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Compare the two quantities below.
Column A: $(x-1)(x)(x+1)$
Column B: $(x)(x)(x)$
Column A: $(x-1)(x)(x+1) = x(x^2-1) = x^3 - x$
Column B: $x \cdot x \cdot x = x^3$
Difference: B $-$ A $= x^3 - (x^3 - x) = x$.
- If $x > 0$: Column B is greater
- If $x = 0$: both equal 0 (equal)
- If $x < 0$: Column A is greater
Since no restriction is placed on $x$, the relationship cannot be determined from the information given.
A firm maintains an allowance for doubtful debts at 5% of trade receivables. This year, trade receivables were $8,000, which represented a 20% decrease from the previous year. How will this change affect the current year's profit?
1. Current Receivables = $8,000. Current Allowance = $8,000 $\times$ 5% = $400.
2. Last Year Receivables = $8,000 / 0.80 = $10,000. Last Year Allowance = $10,000 $\times$ 5% = $500.
3. Change = $500 - $400 = $100 reduction in allowance.
A reduction in allowance is credited to the income statement, thus increasing profit by $100.
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