Sale A sold for $240,000 with 1,500 square feet, and Sale B sold for $375,000 with 2,500 square feet. Using the equal-weighted mean of their overall price-per-square-foot rates, what value is indicated for a 2,000-square-foot subject?
Correct Answer
C) $310,000
240000 / 1500 = 160; 375000 / 2500 = 150; ((160 + 150) / 2) × 2000 = 310000. Common errors: pooling total prices and areas instead of averaging the unit rates gives $307,500; using only A’s unit rate gives $320,000; using only B’s unit rate gives $300,000.
Why This Is the Correct Answer
Option C is correct because the question specifies the equal mean of the two overall price-per-square-foot rates. $240,000 / 1,500 = $160 and $375,000 / 2,500 = $150, so the mean is ($160 + $150) / 2 = $155. $155 × 2,000 = $310,000.
Why the Other Options Are Wrong
Option A: $300,000
Option A, $300,000, uses only B's unit rate: $150 × 2,000. The question asks for the mean of both rates, $155, giving $310,000.
Option B: $307,500
Option B, $307,500, pools total prices and areas: ($240,000 + $375,000) / (1,500 + 2,500) × 2,000. That weighted rate ($153.75) is not the equal mean of the unit rates the question specifies; the equal mean gives $310,000.
Option D: $320,000
Option D, $320,000, uses only A's unit rate: $160 × 2,000. Averaging A's $160 with B's $150 gives $155, and $155 × 2,000 = $310,000.
Rate first, then average
For an equal mean of unit rates, compute each sale's rate first, then average the rates.
How to use: Use this when a question asks for the mean price per square foot of several sales.
Exam Tip
Note whether the question asks for an equal mean of rates or a pooled total; the two give different answers.
Common Mistakes to Avoid
- -Pooling totals when an equal mean of rates is asked for
- -Using only one sale's unit rate
- -Averaging sale prices instead of unit rates
Concept Deep Dive
Analysis
This question tests applying the simple mean of unit rates as instructed. Each sale's price per square foot is computed first, then the two rates are averaged and applied to the subject's size. A: $240,000 / 1,500 = $160; B: $375,000 / 2,500 = $150; mean $155 × 2,000 = $310,000.
Background Knowledge
Units of comparison, such as price per square foot, restate each sale price in common terms. A simple mean gives each sale equal weight, while pooling totals weights larger sales more heavily, so the two methods can give different results. Exam questions that specify a method expect that method to be followed.
Real-World Application
An instructor gives trainees two sales and asks them to apply the equal mean of their price-per-square-foot rates to a 2,000-square-foot house. Some trainees pool prices and areas and get $307,500. The instructor shows that averaging the $160 and $150 rates gives $155 and $310,000.
More Sales Comparison Questions
Which stated cause of supported value loss is external?
Improvement cost new is $450,000. Separately supported improvement depreciation deductions of $45,000, $25,000, $15,000 are expressly nonoverlapping and not already excluded from cost new. Add supported site value of $125,000, already reflecting any site losses. What total indicated value results?
Which two depreciation categories may each be classified as curable or incurable by comparing the cost to remedy a deficiency with the value gained?
Improvement cost new is $800,000. Separately supported improvement depreciation deductions of $120,000, $80,000, $40,000 are expressly nonoverlapping and not already excluded from cost new. No site is included. What depreciated improvement amount results?
The principle of anticipation in real estate valuation states that:
Which highest-and-best-use criterion addresses whether a proposed use is allowed by zoning and applicable legal restrictions?
Three comparables produce adjusted indications of $312,000, $309,000 and $315,000, requiring gross adjustments of 9%, 14% and 22% respectively. Verification also establishes that the first sale is the closest competitive substitute and its adjustments are better supported than the other two. Which indication deserves the most weight on those facts?
When reconciling value indications from the three approaches to value, an appraiser should:
A property sold at a cash-equivalent price of $1,062,500. Its stabilized annual NOI is $85,000. What is the indicated overall rate?
In reconciliation, an appraiser should:
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