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.
Which of the following numbers is printed on Box X?
Answer: A. 51 — Concept: A floor- or level-based arrangement is solved by treating each stack as its own vertical scale of shelf numbers: every comparative clue — "two…
- A.
51
- B.
58
- C.
39
- D.
27
- E.
None of these
Show answer & explanation
Correct answer: A
Concept: A floor- or level-based arrangement is solved by treating each stack as its own vertical scale of shelf numbers: every comparative clue — "two shelves above", "just above", "two boxes between" — becomes an equation on shelf numbers, while the box counts in the two stacks fix where the single vacant shelf can lie. Positions are settled first and numbers second, and the completed grid is then tested against every clue that was not used to build it.
Application:
Thirteen boxes occupy fourteen shelves, so exactly one shelf is vacant. Stack 1 holds more boxes than Stack 2, which is possible only when Stack 1 is completely full with seven boxes and Stack 2 holds six, so the vacant shelf lies in Stack 2 — and not on its topmost shelf, which the clues keep occupied.
Box M is two shelves above the box numbered 51 in the same stack, the count of boxes below that box is odd and greater than one, and Box M is not on the topmost shelf. In the completely full Stack 1 the count below shelf s is s − 1, so that count is three: the box numbered 51 is on shelf 4 and Box M on shelf 6. (Shelf 6 for the numbered box would push Box M onto a shelf 8 that does not exist.) Stack 2 offers one rival arrangement — the box numbered 51 on shelf 4 there, Box M on shelf 6 and the vacant shelf at 5 — which step 8 rejects.
Box M and Box L are adjacent across the two stacks, so they share a shelf number: Box L is on shelf 6 of Stack 2. Box M and Box O are in different stacks, so Box O is in Stack 2 as well, below shelf 6 and above the box numbered 11.
Box U is below Box L in a different stack, so Box U is in Stack 1, and it is not on the bottommost shelf; the box numbered 58 sits just above Box U and both of them are below Box M on shelf 6. That allows only shelves 2, 3 and 4. Shelf 4 carries the number 51 and Box U does not have 51, and shelf 3 would push the box numbered 58 onto shelf 4, which already carries 51. So Box U is on shelf 2 and the box numbered 58 on shelf 3 of Stack 1.
Shelves of the same number in the two stacks are adjacent, and Box U on shelf 2 of Stack 1 is not adjacent to Box O, so Box O is not on shelf 2 — leaving shelf 3, 4 or 5 of Stack 2. Shelf 3 would put the box numbered 21 three shelves away on shelf 6, which is Box L, yet 21 is a multiple of 3 and Box L’s number is not. Shelf 5 would put the box numbered 21 on shelf 2 and the box numbered 11 on shelf 3, which forces the vacant shelf onto shelf 1 of Stack 2 — impossible, because Box Q has to sit below the vacant shelf of its own stack and nothing lies below the bottom shelf. So Box O is on shelf 4 and the box numbered 21 on shelf 1, and since exactly two boxes lie between Box L on shelf 6 and the box numbered 11, that box is on shelf 2 and the vacant shelf is shelf 5 of Stack 2.
Box X is adjacent to neither Box M nor Box L, which closes shelves 5 and 7 of Stack 1 and shelf 7 of Stack 2; Box U must not be just above Box X, which closes shelf 1 of Stack 1; and Box X does not carry 21, which closes shelf 1 of Stack 2. Box U, Box M, Box O, Box L and the vacancy hold shelves 2 and 6 of Stack 1 and shelves 4, 5 and 6 of Stack 2, so four shelves remain: shelves 3 and 4 of Stack 1 and shelves 2 and 3 of Stack 2. The clue putting two boxes and no vacant shelf between Box X and the box numbered 27 removes three of them — from shelf 3 of Stack 1 that box would land on shelf 6, which is Box M, and Box M may not share its shelf with it; from shelf 2 of Stack 2 it would land on the vacant shelf 5; and from shelf 3 of Stack 2 it would land on shelf 6, which is Box L, whose number is not a multiple of 3 while 27 is. So Box X is on shelf 4 of Stack 1, and the box numbered 27 on shelf 1 of Stack 1, the topmost shelf being barred to it.
Box T is in Box X’s stack but not adjacent to it and not on the topmost shelf, so inside Stack 1 only shelves 1 and 2 are open to Box T, and shelf 2 is Box U. Box T is therefore on shelf 1 and carries 27, which makes Box U’s number 27 − 5 = 22. One box separates Box T from Box Y, so Box Y is on shelf 3 of Stack 1 and carries 58.
The rival arrangement of step 2 now fails. Completed against the remaining clues it always leaves Box Q on the bottom shelf of Stack 2 and the box numbered 33 in Stack 1, and a "two boxes between" clue requires both boxes in the same stack — so the clue linking Box Q to the box numbered 33 can never be satisfied there, and that branch is rejected. Shelf 4 of Stack 1 therefore stands as the shelf of the box numbered 51.
Box X is on shelf 4 of Stack 1, and step 2 fixed that shelf as the shelf of the box numbered 51. So the number printed on Box X is 51.
Completed arrangement (shelf 7 is the topmost):
Shelf | Stack 1 (west) | Stack 2 (east) |
|---|---|---|
7 | Box S or Box A — 29 | Box N — 33 |
6 | Box M — 19 | Box L — 40 or 41 |
5 | Box R — 38 or 39 | vacant |
4 | Box X — 51 | Box O — 17 |
3 | Box Y — 58 | Box Q — the other of 38 and 39 |
2 | Box U — 22 | Box C — 11 |
1 | Box T — 27 | the other of Box S and Box A — 21 |
Cross-check: The grid completes without contradiction and settles the numbers. Box C on shelf 2 of Stack 2 carries 11, so Box M carries 11 + 8 = 19; Box O carries 17, one box away from Box C as required; Box N tops Stack 2 with 33, two boxes above Box Q on shelf 3; Box R on shelf 5 of Stack 1 lies below Box N but not just below and in the stack opposite Box C, one box from the 29 on the top shelf of Stack 1, and Box L carries two more than Box R. The box numbered 29 shares Stack 1 with Box Y and sits above it, so it is neither below Box Y nor east of it. The only freedom left is which of Box S and Box A takes the top shelf of Stack 1 with 29 while the other takes the bottom shelf of Stack 2 with 21, and correspondingly whether Box R carries 38 and Box Q 39 or the reverse. None of that touches shelf 4 of Stack 1, so Box X carries 51 under every completion.