A store increased the original price of a shirt by a certain percent and then decreased the new price by the same percent. Given that the resulting price was $84\%$ of the original price, by what percent was the price increased and decreased?

A. 16

B. 20

C. 28

D. 36

E. 40

1. 2019 AMC 8 官方解析

一个商店把一件衬衫的价格先是提高了一定的百分比，而后又降低了同样的百分比．于是最终的价格只有最初价格的$84\%$，则先增长而又下降的这个百分比是多少？

Denote the percent as $x$.

$(1 - x\%)(1 + x\%) = 84\%$

$1 - (x\%)^2 = 84\%$

$(x\%)^2 = 16\%$

$x\% = 40\%$.

As we don't define here a negative percentage.

So the answer is E.