Two value indications are $296,000 and $334,000. What is the difference as a percentage of the lower indication, rounded to one decimal place?
Correct Answer
B) 12.8%
Subtract the lower indication from the higher: $38,000. Divide that difference by the stated lower base, $296,000, and multiply by 100. The result is 12.8%. Using the higher indication as the base answers a different question.
Why This Is the Correct Answer
Option B is correct because $334,000 − $296,000 = $38,000, and $38,000 ÷ $296,000 × 100 = 12.84%, which rounds to 12.8%. The question names the lower indication as the base, so $296,000 is the divisor.
Why the Other Options Are Wrong
Option A: 11.4%
Option A, 11.4%, uses the higher indication as the base: $38,000 ÷ $334,000 × 100 = 11.4%. The question asks for the lower indication as the base, which gives $38,000 ÷ $296,000 × 100 = 12.8%.
Option C: 12.1%
Option C, 12.1%, divides the $38,000 difference by the average of the two indications, ($296,000 + $334,000) ÷ 2 = $315,000: $38,000 ÷ $315,000 × 100 = 12.1%. The question names the lower indication as the base, so $38,000 ÷ $296,000 × 100 = 12.8%.
Option D: 38.0%
Option D, 38.0%, treats the $38,000 dollar difference as if it were a percentage. The difference must be divided by the $296,000 base: $38,000 ÷ $296,000 × 100 = 12.8%.
Divide by the named base
Find the difference, divide by whichever figure the question names as the base, then round only at the end.
How to use: Use this on any percentage difference or spread question.
Exam Tip
Before dividing, underline which figure is the base, and carry an extra decimal place so you can round correctly to the stated precision.
Common Mistakes to Avoid
- -Dividing by the higher indication when the lower is the stated base
- -Dividing by the average of the two indications instead of the stated base
- -Reading the dollar difference as a percentage
Concept Deep Dive
Analysis
This calculation tests percentage difference with a stated base and a stated rounding rule. Subtract the lower indication from the higher, divide by the lower indication, multiply by 100 and round to the nearest tenth. Both the base and the rounding step change the answer.
Background Knowledge
Percentage difference compares a dollar difference to a stated base. Appraisers use the spread between indications to judge how consistent the approaches are and whether a difference needs investigation. Stating the base and the rounding clearly avoids confusion.
Real-World Application
An appraiser compares a cost indication of $334,000 with a sales indication of $296,000. Measured against the lower figure, the spread is about 12.8%, large enough that she re-checks her cost inputs. She finds an overstated quality rating and corrects it.
More Reconciliation Questions
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