A quarter-quarter section in the rectangular survey system measures:
Correct Answer
D) One quarter mile on each side
Why this is correct: The rectangular survey system defines a standard section as one mile on each side, containing 640 acres. A quarter-section is created by dividing the section in half both north-south and east-west, resulting in a parcel one half mile on each side (160 acres). A quarter-quarter section is created by dividing a quarter-section in half again in both directions. This final division results in a parcel one quarter mile on each side, containing 40 acres (one quarter of a quarter-section). Why the other choices are wrong: "One eighth mile on each side" describes a smaller parcel, such as a quarter of a quarter-quarter section. "One full mile on each side" describes the original 640-acre section itself. "One half mile on each side" describes a quarter-section, not a quarter-quarter section. Exam tip: Remember the sequence: Section (1 mi), Quarter-Section (1/2 mi), Quarter-Quarter Section (1/4 mi). The side length halves with each 'quartering'.
Why This Is the Correct Answer
Option D is correct because a quarter-quarter section measures one quarter mile on each side. Starting from a section at one mile square, the first quartering yields half a mile per side and the second yields a quarter mile per side. That side length of 1,320 feet squared is 1,742,400 square feet, which divided by 43,560 is 40 acres, matching the familiar forty-acre parcel. The two checks, linear and area, confirm each other.
Why the Other Options Are Wrong
Option A: One eighth mile on each side
One eighth mile on each side, or 660 feet, describes a parcel of about 10 acres, which is a quarter of a quarter of a quarter section. Selecting it means halving the dimension one time too many. It is the natural error for a candidate who remembers that each step halves the side but loses count of the steps.
Option B: One full mile on each side
One full mile on each side is the entire section, containing 640 acres, which is the starting point before any aliquot division. Choosing it means reading the section reference and ignoring both quartering calls. The description explicitly divides that section twice.
Option C: One half mile on each side
One half mile on each side is a quarter section of 160 acres, the result of only the first quartering. This is the most tempting wrong answer because it correctly applies one division and stops. The doubled word quarter-quarter is the signal that two successive divisions apply.
Halve the side, quarter the acres
Every quartering cuts the side length in half and the acreage to one fourth. Run the ladder: one mile and 640 acres, half a mile and 160, a quarter mile and 40, an eighth of a mile and 10.
How to use: Count how many times the word quarter appears in the description and step down the ladder that many times. Then answer in whichever unit the question asks for, side length or acreage.
Exam Tip
Note whether the question wants a linear dimension or an area. Answer choices in miles are asking for side length, and a candidate reciting 40 acres from memory can still miss the question.
Common Mistakes to Avoid
- -Answering with acreage when the question asks for side length
- -Applying only one quartering to a quarter-quarter description
- -Forgetting that 43,560 square feet make an acre when converting
- -Assuming nominal aliquot dimensions in sections that contain government lots
Concept Deep Dive
Analysis
This tests the geometry rather than just the acreage of aliquot subdivisions in the Public Land Survey System. A section measures one mile on each side and contains 640 acres. Quartering it halves both dimensions, so a quarter section is one half mile square and holds 160 acres. Quartering again halves both dimensions once more, making a quarter-quarter section one quarter mile on each side, which is 1,320 feet, and 1,320 squared divided by 43,560 square feet per acre gives exactly 40 acres. The pattern worth internalizing is that each quartering halves the linear dimension while dividing the area by four, so acreage falls faster than the side length. Candidates who track only acreage often lose the linear measure, and surveyors' descriptions and per-front-foot analyses require both.
Background Knowledge
You need the PLSS framework: townships of 36 sections, sections one mile square containing 640 acres, and aliquot subdivision by repeated halving and quartering. You also need the conversion constants, 5,280 feet per mile and 43,560 square feet per acre, and awareness that sections on the north and west edges of a township contain government lots rather than exact aliquot acreages.
Real-World Application
Appraising a 40-acre irrigated tract described as the NE quarter of the SW quarter, you confirm the nominal 1,320-foot dimensions against the plat before computing price per acre for your comparables, and you check whether the parcel is a government lot with a surveyed acreage that differs from the nominal 40.
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