A comparable grid has a signed net adjustment of +$18,000 and a gross adjustment of $22,000. What is the total magnitude of its negative adjustments?
Correct Answer
A) $2,000
Let P and N be positive and negative magnitudes; P − N = 18000 and P + N = 22000; N = (22000 − 18000) / 2 = 2000. Common errors: not halving the difference between gross and net gives $4,000; adding gross and net gives $40,000; reporting the net adjustment gives $18,000.
Why This Is the Correct Answer
Option A is correct because P − N = $18,000 and P + N = $22,000. Subtracting the first equation from the second gives 2N = $4,000, so N = $2,000. Check: P = $20,000, so $20,000 − $2,000 = $18,000 net and $20,000 + $2,000 = $22,000 gross.
Why the Other Options Are Wrong
Option B: $4,000
Option B, $4,000, is the difference between gross and net ($22,000 − $18,000) without halving it. That difference equals 2N, so N = $4,000 / 2 = $2,000.
Option C: $18,000
Option C, $18,000, simply reports the net adjustment. The net is the positive total minus the negatives; solving the equations gives negatives of $2,000.
Option D: $40,000
Option D, $40,000, adds gross and net ($22,000 + $18,000). That sum equals 2P, twice the positive adjustments, not the negatives; the negatives are ($22,000 − $18,000) / 2 = $2,000.
Half the gap
The adjustments opposite in sign to the net equal half the gap between gross and net.
How to use: Use this to recover hidden adjustment totals from net and gross figures.
Exam Tip
Set up the two equations P − N = net and P + N = gross and check your answer by plugging it back in.
Common Mistakes to Avoid
- -Forgetting to halve the difference between gross and net
- -Adding gross and net to find the negatives
- -Confusing the net total with the negative adjustments
Concept Deep Dive
Analysis
This question tests the algebra linking net and gross adjustments. Let P be total positive adjustments and N the magnitude of negative adjustments: net is P − N and gross is P + N. Solving gives N = (gross − net) / 2 = ($22,000 − $18,000) / 2 = $2,000.
Background Knowledge
Net adjustment is the signed sum of all adjustments, while gross adjustment is the sum of their absolute values. Because positives and negatives cancel in the net but not the gross, the gap between the two reveals the size of the adjustments running against the net direction. These totals appear on the sales comparison grid.
Real-World Application
A reviewer sees a comparable with a +$18,000 net and $22,000 gross adjustment on a grid. Using the two totals, the reviewer determines the comparable carried $20,000 of positive and $2,000 of negative adjustments. This tells the reviewer the comparable was mostly inferior to the subject.
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