18Directions: Each question below is followed by two statements numbered I and…

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18

Directions: Each question below is followed by two statements numbered I and II. You have to decide whether the data provided in the statements is sufficient to answer the question. Read both statements carefully and give answer:

Six boxes, J, K, L, M, N, and O, are stacked one above the other in a vertical arrangement, not necessarily in the same order. Which box is kept third from the bottom?

Statement I: Box L is kept immediately above box M. Box J is kept two boxes above box M. Box N is adjacent to box M but below box K.

Statement II: Box K is kept above box N. Box O is kept below box J. More than one box is placed between box K and box O. Box M is not kept at the top or bottom.

  1. A.

    Data given in statement I alone is sufficient to answer

  2. B.

    Data given in both statements I and II together are sufficient to answer

  3. C.

    Data given in statement II alone is sufficient to answer

  4. D.

    Data given in either statement I alone or statement II alone is sufficient to answer

  5. E.

    Data given in both statements I and II together are not sufficient to answer

Attempted by 2 students.

Show answer & explanation

Correct answer: B

Concept: A data-sufficiency statement (or a combination of statements) is sufficient for a question only when it forces the unknown down to exactly one configuration; if two or more layouts stay consistent with the clues given and disagree on the value being asked, that data does not decide the question.

Statement I alone: L sits immediately above M, J sits two positions above M, and N is adjacent to M but below K.

  1. Since L is directly above M and N must also be adjacent to M, N has to occupy the slot immediately below M (the slot above M is already taken by L).

  2. With N = M − 1, L = M + 1 and J = M + 2 all needing to fit inside six stacked slots (1 to 6, bottom to top), M can only be 2, 3 or 4.

  3. If M = 4, the two boxes left over for K and O occupy slots 1 and 2 — both below N (slot 3) — so neither can be 'above N,' which the clue about N being below K requires; M = 4 is impossible.

  4. If M = 2, boxes N, M, L, J occupy slots 1–4, leaving slots 5 and 6 for K and O in either order — this is a valid layout.

  5. If M = 3, boxes N, M, L, J occupy slots 2–5, leaving slots 1 and 6 for K and O; K must be above N (slot 2), so K takes slot 6 and O takes slot 1 — this is also a valid layout.

  6. Two different layouts (M in slot 2, or M in slot 3) both satisfy every clue in Statement I, and they place a different box third from the bottom in each — so Statement I alone does not fix the answer.

Statement II alone: K is above N, O is below J, more than one box sits between K and O, and M is neither at the top nor the bottom. These clues never mention L at all, so its slot is left completely open; multiple full six-box arrangements can satisfy every one of these conditions while disagreeing on which box ends up third from the bottom — Statement II alone does not fix the answer either.

Both statements together:

  1. Statement I narrows the layout to exactly two candidates: M in slot 2 (with K and O filling slots 5 and 6 in some order) or M in slot 3 (with K in slot 6 and O in slot 1).

  2. Statement II adds that O must sit below J. In the M = 2 candidate, J occupies slot 4, but the only slots left for O are 5 and 6 — both above J, not below — so this candidate is ruled out.

  3. In the M = 3 candidate, O is in slot 1 and J is in slot 5, so O is below J, exactly as Statement II requires; every other clue in both statements also checks out for this layout.

  4. Only the M = 3 layout survives once both statements are applied together, so the stack is fully and uniquely determined: O, N, M, L, J, K from bottom to top.

Cross-check: In the surviving layout (slot 1→6: O, N, M, L, J, K): L is immediately above M ✓; J is two slots above M ✓; N is adjacent to M and below K ✓ (Statement I); K is above N ✓; O is below J ✓; K and O are four slots apart, more than one box between them ✓; M sits at slot 3, neither top nor bottom ✓ (Statement II). Every clue holds, confirming this is the only valid stack.

Answer: Statement I alone and Statement II alone are each insufficient, but the two together fix the stack uniquely, with M third from the bottom — so the data in both statements together, but not either alone, is sufficient to answer the question.

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