An appraiser is updating the market conditions analysis for a subdivision. Compared with two years ago, active listings are up 20% and the average monthly pace of closed sales is down 20%. By what percentage has the months of housing supply increased?
Correct Answer
C) 50%
Months of housing supply is listings divided by the monthly pace, so the new figure is 1.20/0.80 = 1.50 times the old one, a 50% increase. For example, 100 listings at 10 sales per month is 10 months, and 120 listings at 8 sales per month is 15 months. Adding the two percentages gives 40%, and reflecting the slower pace alone gives 1/0.80, or 25%. Treating the listing rise as a second 20% cut in pace gives 1/(0.80 × 0.80), or 56%.
Why This Is the Correct Answer
Option C is correct because months of housing supply equals listings divided by pace, so the new figure is 1.20/0.80 = 1.50 times the old one. That is a 50% increase. Sample figures confirm it: 100/10 = 10 months becomes 120/8 = 15 months.
Why the Other Options Are Wrong
Option A: 25%
Option A shows 25%, which reflects the slower pace and leaves out the listing rise: 1/0.80 = 1.25. Both parts of the ratio changed, so the factor is 1.20/0.80 = 1.50, a 50% increase.
Option B: 40%
Option B shows 40%, which comes from adding 20% and 20%. Months of housing supply is a ratio, so the changes combine as 1.20/0.80 = 1.50, a 50% increase.
Option D: 56%
Option D shows 56%, which comes from treating the listing rise as a second 20% cut in pace: 1/(0.80 × 0.80) = 1.5625. A 20% rise in listings multiplies the numerator by 1.20, so the factor is 1.20/0.80 = 1.50, a 50% increase.
Ratios divide, they do not add
Write each change as a factor, such as 1.20 for up 20% and 0.80 for down 20%, then divide top by bottom. A quick test with 100 listings and 10 sales confirms the result.
How to use: Use this factor method when you are given percentage changes in a ratio's parts rather than the counts.
Exam Tip
When you see percentages and no base figures, choose easy numbers and compute the before and after values. This exposes the shortcut of adding the two percentages.
Common Mistakes to Avoid
- -Adding the two percentage changes
- -Reflecting the change in pace and ignoring the change in listings
- -Dividing by 0.80 for a 20% rise in listings instead of multiplying by 1.20
Concept Deep Dive
Analysis
With no listing or sales counts available, the answer comes from the structure of the ratio. Listings are the numerator and pace is the denominator, so the two changes combine by division rather than addition. Plugging in convenient numbers is a reliable way to confirm the result.
Background Knowledge
Months of housing supply is total listings divided by the monthly absorption rate. A change in a ratio is found by dividing the numerator's factor by the denominator's factor. This is why supply can move faster than either of its components when listings rise and sales slow at once.
Real-World Application
A market report states that listings are up by a fifth and sales are down by a fifth from two years earlier. An appraiser summarizing the change converts those moves to factors and describes supply as about one and a half times its earlier level, then checks that against the underlying counts.
More Market Questions
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