Difference between revisions of "1988 AJHSME Problems/Problem 22"

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<math>\text{(D)}\ \text{The sale price is lower than the original price.}</math>
 
<math>\text{(D)}\ \text{The sale price is lower than the original price.}</math>
  
<math>\text{(E)}\ \text{The same price is the same as the original price.}</math>
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<math>\text{(E)}\ \text{The sale price is the same as the original price.}</math>
  
 
==Solution==
 
==Solution==

Revision as of 10:39, 20 August 2011

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?

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

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

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

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

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

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 $\rightarrow \boxed{\text{E}}$

See Also

1988 AJHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 21
Followed by
Problem 23
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All AJHSME/AMC 8 Problems and Solutions