The quantities x and y are positive. If x is decreased by 20 percent and y is increased by 20 percent, then the product of x and y is
Correct answer: B. decreased by 4%
- A. unchanged
- B. decreased by 4%
- C. increased by 5%
- D. decreased by 6%
Explanation
Let's assume that the original values of x and y are X and Y, respectively.If x is decreased by 20%, then its new value is:x = X - 0.2X = 0.8XIf y is increased by 20%, then its new value is:y = Y + 0.2Y = 1.2YThe product of x and y is:xy = (0.8X)(1.2Y) = 0.96XYSo the new product is 0.96 times the original product.This means that the product of x and y is decreased by 4%.Therefore, the answer is (B) decreased by 4%
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Quantitative reasoning applies arithmetic and basic algebra to numerical relationships, including percentages, ratios, averages, fractions, proportions, profit and loss, rates, time, work and measurement. Questions focus on translating words into equations, choosing an efficient method and checking whether the result is numerically reasonable.
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