“Valueless” appears to be the opposite of “Invaluable,” but “Invaluable” actually means “extremely valuable.” Choose the pair that similarly contrasts a negative quality with its positive counterpart.

Introduction / Context:
This item plays on a common vocabulary trap: “invaluable” sounds like “without value,” but it actually means “priceless” or “extremely valuable.” The stem thus presents a misleading apparent antonym pair. We must choose a pair that, like the stem, sets a negative quality against its positive, countervailing counterpart.

Given Data / Assumptions:

• “Valueless” (worthless) vs “Invaluable” (extremely valuable) form a high-contrast semantic pairing.
• We need a comparably strong contrast of dispositions or behaviors.

Concept / Approach:
“Miserly : Philanthropic” provides a clean antonymic contrast of traits around giving/using money and resources: “miserly” hoards; “philanthropic” gives generously. Other choices either compare degrees of price (“Costly : Cut-rate”), mix noun/quality without direct antonymy (“Frugality : Wealth”), or pair unrelated notions (“Thriftiness : Cheap” is not a true antonym set—thriftiness can be prudent, not “cheap”).

Step-by-Step Solution:
1) Identify that the stem is a contrast pair, not a synonym pair.2) Select the option with a clear negative ↔ positive trait opposition.3) Choose “Miserly : Philanthropic.”

Verification / Alternative check:
Dictionary senses confirm “invaluable” = extremely valuable, not worthless. The chosen pair mirrors a similarly stark opposition.

Why Other Options Are Wrong:

• Costly : Cut-rate: Price descriptors, but not a value/virtue contrast.
• Frugality : Wealth: Category mismatch (a habit vs a possession level).
• Thriftiness : Cheap: Not strict antonyms; one can be thrifty without being cheap.

Common Pitfalls:
Assuming the “in-” prefix always negates; here it intensifies value.

Final Answer:
Miserly : Philanthropic