In the rectangular survey system, how many acres are contained in the NE 1/4 of the SW 1/4 of Section 15?
Correct Answer
B) 40 acres
A full section contains 640 acres. The SW 1/4 contains 160 acres (640 ÷ 4), and the NE 1/4 of that contains 40 acres (160 ÷ 4). The calculation works from right to left in the legal description.
Why This Is the Correct Answer
Option B (40 acres) is correct because we must calculate the subdivisions sequentially from right to left. Starting with Section 15 (640 acres), we first find the SW 1/4, which equals 640 ÷ 4 = 160 acres. Then we take the NE 1/4 of that 160-acre parcel, which equals 160 ÷ 4 = 40 acres. This demonstrates the fundamental principle that each 1/4 subdivision reduces the acreage by a factor of 4.
Why the Other Options Are Wrong
Option A: 10 acres
10 acres would result from an additional subdivision (like 1/4 of 40 acres), but the legal description only calls for two levels of 1/4 subdivisions, not three.
Option C: 80 acres
80 acres represents only one level of subdivision (640 ÷ 8), failing to account for the two separate 1/4 divisions specified in the legal description.
Option D: 160 acres
160 acres represents only the SW 1/4 of the section, ignoring the additional NE 1/4 subdivision that further reduces the acreage.
The 640-4-4 Rule
Remember '640 Start, Divide by 4 for each Quarter' - Start with 640 acres for any full section, then divide by 4 for each 1/4 mentioned in the legal description, working from right to left.
How to use: When you see a legal description with quarters, count the number of '1/4' fractions, start with 640, and divide by 4 that many times. For 'NE 1/4 of SW 1/4': 640 ÷ 4 ÷ 4 = 40 acres.
Exam Tip
Always work legal descriptions from right to left, and remember that each 1/4 subdivision divides the previous acreage by 4, not by 2.
Common Mistakes to Avoid
- -Working from left to right instead of right to left in the legal description
- -Forgetting that 1/4 means divide by 4, not multiply by 0.25 of the original 640 acres
- -Miscounting the number of subdivisions and stopping after only one calculation
Concept Deep Dive
Analysis
This question tests understanding of the rectangular survey system's hierarchical subdivision of land parcels. The rectangular survey system divides land into townships and sections, with each section containing exactly 640 acres. Legal descriptions in this system work by progressively subdividing larger parcels into smaller ones, with each subdivision representing a fraction of the parent parcel. The key skill being tested is the ability to calculate acreage by working through multiple levels of subdivision from right to left in the legal description.
Background Knowledge
The rectangular survey system is based on a grid system where each section contains exactly 640 acres (one square mile). Legal descriptions using this system specify progressively smaller parcels through fractional subdivisions, typically in quarters (1/4), and these fractions must be calculated from right to left in the description.
Real-World Application
Appraisers frequently encounter partial section descriptions in rural property appraisals, estate divisions, and agricultural land valuations where precise acreage calculations are essential for determining property values and ensuring accurate comparable sales analysis.
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