Directions : Study the following information carefully and answer the…
2023
Directions : Study the following information carefully and answer the questions given below:
Thirteen boxes are kept in two stacks i.e., Stack 1 and Stack 2 where Stack 1 is in west of Stack 2. Each stack has seven shelves and one box is placed in each shelf. Stack 1 contains more boxes than Stack 2. Different numbers are printed on each of the boxes. If a box is kept between two boxes, then these boxes are kept in the same stack, unless stated otherwise. If a box is immediately above or below another box then they are in the same stack unless stated otherwise. One of the shelves is vacant in any of the stack. Adjacent shelf means just above, just below shelf of same stack and immediate left/right shelf of another stack. Box M is kept two shelves above the box which has number 51 on it. More than one odd number of boxes are kept below the box which has number 51 on it. Box M and the box which has number 21 on it is not kept in the topmost shelf. Two boxes are kept between Box L and the box which has the number 11 on it. Box M and Box L are kept in the adjacent shelf of different stacks. Box O’s shelf is below box M’s shelf and above the shelf of the box which has number 11 on it. Two boxes are kept between Box O and the box which has number 21 on it (no vacant shelf between them). Box M and Box O are not kept in the same stack. Box O and Box X do not have number 51 and number 21 on it respectively. Two boxes are kept between Box X and the box which has number 27 on it (no vacant shelf between them). Box M and the box which has number 27 on it, are neither kept in the adjacent shelf nor in the same shelf. Neither the topmost shelf is vacant nor the shelf just below box O is vacant. Box X and the box which has number 21 on it are not kept in the adjacent shelf of Box L. Neither Box X and Box M are kept in the adjacent shelf nor the box which has number 27 on it is kept in the topmost shelf. The box which has number 58 on it is kept just above Box U and these boxes are kept below box M. Box U neither has number 11 on it nor it is placed in the adjacent shelf of Box O. Box U is kept below Box L (in different stack) but not on the bottommost shelf. One box is kept between Box T and Box Y. Box X and Box T are not kept in the adjacent shelf but kept in the same stack. Box U neither have number 51 on it nor it is kept just above Box X. Box T is neither kept in the topmost shelf nor has number 21 on it. Two boxes are kept between the Box Q and the box which has number 33 on it. Box L and Box O don’t have the number of multiple of 3 on it. Box Q is not placed just above Box X. Box Q is placed below the vacant shelf in same stack but not just below. Box R is kept below Box N but not just below. Box N and Box T are not placed in the same stack. One box is placed between Box R and the box which has number 29 on it. The box which has number 29 on it is neither kept in the east of Box Y nor below box Y. The number on Box L is two more than the number on Box R. The number on Box U is 5 less than the number on Box T. One box is placed between the box which has number 17 on it and Box C. One box is kept between the Box S and the box which has number 38 on it. Box C and Box R are not placed in the same stack. Box C is not placed in the topmost shelf. One Box is placed between the Box A and the box which has number 39 on it. The number on Box M is 8 more than the number on Box C.
How many boxes are kept above box M in the same stack?
- A.
Two
- B.
One
- C.
Three
- D.
Four
- E.
None of these
Show answer & explanation
Correct answer: B
Concept
In a two-stack (column) puzzle, every positional clue ('two shelves above', 'X boxes between', 'adjacent shelf of different stacks', 'just above/below') is a constraint that pins a box to a fixed shelf number. The method is to convert each clue into a relation, lock the most restrictive ones first to fix anchor positions, then propagate. 'How many boxes are above box M in the same stack' is read directly off M's final shelf number once the grid is solved.
Building the grid
There are 13 boxes across two stacks of seven shelves each, so exactly one shelf is vacant. Since Stack 1 holds more boxes than Stack 2, Stack 1 is full (7 boxes) and the single vacant shelf lies in Stack 2 (6 boxes). Working the anchor clues in order:
Box M sits two shelves above box 51, with more than one odd-numbered box below it; combined with 'O is below M and above box 11' and the 'two boxes between O and 21' / 'two boxes between X and 27' (no vacancy between) chains, M is forced to shelf 2 of Stack 1.
Box L is in the adjacent shelf of a different stack from M, placing L at shelf 2 of Stack 2; box 51 (X) lands at shelf 4 of Stack 1 and box 29 (O) at shelf 4 of Stack 2.
'58 just above U, both below M' fixes box 58 (Y) at shelf 5 and U at shelf 6 of Stack 1; box 27 (T) takes shelf 7 of Stack 1.
Q lies below the vacant shelf (not just below) with two boxes between Q and 33; this forces the vacant shelf to shelf 3 of Stack 2, box 33 (N) to shelf 1, and Q to shelf 5 of Stack 2.
R is below N (not just below) with one box between R and 29, giving R (=box 11) shelf 6 of Stack 2; the remaining 17 / 38 / 39 and C-R different-stack clues place S(17) at shelf 1 and C(38) at shelf 3 of Stack 1, with A(21) at shelf 7 of Stack 2.
Final arrangement (shelf 1 = top)
Shelf | Stack 1 (West) | Stack 2 (East) |
|---|---|---|
1 | S (17) | N (33) |
2 | M (46) | L (13) |
3 | C (38) | Vacant |
4 | X (51) | O (29) |
5 | Y (58) | Q (39) |
6 | U (22) | R (11) |
7 | T (27) | A (21) |
Application
Box M occupies shelf 2 of Stack 1. The only shelf above it in the same stack is shelf 1, which holds box S. Hence exactly one box is kept above box M in its stack.
Cross-check
The number relations confirm the grid: U is 5 less than T (22 = 27 − 5), L is 2 more than R (13 = 11 + 2), and M is 8 more than C (46 = 38 + 8). All three hold, so the arrangement is consistent and the count above M is one.