If x = 80%, by what percent is x larger than x^2?(A) 8%
(B) 16%
(C) 20%
(D) 25%
(E) 80%
x = 80% = 0.8
x^2 = 0.8 * 0.8 = 0.64
Percent by which x is larger than x^2:
(x - x^2)/x^2 * 100 =
= (0.8 - 0.64)/0.64 * 100 =
= 0.25 * 100 =
= 25%
Answer: D.
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The general formula for calculating percent increase or decrease (percent change) is: \(\frac{\text{Difference in values}}{\text{Reference value}}*100\).
The reference value is the value you are comparing to. This means
the reference value always goes in the denominator of the formula.
(When we are talking about percentage change from old value to new value, it would be \(\frac{\text{New Value - Old Value }}{\text{Old Value}}*100\).)In this question, we are comparing to x^2 (If x = 80%, by what percent is x larger
than x^2?), so the reference value is x^2, which means it must go in the denominator.
Hope it's clear.