Two value indications are $340,000 and $392,000. What is the difference as a percentage of the lower indication, rounded to one decimal place?
Correct Answer
A) 15.3%
Subtract the lower indication from the higher: $52,000. Divide that difference by the stated lower base, $340,000, and multiply by 100. The result is 15.3%. Using the higher indication as the base answers a different question.
Why This Is the Correct Answer
Option A is correct because ($392,000 - $340,000) / $340,000 x 100 = $52,000 / $340,000 x 100 = 15.29%, which rounds to 15.3%. The stem specifies the lower indication as the base.
Why the Other Options Are Wrong
Option B: 13.3%
Option B, 13.3%, comes from $52,000 / $392,000 x 100 = 13.3%, which uses the higher indication as the base. The stem asks for the lower base, giving 15.3%.
Option C: 7.6%
Option C, 7.6%, matches dividing only half the spread by the lower base: $26,000 / $340,000 x 100 = 7.6%. The full difference of $52,000 must be used, giving 15.3%.
Option D: 52.0%
Option D, 52.0%, treats the $52,000 dollar difference as if it were a percentage. The difference must be divided by $340,000 and multiplied by 100, giving 15.3%.
Difference over the named base
Percent difference equals the dollar difference divided by the base the question names. Lower base gives a larger percentage than higher base.
How to use: Use it to check which base a percentage question requires before dividing.
Exam Tip
Underline the words that identify the base, such as of the lower indication. If both base choices appear as options, the wrong base is a planted trap.
Common Mistakes to Avoid
- -Dividing by the higher indication when the lower is specified
- -Reporting the dollar difference as a percentage
- -Rounding before finishing the division
Concept Deep Dive
Analysis
This calculation tests computing a percentage spread on a specified base. The difference between the indications is $52,000, and the stem says to express it as a percentage of the lower indication, $340,000. Using a different base or a different difference answers another question.
Background Knowledge
In reconciliation, appraisers often measure how far apart value indications are to judge consistency and the need for further analysis. A percentage difference depends on the base chosen, so the same dollar spread gives different percentages on the lower and higher figures. The final reconciliation still weighs the approach that best measures the benefits the property yields.
Real-World Application
An appraiser's sales comparison approach indicates $392,000 while the cost approach indicates $340,000. The appraiser computes the spread relative to the lower figure to describe the range in the report. The appraiser then explains which approach deserves more weight and why.
More Reconciliation Questions
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Which considerations provide the soundest basis for reconciling appraisal indications?
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