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Data Sufficiency — Coding language: Which code word means ‘‘flower’’? Statement I: ‘‘de fu la pane’’ means ‘‘rose flower is beautiful’’ and ‘‘la quiz’’ means ‘‘beautiful tree’’. Statement II: ‘‘de la chin’’ means ‘‘red rose flower’’ and ‘‘pa chin’’ means ‘‘red tea’’. Decide which statements are sufficient to answer the question. Choose the correct sufficiency option.

Difficulty: Medium

Statement I alone is sufficient, but Statement II alone is not sufficient.
Statement II alone is sufficient, but Statement I alone is not sufficient.
Both statements I and II together are sufficient, but neither alone is sufficient.
Either statement I or statement II alone is sufficient.
Even both statements I and II together are not sufficient.

Correct Answer: Both statements I and II together are sufficient, but neither alone is sufficient.

Explanation:

From Statement I
The word set {rose, flower, is, beautiful} maps to {de, fu, la, pane} and ‘‘beautiful tree’’ maps to {la, quiz}. Hence the possible codes for ‘‘flower’’ from Statement I are among {de, fu, pane} (cannot be pinned down alone).

From Statement II
The word set {red, rose, flower} maps to {de, la, chin} and ‘‘red tea’’ maps to {pa, chin}. Thus the possible codes for ‘‘flower’’ from Statement II are among {de, la} (also not unique alone).

Combine (I + II)
Intersect the candidate sets for ‘‘flower’’: {de, fu, pane} ∩ {de, la} = {de}.Therefore, the code for ‘‘flower’’ is de.

Final Answer
Both statements I and II together are sufficient, but neither alone is sufficient.

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