The sale-price range is $45,000 and the maximum is $385,000. Find the minimum price.
Correct Answer
C) $340,000
Minimum=maximum−range=385000−45000=340000. Adding the range would give a number above the stated maximum.
Why This Is the Correct Answer
Option C is correct because minimum = maximum − range = $385,000 − $45,000 = $340,000. The range is defined as the maximum value minus the minimum value. Rearranging that definition gives the minimum directly.
Why the Other Options Are Wrong
Option A: $430,000
Option A, $430,000, comes from adding the range to the maximum, $385,000 + $45,000. That gives a figure above the stated maximum, which is impossible; the correct minimum is $385,000 − $45,000 = $340,000.
Option B: $45,000
Option B, $45,000, is the range itself, not the minimum price. The minimum is $385,000 − $45,000 = $340,000.
Option D: $385,000
Option D, $385,000, is the maximum, not the minimum. Subtracting the range gives $385,000 − $45,000 = $340,000.
Max minus range equals min
Since range is max minus min, the minimum is what is left when you take the range away from the maximum.
How to use: Use this when a question gives the range and one endpoint and asks for the other.
Exam Tip
Check that your minimum is below the maximum; an answer above the maximum signals you added instead of subtracted.
Common Mistakes to Avoid
- -Adding the range to the maximum
- -Reporting the range as the minimum
- -Reporting the maximum as the minimum
Concept Deep Dive
Analysis
This question tests rearranging the range formula, range = maximum − minimum. Solving for the minimum gives minimum = maximum − range. The distractors come from adding instead of subtracting or reporting one of the given numbers.
Background Knowledge
The range is the simplest measure of dispersion, equal to the largest value minus the smallest. It is sensitive to extreme values because it depends only on the two endpoints. Knowing any two of maximum, minimum and range lets you find the third.
Real-World Application
An appraiser's summary notes that sales topped out at $385,000 with a $45,000 range. A reader can quickly infer that the lowest sale was $340,000, giving a clear picture of the price bracket.
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