A 12-acre subdivision has 20% of its acreage reserved for roads and other nonlot uses. The density limit is four lots per net acre. Ignoring all other layout and approval constraints, what is the maximum whole number of lots allowed by this density calculation?
Correct Answer
B) 38 lots
Net acreage = 12 × (1 − 0.20) = 9.6 acres; density limit = 9.6 × 4 = 38.4 lots; greatest whole number not exceeding the limit = 38. The indicated quantity is 38 lots. This is the result under the stated inputs, not a universal market ratio or an approval of a proposed development. Common errors: applying the density to gross acreage gives 48 lots; applying the density to the reserved acreage gives 10 lots; rounding 38.4 lots up instead of down gives 39 lots.
Why This Is the Correct Answer
Option B is correct because net acreage is 12 × (1 − 0.20) = 9.6 acres, and 9.6 × 4 = 38.4 lots. Since 39 lots would exceed the density limit, the maximum whole number allowed is 38 lots.
Why the Other Options Are Wrong
Option A: 10 lots
Option A, 10 lots, applies the density to the reserved acreage: 12 × 0.20 × 4 = 9.6, about 10 lots. Density applies to the net lot acreage, 9.6 acres × 4 = 38.4, or 38 lots.
Option C: 39 lots
Option C, 39 lots, rounds 38.4 up instead of down. Thirty-nine lots would exceed the limit of 38.4, so the maximum whole number is 38.
Option D: 48 lots
Option D, 48 lots, applies the density to gross acreage: 12 × 4 = 48. The limit is per net acre, so the 20% reserved for roads must be removed first, giving 38 lots.
Net first, then round down
Strip out roads and other nonlot land, multiply by the density, and drop any fraction because a limit cannot be exceeded.
How to use: Use this whenever a density problem involves reserved land and a fractional result.
Exam Tip
Check whether the density is per gross or per net acre, and round down when the result is a maximum.
Common Mistakes to Avoid
- -Applying net density to gross acreage
- -Rounding a maximum lot count up
- -Applying the density to the reserved acreage
Concept Deep Dive
Analysis
This question tests applying a density limit to net acreage. You remove the reserved acreage first, multiply net acres by the density, and round down because a fractional lot cannot exceed the limit. Each distractor misapplies one of these steps.
Background Knowledge
Zoning regulates density or intensity of use, often expressed as lots or units per gross or net acre. Appraisers apply density limits to estimate the number of lots a site can yield as part of highest and best use and development analysis.
Real-World Application
An appraiser estimating lot yield for a proposed subdivision learns that about 20% of the land will go to streets and drainage. Applying the zoning's lots-per-net-acre limit to the remaining acreage, the appraiser rounds down to the maximum whole number of lots.
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