Sapphire : Emerald : Diamond :: From the options given, choose the item that belongs to the same category of precious gemstones (maintain the same-class/set relationship and ignore metals or alloys).

Introduction / Context:
Analogy questions frequently test your ability to recognize a common property shared by all members of a given set and then extend that membership to a correct fourth item. In the stem, the items “Sapphire,” “Emerald,” and “Diamond” are all well-known precious gemstones used in jewelry and valued for their rarity, hardness, and brilliance. The task is to pick, from the options, the item that belongs to the same class (precious gemstones), not merely anything valuable or shiny.

Given Data / Assumptions:

• Sapphire, emerald, and diamond are categorized as precious gemstones.
• The correct answer must be another gemstone of comparable category.
• Some options may be valuable substances (e.g., metals) or materials (e.g., alloys) but are not gemstones.
• We ignore market price fluctuations; the analogy is about category/class, not current value.

Concept / Approach:
The governing relation here is “members of the same set.” Specifically, it is a taxonomy/class-membership analogy: all given exemplars are gemstones. Therefore, the correct completion must be another gemstone. Precious metals (gold, silver) and alloys (bronze) are valuable materials but do not belong to the gemstone category. A canonical gemstone that fits the same class as sapphire, emerald, and diamond is “ruby,” which, like sapphire, is a corundum mineral used as a precious stone.

Step-by-Step Solution:
1) Identify the shared property among the given three: they are all precious gemstones (not metals, not alloys).2) Scan the options for a member of the same class: Ruby (gemstone), Gold (metal), Silver (metal), Bronze (alloy), None of these (meta-option).3) Select the gemstone option: Ruby.4) Confirm set membership: Ruby is widely recognized as a precious gemstone comparable in category to sapphire, emerald, and diamond.

Verification / Alternative check:
Cross-checking basic classification: Ruby is a variety of the mineral corundum (aluminium oxide), just like sapphire; emerald is a variety of beryl; diamond is pure carbon in crystalline form. All are gemstones used in fine jewelry. Gold and silver are elemental metals, and bronze is a copper-based alloy; none of these are gemstones. Hence the set-membership test chooses ruby unambiguously.

Why Other Options Are Wrong:

• Gold: A precious metal, not a gemstone; fails class membership.
• Silver: A precious metal, not a gemstone; fails class membership.
• Bronze: An alloy (copper with tin and other elements), not a gemstone.
• None of these: Incorrect because “Ruby” is a valid gemstone that fits the set.

Common Pitfalls:
Confusing “valuable” with “gemstone.” Metals and alloys, although valuable, do not belong to the gemstone class. Another pitfall is picking an option because it is commonly used in jewelry settings (e.g., gold, silver); remember the analogy asks for an item of the same category as the given stones, not a material used to mount them.

Final Answer:
Ruby