A worker's wage is increased by 30% and subsequently cut by 30%. What is the net percentage change?
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Answer: C. 9% decrease
Explanation
Successive percentage changes of equal magnitude in opposite directions always yield a net decrease. Squaring the percentage value of thirty and dividing by one hundred gives nine percent. The net result of a thirty percent increase followed by a thirty percent decrease is a nine percent decrease. Successive percentage increases and decreases do not cancel each other out due to shifting base values. The formula for equal successive percentage changes is negative x squared over one hundred. Percentage calculations depend heavily on the magnitude of the base value at each step.
Stock market traders understand that a fifty percent loss requires a one hundred percent gain to recover. Retail pricing strategies account for successive markups and markdowns without assuming zero net change. Economic analyses of tax rate fluctuations use successive percentage formulas to measure revenue impacts. Option a incorrectly assumes a massive price surge despite an equal percentage reduction. Option b overestimates the net change by misapplying the compounding percentage formula. Option d assumes the increases and cancels out linearly which violates fundamental percentage rules.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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