Directions: Study the following information carefully and answer the questions given below.
Seven boxes – P, Q, R, S, T, U, and V are stacked one above the other but not necessarily in the same order. At most two boxes are placed below box Q. Box U is placed one of the places above box T, but not exactly above. Two boxes are placed between box R and box S, where box S is above box R. Box R is placed exactly above box Q. Box P is placed at one of the places below box S. Number of boxes above box P is the same as the number of boxes below box V. At least five boxes are placed below box S. Box T is placed near Box V.
If we rearrange all the boxes in alphabetical order from bottom to top, then the position of how many boxes remains unchanged?
- AOption (a)
One
- BOption (b)
Three
- COption (c)
Four
- DOption (d)
Five
- EOption (e)
None
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Correct answer
None
Why this answer is correct
Seven boxes P, Q, R, S, T, U, and V are stacked one above the other.
- At most two boxes are placed below box Q. (Here the word ‘at most’ means Maximum.)
- Box R is placed exactly above box Q.
Following are the possibilities we get,
| Case 1 | Case 2 | Case 3 | |
|---|---|---|---|
| Top | |||
| Box R | |||
| Box R | Box Q | ||
| Box R | Box Q | ||
| Bottom | Box Q |
- Two boxes are placed between box R and box S, where box S is above box R.
- At least five boxes are placed below box S.
Here, this statement is violated in case 1, so it is eliminated.
| Case 2 | Case 3 | |
|---|---|---|
| Top | Box S | |
| Box S | ||
| Box R | ||
| Box R | Box Q | |
| Box Q | ||
| Bottom |
- Number of boxes above box P is the same as the number of boxes below box V.
- Box P is placed at one of the places below box S.
Here, this statement is not possible in case 2, so it is eliminated and the following are the possibilities we get in case 3,
| Case 3a | Case 3b | |
|---|---|---|
| Top | Box S | Box S |
| Box P | Box V | |
| Box R | Box R | |
| Box Q | Box Q | |
| Box V | Box P | |
| Bottom |
- Box U is placed in one of the places above box T, but not exactly above.
- Box T is placed near Box V.
Here, this statement is not possible in case 3b, so it is eliminated. So, the final arrangement is,
| Boxes | |
|---|---|
| Top | Box S |
| Box P | |
| Box U | |
| Box R | |
| Box Q | |
| Box V | |
| Bottom | Box T |
If we rearrange all the boxes in alphabetical order from bottom to top, then
| Boxes | Alphabetical order | |
|---|---|---|
| Top | Box S | Box V |
| Box P | Box U | |
| Box U | Box T | |
| Box R | Box S | |
| Box Q | Box R | |
| Box V | Box Q | |
| Bottom | Box T | Box P |
Clearly, the position of None (None of the boxes) remains unchanged.
Additional Information
The word 'at least' means the minimum number, while 'at most' means the maximum number.