Two quantities X and Y trail a third quantity Z by 20% and 28% respectively. By what percentage does quantity Y fall short of quantity X?
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Answer: C. 10%
Explanation
Letting the third reference quantity Z be one hundred, quantity X equals eighty and quantity Y equals seventy two. The absolute difference between quantity X and quantity Y is eight units based on these established values. Dividing the difference of eight by quantity X which is eighty yields a percentage shortfall of exactly ten percent. Comparative percentage calculations require identifying the exact base quantity against which the relative difference is measured. Setting a reference variable to one hundred simplifies the conversion of percentage discounts into concrete numerical values. Fractional reduction formulas divide absolute differences by the primary comparison baseline to determine percentage shortfalls.
Eight percent incorrectly assumes the absolute difference equals the percentage without dividing by the base quantity X. Nine percent is mathematically inconsistent with the exact ratio of eight to eighty derived from the problem values. Eleven percent overestimates the percentage shortfall through an incorrect choice of comparison denominator.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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