Define a period statistic as expired listings divided by expired plus closed listings. During that period, 18 expired and 54 closed. What ratio results? This statistic is conditional on the two named outcomes.
Correct Answer
A) 0.25 ratio
Expired share among specified outcomes = 18/(18 + 54) = 18/72 = 0.25. Keep the stated numerator, denominator and units distinct. Common errors: dividing by closed listings only gives 0.33 ratio; reporting the closed share instead of the expired share gives 0.75 ratio; inverting the ratio gives 4.00 ratio.
Why This Is the Correct Answer
Option A is correct because the defined statistic is expired / (expired + closed) = 18 / (18 + 54) = 18 / 72 = 0.25. This is the expired share among the two named outcomes during the period.
Why the Other Options Are Wrong
Option B: 0.33 ratio
Option B is wrong because 0.33 comes from dividing the expired listings by the closed listings only (18 / 54 = 0.33). The defined denominator is expired plus closed, so the ratio is 18 / 72 = 0.25.
Option C: 0.75 ratio
Option C is wrong because 0.75 is the closed share, not the expired share (54 / 72 = 0.75). The statistic asks for expired listings on top: 18 / 72 = 0.25.
Option D: 4.00 ratio
Option D is wrong because 4.00 comes from inverting the ratio (72 / 18 = 4.00). The defined statistic places expired listings in the numerator: 18 / 72 = 0.25.
Follow the definition literally
Write the formula from the stem first, then plug in numbers: expired on top, expired plus closed on the bottom. The definition is the recipe.
How to use: Use this habit whenever a question defines its own ratio.
Exam Tip
When a question defines a statistic, write the formula exactly as stated before calculating, then check that the numerator is the item asked for.
Common Mistakes to Avoid
- -Using only closed listings as the denominator
- -Reporting the closed share instead of the expired share
- -Inverting the defined ratio
Concept Deep Dive
Analysis
This question tests careful use of a defined ratio. The statistic is expired listings divided by the sum of expired and closed listings. Setting up the numerator and denominator exactly as defined gives the answer.
Background Knowledge
Expired and withdrawn listings, along with pending sales, can supplement market research by showing how many listings fail to sell. A higher expired share among listing outcomes can suggest weaker demand or overpricing relative to the market.
Real-World Application
An appraiser studying a condo segment finds that 18 listings expired and 54 closed during the period. The 0.25 expired share among those two outcomes is reported as supplemental evidence that a meaningful portion of listings failed to sell before their listing periods ended, which the appraiser weighs with price, days-on-market and inventory data.
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