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Difference between revisions of "1985 AJHSME Problems/Problem 21"

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==Solution==
 
==Solution==
  
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If he gets a <math>10\% </math> raise, then his new salary is <math>1.1</math> of what it was before. He gets <math>4</math> raises, so his new salary is <math>1.1^4</math> of the previous salary. We want to know the percent of increase from <math>1</math>, so we just need <math>1.1^4-1</math> as a percent.
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assume his salary is 100 dollars then the next year he would have 110 dollars then the next year he would have 121 dollars then the next year he would have 133.1 dollars so therefore it is A
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If you know your powers of <math>11</math> well, then you can just do <math>1.4641-1=.4641>45\% </math>, so the answer is <math>\boxed{\text{E}}</math>
 
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If you don't know this, then first we note that <math>1.1^4</math> clearly does not have a whole number percent representation, so the only possible choices are <math>\text{A}</math> and <math>\text{E}</math>. We also have <cmath>1.1^4=1.21^2>1.2^2=1.44</cmath>
 
  
 
so the percent is greater than <math>40\% </math> and the only choice left is <math>\boxed{\text{E}}</math>.
 
so the percent is greater than <math>40\% </math> and the only choice left is <math>\boxed{\text{E}}</math>.

Revision as of 13:33, 8 November 2015

Problem

Mr. Green receives a $10\%$ raise every year. His salary after four such raises has gone up by what percent?

$\text{(A)}\ \text{less than }40\% \qquad \text{(B)}\ 40\% \qquad \text{(C)}\ 44\% \qquad \text{(D)}\ 45\% \qquad \text{(E)}\ \text{more than }45\%$

Solution

assume his salary is 100 dollars then the next year he would have 110 dollars then the next year he would have 121 dollars then the next year he would have 133.1 dollars so therefore it is A

so the percent is greater than $40\%$ and the only choice left is $\boxed{\text{E}}$.

See Also

1985 AJHSME (Problems • Answer Key • Resources)
Preceded by
Problem 20 		Followed by
Problem 22
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AJHSME/AMC 8 Problems and Solutions


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