In the rectangular survey system, the NE 1/4 of the SW 1/4 of Section 16 contains how many acres?
Correct Answer
C) 40 acres
A section contains 640 acres. The SW 1/4 contains 160 acres (640 ÷ 4), and the NE 1/4 of that quarter contains 40 acres (160 ÷ 4).
Why This Is the Correct Answer
Option C is correct because we start with a full section of 640 acres and apply two successive quarter divisions. The SW 1/4 of Section 16 equals 640 ÷ 4 = 160 acres. Then, the NE 1/4 of that SW quarter equals 160 ÷ 4 = 40 acres. Each quarter division reduces the acreage by a factor of four, so two quarter divisions result in 640 ÷ 16 = 40 acres.
Why the Other Options Are Wrong
Option A: 10 acres
10 acres would result from three successive quarter divisions (640 ÷ 64), but this problem only involves two quarter divisions.
Option B: 20 acres
20 acres is not achievable through standard quarter divisions of a section, as it would require dividing by 32, which doesn't align with the quarter-section subdivision pattern.
Option D: 80 acres
80 acres would result from only one quarter division (640 ÷ 8), but this problem involves two successive quarter divisions, requiring division by 16 instead of 8.
The 640-160-40-10 Cascade
Remember the sequence: 640 (full section) → 160 (quarter) → 40 (quarter of quarter) → 10 (quarter of quarter of quarter). Each step divides by 4.
How to use: Count the number of 'quarter' references in the legal description, then divide 640 by 4 raised to that power. Two quarters = 640 ÷ 4² = 640 ÷ 16 = 40 acres.
Exam Tip
Always start with 640 acres for a full section, then divide by 4 for each quarter mentioned in the legal description, working from right to left in the description.
Common Mistakes to Avoid
- -Forgetting that a full section contains 640 acres, not 160 acres
- -Dividing by 2 instead of 4 for each quarter subdivision
- -Reading the legal description from left to right instead of right to left
Concept Deep Dive
Analysis
This question tests understanding of the rectangular survey system (also called the Public Land Survey System), specifically how to calculate acreage within subdivided sections. The rectangular survey system divides land into 6-mile square townships, which are further divided into 36 one-square-mile sections of 640 acres each. Sections can be subdivided into quarters, and those quarters can be further subdivided into smaller quarters. Understanding this hierarchical subdivision system is crucial for property description and acreage calculations in real estate appraisal.
Background Knowledge
The rectangular survey system is based on a grid pattern where each section contains exactly 640 acres (one square mile). When a section is divided into quarters, each quarter contains 160 acres, and when those quarters are further subdivided, each resulting parcel contains 40 acres.
Real-World Application
Appraisers frequently encounter legal descriptions using rectangular survey system notation when valuing rural properties, agricultural land, or properties in western states where this system is prevalent.
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