A home of 2,000 square feet sold for $340,000. What is the price per square foot?
Correct Answer
D) $170
Why this is correct: Price per square foot is calculated by dividing sale price by area. $340,000 ÷ 2,000 sq ft = $170 per sq ft, as shown in the original explanation. Why the other choices are wrong: "$150" is incorrect; 340,000/2,000 = 170, not 150. "$160" is wrong; 340,000/2,000 = 170. "$180" is false; 340,000/2,000 = 170. Exam tip: Always double-check division; price per unit is a common exam calculation.
Why This Is the Correct Answer
Dividing $340,000 by 2,000 square feet gives exactly $170 per square foot, which is option D. Set the problem up as price over area every time, and confirm the decimal by rough estimation: 2,000 times $170 is $340,000, so the answer reconciles. Because both figures in this stem are clean, any answer other than $170 comes from changing one of the two inputs rather than from the division itself.
Why the Other Options Are Wrong
Option A: $150
$150 per square foot would require about 2,267 square feet of area at this price, which is the figure you get by folding a finished basement or an attached garage into the denominator. Adding non-living area to living area always drives the unit rate down and makes the property look cheaper than it is. Keep garages, basements, and unfinished space out of gross living area.
Option B: $160
$160 per square foot implies roughly 2,125 square feet, the result of adding a porch, an enclosed patio, or a low-ceiling bonus room into the measured area. It is a small error in the denominator that produces a visible error in the rate. Any space counted must meet the finished, above-grade, and ceiling-height requirements.
Option C: $180
$180 per square foot implies about 1,889 square feet, which is what happens if you round the area down to 1,900 or leave out a finished area you measured. Rounding the denominator before dividing is the mirror image of rounding the price, and both distort the rate. Divide with the actual measurements and round only the final result.
Price Over Area, Always
Write the fraction before you touch the calculator: dollars on top, square feet on the bottom. Dollars per square foot literally reads as dollars divided by square feet, so the words tell you the order of operations.
How to use: Whenever a stem says 'per' anything, put the unit after the word 'per' in the denominator. Then multiply your answer back by that denominator to confirm you land on the original price.
Exam Tip
On clean-number problems, work the multiplication in reverse to check yourself. Two seconds of verification protects an easy point you cannot afford to lose.
Common Mistakes to Avoid
- -Including garage or basement area in the square footage used for the rate
- -Comparing a subject rate based on GLA to comparable rates based on total finished area
- -Treating price per square foot as a value conclusion rather than a screening tool
Concept Deep Dive
Analysis
Price per square foot is a unit of comparison, meaning a rate built by dividing a sale price by a quantity of the subject's measured area. The arithmetic is trivial; the appraisal content is in the denominator, because a rate is meaningful only when the area is measured the same way for the subject and for every comparable. Standard practice measures gross living area above grade to the exterior walls, excluding garages, unfinished space, and below-grade rooms, which are reported and compared on separate lines. Unit rates are used to test reasonableness and to bracket a conclusion, not to substitute for a full adjustment grid.
Background Knowledge
You need the definition of a unit of comparison and the convention that residential price per square foot is based on gross living area above grade. You also need comfort with basic division and the habit of checking the result by multiplying back.
Real-World Application
An appraiser screening candidate comparables computes price per square foot for each sale to spot outliers, then investigates any sale whose rate falls far from the group before deciding whether it belongs in the grid.
More Statistics Questions
A set of comparable sales has a mean of $250,000 and a standard deviation of $20,000. What is the coefficient of variation?
A property sold for $400,000 and resold three years later for $463,050 with no physical change. What compound annual rate does this indicate?
A histogram of neighborhood sale prices shows two distinct peaks. What does this most likely mean?
What does it mean to validate a regression model?
In a market study, what does a frequency distribution of sale prices show?
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An appraiser presents a statistical analysis in a report. What must accompany it for the reader to weigh it?
An R-squared of 0.86 in a sales model indicates that:
Which measure would best summarize the most common lot size in a subdivision?
Paired sales analysis and regression differ mainly in that regression:
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