1988 AJHSME Problems/Problem 22

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Problem

Tom's Hat Shoppe increased all original prices by $25\%$ . Now the shoppe is having a sale where all prices are $20\%$ off these increased prices. Which statement best describes the sale price of an item?

$\text{(A)}\ \text{The sale price is }5\% \text{ higher than the original price.}$

$\text{(B)}\ \text{The sale price is higher than the original price, but by less than }5\% .$

$\text{(C)}\ \text{The sale price is higher than the original price, but by more than }5\% .$

$\text{(D)}\ \text{The sale price is lower than the original price.}$

$\text{(E)}\ \text{The same price is the same as the original price.}$

Solution

Let the original price of an item be $x$ . The shoppe originally increased this to $1.25x$ . The sale brings it down to $.8(1.25x)=x$ , which is the same as the original $\rightarrow \boxed{\text{E}}$

1988 AJHSME (Problems • Resources)
Preceded by Problem 21	Followed by Problem 23
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1988 AJHSME Problems/Problem 22

From AoPSWiki

Problem

Solution

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