A shop keeper offers a discount of 20% on a jacket and sales tax levied on the jacket is 15%.Quantity X: if a person first paid the tax then took the discount.Quantity Y: if a person first took the discount then paid the tax.
Correct answer: D. Quantity X and Quantity Y are equal.
- A. Quantity X is greater than Quantity Y.
- B. Quantity Y is greater than Quantity X.
- C. The relationship cannot be determined.
- D. Quantity X and Quantity Y are equal.
Explanation
The key to solving this question is recognizing that percentage calculations are independent of the order in which they are applied when both are applied consecutively to the same base amount. In both Quantity X and Quantity Y, the final price is calculated as 0.92x:For Quantity X, applying the tax first and then the discount gives us a final amount of 0.92x. Similarly, for Quantity Y, applying the discount first and then the tax also results in a final amount of 0.92x.This demonstrates that the sequence of applying a discount and a tax does not affect the final price. Therefore, the correct choice is that both quantities are equal.
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About Quantitative Reasoning
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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