For the same competitive sample, mean sale price is $390,000 and mean original list price is $400,000. What is the ratio of these two means as a percentage? It need not equal the arithmetic mean of the individual sale/list ratios.
Correct Answer
C) 97.5 percent
Ratio of means=$390,000/$400,000×100=97.5%. This is the stated sample measure, not an automatic market-condition classification or value adjustment. Common errors: inverting the ratio (list ÷ sale) gives 102.6 percent; reporting the discount instead of the ratio gives 2.5 percent; reporting the decimal ratio without converting it to a percentage gives 1.0 percent.
Why This Is the Correct Answer
Option C is correct because the ratio of means is $390,000 / $400,000 x 100 = 97.5%. Sale price is on top and list price on the bottom, and the result is converted to a percentage.
Why the Other Options Are Wrong
Option A: 1.0 percent
Option A, 1.0 percent, comes from leaving the decimal ratio unconverted: $390,000 / $400,000 = 0.975, about 1.0 when rounded. Multiplying by 100 gives the correct 97.5%.
Option B: 2.5 percent
Option B, 2.5 percent, reports the discount rather than the ratio: ($400,000 - $390,000) / $400,000 x 100 = 2.5%. The ratio of sale to list is $390,000 / $400,000 x 100 = 97.5%.
Option D: 102.6 percent
Option D, 102.6 percent, inverts the ratio as list over sale: $400,000 / $390,000 x 100, about 102.6%. The correct calculation is $390,000 / $400,000 x 100 = 97.5%.
Sold over asked
Sale-to-list is what it sold for over what was asked. Below 100% means buyers paid less than asking.
How to use: Use this to keep sale price in the numerator and catch inverted answers.
Exam Tip
Check whether the answer should be a ratio or a discount. A sale-to-list ratio near 100% and a discount near 0% are different measures.
Common Mistakes to Avoid
- -Inverting the ratio to list over sale
- -Reporting the discount instead of the ratio
- -Forgetting to convert the decimal to a percentage
Concept Deep Dive
Analysis
This question tests computing a ratio of mean prices and expressing it as a percentage. Mean sale price is divided by mean original list price and multiplied by 100. The stem notes this differs from averaging individual sale-to-list ratios.
Background Knowledge
Sale-to-list price ratios indicate how close sellers come to their asking prices and help describe market conditions. A ratio of means can differ from the mean of individual ratios, so the measure must be defined clearly. It is an indicator, not an automatic value adjustment.
Real-World Application
An appraiser reviewing a market finds average sale prices running at 97.5% of original list prices. She reports this as one sign of negotiating room for buyers and compares it with prior periods.
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