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 between Box T and Box C?

  1. A.

    Two

  2. B.

    Four

  3. C.

    Three

  4. D.

    One

  5. E.

    None of these

Show answer & explanation

Correct answer: E

Concept

This is a two-stack box-arrangement puzzle where each stack has seven shelves and, overall, exactly one shelf is vacant. The passage's own rules matter as much as the specific clues: “between” and “immediately above/below” always tie the two boxes to the SAME stack unless stated otherwise, but a plain “above/below” (without “immediately”) only compares shelf numbers and does not require the two boxes to share a stack — except when it is used to count “boxes below” a box, which is always counted within that box's own stack. Since Stack 1 must hold more boxes than Stack 2 while both have seven shelves, Stack 1 has to be the full stack (all seven shelves occupied) and the one vacant shelf sits in Stack 2. Because a “boxes between” count is only meaningful for two boxes that share a stack, the real question here is not just how many boxes sit between Box T and Box C — it is first whether they share a stack at all.

Building the grid

Start from the most rigid anchor chains and work outward:

  1. Box M sits two shelves above the box numbered 51, and more than one odd number of boxes lie below that numbered box within its own stack — only three fits both conditions, which pins the numbered-51 box four shelves up and Box M two shelves above it.

  2. Box O's shelf lies below Box M's shelf and above the numbered-11 box's shelf (a plain shelf-number comparison, since Box M and Box O are stated to be in different stacks), and Box M and Box L share the same shelf number but sit in different stacks — so Box L lands on Box M's shelf, in the other stack.

  3. Box U sits below Box L but in a different stack, with the numbered-58 box just above it in Box U's own stack, and both below Box M's shelf; this, together with the one-box gap between Box T and Box Y and the not-adjacent-but-same-stack rule for Box X and Box T, threads Box U, Box X, Box Y and Box T into the SAME full stack as Box M.

  4. Separately, Box C is fixed by the one-box gap to the numbered-17 box, by never sitting on the topmost shelf, by never sharing a stack with Box R, and by Box M's number being eight more than Box C's; working this chain independently seats Box C in the OTHER stack — the one carrying the single vacant shelf.

Locating T and C

Running every clue through to a fully filled grid: Box T settles onto the bottom shelf of the full, seven-box stack that also holds Box M, Box X, Box Y and Box U. Box C settles into the other stack entirely — the one with the vacant shelf — two shelves up from its own bottom. Box T and Box C are therefore never in the same stack.

Result

The passage states its own rule plainly: a “boxes between” count only applies “if a box is kept between two boxes” that are “in the same stack, unless stated otherwise.” Since Box T and Box C sit in different stacks, no such count exists among the listed values, so the number of boxes kept between Box T and Box C is best described as none of these.

Cross-check

Working backward confirms it: every clue that anchors Box T (the Box T-Box Y gap, the same-stack-but-not-adjacent rule with Box X, and the two-box gap to the numbered-27 box) keeps it inside the full seven-box stack with Box M, while every clue that anchors Box C (the gap to the numbered-17 box, never the topmost shelf, never sharing a stack with Box R, and the Box M–Box C number relation) keeps it in the other stack, the one with the vacant shelf. No arrangement that satisfies every clue in the passage puts Box T and Box C together, so no numeric gap — three included — can be correct.

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