1985 AJHSME Problems/Problem 21
Revision as of 17:28, 13 January 2009 by 5849206328x (talk | contribs) (New page: ==Problem== Mr. Green receives a <math>10\% </math> raise every year. His salary after four such raises has gone up by what percent? <math>\text{(A)}\ \text{less than }40\% \qquad \text...)
Problem
Mr. Green receives a 
raise every year. His salary after four such raises has gone up by what percent?
Solution
If he gets a raise, then his new salary is 
of what it was before. He gets 
raises, so his new salary is 
of the previous salary. We want to know the percent of increase from 
, so we just need 
as a percent.
If you know your powers of 
well, then you can just do 
, so the answer is 
If you don't know this, then first we note that clearly does not have a whole number percent representation, so the only possible choices are 
and 
. We also have ![\[1.1^4=1.21^2>1.2^2=1.44\]](http://latex.artofproblemsolving.com/1/8/3/1833150c45a314697bdb371ea339a3f109747a88.png)
so the percent is greater than 
and the only choice left is .
