In the measurement analogy “Yard is to inch as quart is to ____”, which unit correctly completes the relationship?

Introduction / Context:
This analogy deals with systems of measurement. A yard and an inch are units used to measure length, where one yard equals a fixed number of inches. Similarly, a quart and an unknown unit relate to volume in the same way. To answer this correctly, you must know which unit of volume plays the same role for a quart that an inch plays for a yard.

Given Data / Assumptions:

• First pair: Yard and inch.
• Second pair: Quart and an unknown unit.
• Options: milk, gallon, liquid, ounce, pint.
• We assume standard imperial or US customary units.

Concept / Approach:
A yard is a larger unit of length made up of smaller units called inches. Specifically, one yard equals thirty six inches. The relationship is “larger unit composed of many smaller units of the same dimension.” For volume, a quart is a larger unit that can be expressed in smaller units. A standard quart in the US system is equal to thirty two fluid ounces. Therefore, ounce plays the same role for quart that inch plays for yard.

Step-by-Step Solution:

Step 1: Analyse the first pair. Yard and inch are both length units. Step 2: Understand their relation. One yard is a fixed number of inches. Step 3: Apply the pattern to volume. A quart is a fixed number of smaller volume units. Step 4: Recall that one quart is equal to two pints, which is also equal to four cups or thirty two fluid ounces. Step 5: Among the options, ounce is the smaller unit of volume contained multiple times in a quart, matching the inch yard relationship.

Verification / Alternative check:
Check each option. Milk and liquid are substances, not units, and cannot stand in a numeric relationship like inch and yard. Gallon is actually larger than a quart, so it reverses the pattern. Pint is also smaller than a quart and is a valid volume unit, but the yard analogy uses the smallest common subunit, the inch, rather than another middle sized unit. Ounce is the widely recognised fluid unit that multiplies into a quart in the same way inches multiply into a yard.

Why Other Options Are Wrong:
Milk and liquid describe what is measured, not the measuring units themselves. Gallon represents a larger measure than quart, so it cannot be the analogue of inch, which is smaller than a yard. Pint is a valid possibility at first glance, but the most direct and commonly tested conversion links quarts and ounces, just as yards and inches are paired in length conversions. Ounce fits the analogy most clearly.

Common Pitfalls:
A common mistake is to pick gallon because many people remember the quart gallon relation. Others choose pint due to familiarity with pint sized containers. The key is to notice that the first pair uses a larger unit and its smallest common subunit in basic conversions, not two large units. The same logic should guide your choice for the quart analogy.

Final Answer:
The unit that completes the analogy is ounce, because a quart is composed of many ounces just as a yard is composed of many inches.