The query filters only on the sizes field, so the most direct supporting index is a single-field index on sizes. Because sizes contains arrays, MongoDB automatically treats the resulting index as a multikey index and creates index entries derived from the array elements. That allows the query { sizes: 'M' } to locate matching documents through the index rather than scanning every document in the collection. Option B indexes item, which is not part of the predicate and therefore does not help this query. Option C contains sizes, but _id is the leading key and the query provides no equality restriction on _id; this prevents efficient use of the later key as a standalone prefix for the query. Option D has the same structural problem because item precedes sizes and is not constrained. MongoDB's index-prefix rules make a targeted { sizes: 1 } index the strongest choice here. In a real workload, DBAs should also consider write overhead and whether additional queries can share a compound index before creating redundant indexes. For this single query pattern, option A is optimal.

Study Guide reference/topic:Indexing and Query Optimization - multikey indexes, array fields, index prefixes, and query support.

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