In a rectangular survey system, the NE 1/4 of the SW 1/4 of Section 15 contains how many acres?
Correct Answer
B) 40 acres
Why this is correct: A standard section in the Rectangular Survey System contains 640 acres. Dividing a section into quarters gives four 160-acre parcels. Dividing one of those quarters again into quarters results in four 40-acre parcels. The description 'NE 1/4 of the SW 1/4' means taking a quarter of a quarter. Calculation: 640 acres / 4 = 160 acres (SW 1/4). 160 acres / 4 = 40 acres (NE 1/4 of the SW 1/4). Why the other choices are wrong: '10 acres' is one-sixteenth of a quarter section, not a quarter of a quarter. '20 acres' is half of a quarter-quarter. '80 acres' is a half of a quarter section. Exam tip: A quarter of a quarter section is always 40 acres (640 / 16).
Why This Is the Correct Answer
Starting with a full section of 640 acres, the SW 1/4 represents one-quarter of the section, which equals 160 acres (640 ÷ 4). The NE 1/4 of the SW 1/4 represents one-quarter of that 160-acre quarter section, which equals 40 acres (160 ÷ 4). This calculation follows the standard rule that any quarter of a quarter section always contains 40 acres. The mathematical progression is: 640 → 160 → 40 acres through successive quarter divisions.
Why the Other Options Are Wrong
Option A: 10 acres
10 acres would represent 1/64th of a section, which would require three levels of quarter divisions (quarter of a quarter of a quarter), not the two levels described in this legal description.
Option C: 20 acres
20 acres would represent 1/32nd of a section, which is not achievable through the standard quarter-section subdivision pattern described in the question.
Option D: 80 acres
80 acres would represent 1/8th of a section, which would be half of a quarter section (such as the N 1/2 of the SW 1/4), not a quarter of a quarter section as described.
The 640-160-40 Cascade
Remember the cascade: 640 → 160 → 40. Full section (640) ÷ 4 = Quarter section (160) ÷ 4 = Quarter-quarter (40). Think '6-1-4' for the digits that matter: 640, 160, 40.
How to use: When you see any 'quarter of a quarter' description, immediately think 40 acres. Count the subdivision levels: one 'quarter' = 160 acres, two 'quarters' = 40 acres.
Exam Tip
Always start with 640 acres for a full section and divide by 4 for each 'quarter' mentioned in the legal description. Draw a simple square and subdivide it visually if needed.
Common Mistakes to Avoid
- -Forgetting that a section contains 640 acres and starting with incorrect base number
- -Miscounting the number of quarter divisions in the legal description
- -Confusing quarter-quarter sections (40 acres) with half-quarter sections (80 acres)
Concept Deep Dive
Analysis
This question tests understanding of the Public Land Survey System (PLSS), specifically how to calculate acreage within subdivisions of a section. The rectangular survey system divides land into townships and sections, with each section containing exactly 640 acres. When a section is subdivided into quarters and sub-quarters, each division represents a fractional portion of the original 640 acres. Understanding this hierarchical subdivision system is crucial for property description and acreage calculations in real estate appraisal.
Background Knowledge
The Public Land Survey System divides land into 6-mile square townships, each containing 36 sections of one square mile (640 acres) each. Sections are commonly subdivided into quarters (160 acres each), and these quarters can be further subdivided into quarter-quarters (40 acres each).
Real-World Application
Appraisers frequently encounter properties described using PLSS legal descriptions, especially in rural areas. Accurate acreage calculation is essential for determining property boundaries, calculating price per acre, and ensuring proper comparable property analysis.
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