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Six boxes A, B, C, D, E, F of different colours are placed one above another. Also, each box has a different number of toffees. No box has the same number of toffees. Only two boxes are placed between B and the green box. No box is placed above B. Box D is placed immediately above the blue box. Only the red box is placed between the green box and A. Only one box is placed between the red and blue boxes. Only one box is placed between D and E. Only one box is placed between the orange box and C. C is not red. How many toffees does the blue box have? (I) E has more than 8 toffees, while C has more than 20 toffees. D has 21 toffees. The boxes with the lowest and second-lowest numbers of toffees have 10 and 12 toffees respectively. A, C, D and F have odd numbers of toffees. (II) A has more toffees than B but not more than D. The difference between the numbers of toffees in F and E is 7. The box with the highest number of toffees has 8 more toffees than F. The total number of toffees in B and A is 31.

1. (a) if the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient.
2. (b) if the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient.
3. (c) if the data either in statement I alone or in statement II alone are sufficient to answer the question.
4. (d) if the data even in both statements I and II together are not sufficient to answer the question.
5. (e) if the data in both statements I and II together are necessary to answer the question.

Correct answer: (e) if the data in both statements I and II together are necessary to answer the question.

Solution

The arrangement clues determine the relative positions and colours of the boxes, but not the exact toffee count of the blue box. Statement I gives partial numerical constraints, and statement II gives another set of constraints; each alone is insufficient. Together, they uniquely determine the blue box’s toffee count, so both are necessary.

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