A subdivision has 180 current active listings and 35 closed sales in the latest three-month quarter. Using only that quarter’s average monthly sales pace, what months of inventory are indicated? Round to one decimal place.
Correct Answer
C) 15.4 months
Monthly sales = 35/3 = 11.67; months of inventory = 180/(35/3) = 15.4 months. Keep the stated numerator, denominator and units distinct. Common errors: dividing by the quarter’s total sales instead of the monthly pace gives 5.1 months; adding the closed sales to the active listings gives 18.4 months; converting the answer to years gives 1.3 months.
Why This Is the Correct Answer
Option C is correct because the monthly pace is 35 / 3 = 11.67 sales, and months of inventory = 180 / 11.67 = 15.4 months. Using the monthly pace keeps the units in months.
Why the Other Options Are Wrong
Option A: 1.3 months
Option A, 1.3 months, converts the correct answer into years: 180 / (35 / 3) / 12 = 1.29, about 1.3. The question asks for months, which is 15.4.
Option B: 5.1 months
Option B, 5.1 months, divides listings by the quarter's total sales instead of the monthly pace: 180 / 35 = 5.1. That figure is in quarters, not months; the correct figure is 180 / (35 / 3) = 15.4.
Option D: 18.4 months
Option D, 18.4 months, adds the closed sales to the active listings: (180 + 35) / (35 / 3) = 18.4. Sold homes are not current inventory, so the correct figure is 15.4.
Make it monthly first
Turn the quarter's sales into a per-month pace before dividing; otherwise your answer is measured in quarters.
How to use: Use this check whenever the sales window is longer than one month.
Exam Tip
Verify units: listings divided by sales per month gives months; listings divided by sales per quarter gives quarters.
Common Mistakes to Avoid
- -Dividing listings by the quarter's total sales
- -Adding closed sales to active listings
- -Reporting months of inventory in years
Concept Deep Dive
Analysis
This question tests months of inventory when sales are given for a three-month quarter. First convert the quarter's sales to a monthly pace, then divide current listings by that pace. Distractors skip the monthly conversion, add sales to listings or convert to years.
Background Knowledge
Months of supply is total listings divided by the monthly absorption rate. When sales cover a multi-month period, they must be divided by the number of months first so the result is expressed in months.
Real-World Application
An appraiser finds 180 active listings and 35 closings in the last quarter in a subdivision. She converts to about 11.7 sales per month and reports roughly 15 months of supply, a sign of ample inventory.
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