Active listing inventory in a defined neighborhood was 640 homes at the start of a quarter and 544 homes at the end of the same quarter (no change in geography or listing definition). What is the percentage change in listing inventory over the quarter?
Correct Answer
B) −15 percent
Percentage change = (544 − 640)/640 × 100 = -15%. Keep the stated numerator, denominator and units distinct. Common errors: dividing by the ending figure instead of the starting figure gives −18 percent; reporting the ending level as a percentage of the starting level gives 85 percent; misplacing the decimal (×10 instead of ×100) gives −2 percent.
Why This Is the Correct Answer
Option B is correct because the percent change is (544 - 640) / 640 x 100 = -15%. The starting inventory of 640 is the base, and the drop of 96 listings is 15% of it.
Why the Other Options Are Wrong
Option A: −18 percent
Option A, -18 percent, comes from dividing by the ending figure instead of the starting figure: (544 - 640) / 544 x 100 = -17.6, about -18. The correct base is 640, giving -15%.
Option C: −2 percent
Option C, -2 percent, comes from misplacing the decimal: (544 - 640) / 640 x 10 = -1.5, shown as -2. Multiplying by 100 gives the correct -15%.
Option D: 85 percent
Option D, 85 percent, reports the ending level as a percentage of the starting level: 544 / 640 x 100 = 85. That is a ratio, not a change; 85 minus 100 gives the -15% change.
New minus old, over old
Percent change equals new minus old, divided by old, times 100; a negative answer means a decline.
How to use: Use this phrase for inventory, price or sales-count changes alike.
Exam Tip
Watch the sign: a decline should produce a negative percent change, which helps eliminate a ratio answer like 85 percent.
Common Mistakes to Avoid
- -Using the ending value as the base
- -Reporting a ratio instead of a change
- -Dropping the negative sign on a decline
Concept Deep Dive
Analysis
This question tests percent change applied to listing inventory. Subtract the starting count from the ending count, divide by the starting count and multiply by 100. A negative result shows inventory fell during the quarter.
Background Knowledge
Listing inventory trends help show whether supply is rising or falling relative to demand. A falling inventory with steady sales generally points to tightening supply. Consistent geography and listing definitions are needed for a valid comparison between periods.
Real-World Application
An appraiser tracking a neighborhood's active listings sees the count drop from 640 to 544 over a quarter. She reports the 15% decline in inventory as part of her support for stable to increasing market conditions, along with sales and price data.
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