Directions : Each of the questions below, consist of a question and three…

2024

Directions : Each of the questions below, consist of a question and three statements numbered I, II and III. You have to decide whether the data provided in the statements are sufficient to answer the question. Read the three statements and Give answer

Five bags of different colours i.e., grey, brown, cyan, orange and golden are placed one above another on different shelves but not necessarily in the same order. The bottommost shelf is numbered as 1, just above it is numbered as 2 and so on till the topmost shelf is numbered as 5. Which among the following bag is placed immediately below the grey colour bag?
Statement I: One bag is placed between brown colour bag and grey colour bag which is placed immediately below orange colour bag. Two bags are placed between golden colour bag and cyan colour bag.
Statement II: Brown colour bag is placed immediately below golden colour bag and neither of them is placed adjacent to cyan colour bag. One bag is placed between cyan colour bag and grey colour bag.
Statement III: Two bags are placed between orange colour bag and brown colour bag. Grey colour bag is placed at the prime numbered shelf and two bags below the cyan colour bag.

  1. A.

    Both statements I and II together are necessary to answer the question whereas statement III alone is not sufficient to answer the question

  2. B.

    Only statement III alone is sufficient to answer the question whereas both statements I and II are not sufficient to answer the question

  3. C.

    All the three statements together are not sufficient to answer the question

  4. D.

    Any two of the given statements are necessary to answer the question

  5. E.

    Only statement II alone is sufficient to answer the question whereas both statements I and III are not sufficient to answer the question

Show answer & explanation

Correct answer: B

Concept

In a data-sufficiency arrangement question, a statement is SUFFICIENT only if it forces a SINGLE, unique answer to the asked question. If a statement still permits two or more valid arrangements that give different answers, it is NOT sufficient — even if it fixes many positions. So we test each statement independently and ask: does it pin down exactly one bag immediately below grey?

Application — Statement I

One bag lies between brown and grey; grey is immediately below orange (orange = grey + 1); two bags lie between golden and cyan. These clues allow two valid stacks, and in them the bag immediately below grey comes out differently (cyan in one, golden in the other). Two different answers → NOT sufficient.

Application — Statement II

Brown is immediately below golden (golden = brown + 1); neither brown nor golden is adjacent to cyan; one bag lies between cyan and grey. This too leaves two valid stacks, giving orange in one and golden in the other for the bag below grey. Two different answers → NOT sufficient.

Application — Statement III

Two bags lie between orange and brown (so |orange − brown| = 3); grey is on a prime-numbered shelf (2, 3 or 5) and is two bags below cyan (so cyan = grey + 2). Work the clues together — the prime + two-below-cyan condition alone is NOT enough, and it is the orange–brown spacing that removes the second case:

  1. grey prime with cyan = grey + 2 leaves two cases: grey = 2 with cyan = 4, or grey = 3 with cyan = 5 (grey = 5 would put cyan on shelf 7, which does not exist).

  2. Test grey = 2, cyan = 4: shelves 1, 3, 5 remain for brown, orange, golden, but no placement gives |orange − brown| = 3, so this case is impossible and is eliminated.

  3. Only grey = 3, cyan = 5 survives. Then orange and brown take shelves 1 and 4 (the only pair three apart), in either order.

  4. The lone remaining shelf 2 must hold golden, which therefore sits immediately below grey on shelf 3.

Swapping orange and brown between shelves 1 and 4 does not change what is below grey, so the answer is fixed. Single, unique answer (golden) → Statement III ALONE is sufficient.

Cross-check / Conclusion

Statement I yields two answers and Statement II yields two answers, so neither alone resolves the stack; Statement III pins exactly one bag (golden) immediately below grey. Hence only Statement III alone is sufficient, while statements I and II are not — which is the marked answer.

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