A 12-acre tract loses 20 percent of its area to streets and drainage, and zoning permits four lots per net acre. How many lots can be platted?
Correct Answer
D) 38 lots
Why this is correct: First, calculate net acreage: 12 acres × (100% - 20%) = 12 × 0.80 = 9.6 net acres. Then, calculate lots: 9.6 net acres × 4 lots per acre = 38.4 lots. Since only whole lots can be platted, round down to 38 lots. Why the other choices are wrong: '48 lots' incorrectly uses gross acreage (12 × 4). '44 lots' and '40 lots' result from miscalculating the 20% loss or rounding errors. Exam tip: In development problems, always apply density (lots per acre) to the net usable area after deducting land for streets, drainage, etc.
Why This Is the Correct Answer
Deduct the 20 percent infrastructure loss first: 12 acres x 0.80 = 9.6 net acres. Apply the permitted density to that net figure: 9.6 x 4 lots per net acre = 38.4 lots. A partial lot cannot be platted or sold, so the yield is truncated to 38 whole lots. That makes 38 the only answer consistent with both the net-acre instruction and the whole-lot constraint.
Why the Other Options Are Wrong
Option A: 48 lots
48 lots is 12 gross acres x 4, which ignores the 20 percent taken by streets and drainage entirely. It is tempting because it is the fastest calculation and uses both numbers in the stem. Applying density to gross land overstates yield on essentially every real subdivision.
Option B: 44 lots
44 lots comes from deducting only part of the infrastructure loss, typically by subtracting a flat four lots from the gross yield instead of shrinking the land base by 20 percent. The 20 percent applies to acreage, not to the lot count, and the two are not interchangeable once rounding is involved. Nothing in the stem supports a partial deduction.
Option C: 40 lots
40 lots results from rounding 9.6 net acres up to 10 acres before multiplying. Rounding the land base is never appropriate; the truncation happens at the end, to the lot count, not at the acreage step. That single premature rounding adds two phantom lots to the yield.
Net Before Density
Say it as a three-beat chant: shrink, multiply, truncate. Shrink the land to net, multiply by the density, then truncate to a whole lot. The order never changes, and the only rounding allowed is the last beat, always downward.
How to use: Whenever a stem gives you an acreage plus any percentage 'lost to' streets, drainage, open space or setbacks, write the net acreage on your scratch paper before you touch the density figure. Then multiply, then chop the decimal.
Exam Tip
Underline the words 'per net acre' the moment you see them; the exam almost always plants a distractor that equals gross acreage times density.
Common Mistakes to Avoid
- -Applying the lots-per-acre density to gross acreage instead of net acreage
- -Rounding the net acreage up or to the nearest whole acre before multiplying
- -Rounding the fractional lot up instead of truncating it downward
Concept Deep Dive
Analysis
This is a subdivision development (land-development) density problem, and the entire question turns on the difference between gross acreage and net acreage. Gross area is everything inside the boundary; net area is what remains after deducting land dedicated to streets, alleys, drainage, detention and other non-saleable infrastructure. Zoning density stated as lots per net acre must be multiplied against the net figure only. Because a lot is an indivisible legal parcel, any fractional result is truncated downward rather than rounded to the nearest whole number. Appraisers use this same arithmetic when testing highest and best use of vacant land and when building a subdivision development analysis.
Background Knowledge
You need to know that development density is normally expressed per net acre and that gross acreage must be reduced by dedications for streets, utilities and drainage before density is applied. You also need the convention that fractional lots are dropped, never rounded up, because a partial lot has no separate legal existence.
Real-World Application
In a subdivision development analysis for a land loan, the appraiser starts with the surveyed gross tract, deducts the engineer's estimate of right-of-way and detention area, applies the zoning density to the remainder, then discounts the projected lot sales over the absorption period.
More Land/Site Questions
Under which condition is the land residual technique most applicable?
Why can the same physical parcel carry different values in two assignments?
In a built-up area where no vacant land has sold for years, which approach to site value is the usual fallback?
How is entrepreneurial profit treated in the subdivision development method?
A land comparable sold 18 months ago in a market rising about 4 percent a year. What adjustment direction applies?
Why does a developer's required profit rise for a longer subdivision project?
How does holding cost enter the valuation of land bought for future development?
Excess land is best described as land that has which characteristic?
Plottage value arises in which of the following situations?
Which of the following is an off-site improvement rather than a site improvement?
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