During a sample period, 9 listings were cancelled and 36 sales closed, for a total of 45 listing endings. What is the cancelled-listing rate as a share of all endings?
Correct Answer
A) 0.20 ratio
Cancelled share among specified endings=9/(9+36)=9/45=0.20. Use the same population, period and price/listing definition throughout. Common errors: dividing by closed sales instead of all endings gives 0.25 ratio; reporting the closed share instead of the cancelled share gives 0.80 ratio; inverting the ratio (closed ÷ cancelled) gives 4.00 ratio.
Why This Is the Correct Answer
Option A is correct because the defined rate is cancelled listings divided by total endings: 9 / (9 + 36) = 9 / 45 = 0.20. The denominator includes both cancelled and closed listings, as the definition requires.
Why the Other Options Are Wrong
Option B: 0.25 ratio
Option B, a 0.25 ratio, comes from dividing by closed sales only: 9 / 36 = 0.25. The definition uses all endings, so the correct figure is 9 / 45 = 0.20.
Option C: 0.80 ratio
Option C, a 0.80 ratio, is the closed share rather than the cancelled share: 36 / 45 = 0.80. The question asks for cancelled listings, 9 / 45 = 0.20.
Option D: 4.00 ratio
Option D, a 4.00 ratio, inverts the comparison as closed divided by cancelled: 36 / 9 = 4.00. The defined rate is 9 / 45 = 0.20.
Part over whole endings
The cancelled rate is the cancelled part over the whole set of endings, cancelled plus closed. Shares of a whole sum to 1, so 0.20 cancelled pairs with 0.80 closed.
How to use: Use the sum-to-one check to spot the complement distractor quickly.
Exam Tip
Identify the whole first: every listing that ended, whether cancelled or closed. Distractors typically swap the denominator, report the complement or invert the ratio.
Common Mistakes to Avoid
- -Dividing cancelled listings by closed sales only
- -Reporting the closed share instead of the cancelled share
- -Inverting the ratio to closed divided by cancelled
Concept Deep Dive
Analysis
This question tests applying a defined ratio exactly as stated. The cancelled-listing rate is cancelled listings divided by all endings, meaning cancelled plus closed. Using the correct numerator and denominator is the whole task.
Background Knowledge
Appraisers may analyze pending sales and expired or withdrawn listings to understand market conditions. A measure like the cancelled-listing rate is meaningful only when its population, period and definition are applied consistently. It is a sample indicator, not by itself a value adjustment.
Real-World Application
While completing a market conditions analysis, an appraiser counts listings that ended during the last six months. A rising share of cancellations relative to all endings may signal weakening demand, which she weighs with other indicators.
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