C) remain unchanged in their positions.
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