https://artofproblemsolving.com/wiki/index.php?title=1961_AHSME_Problems/Problem_18&feed=atom&action=history 1961 AHSME Problems/Problem 18 - Revision history 2022-01-20T06:25:31Z Revision history for this page on the wiki MediaWiki 1.31.1 https://artofproblemsolving.com/wiki/index.php?title=1961_AHSME_Problems/Problem_18&diff=94659&oldid=prev Rockmanex3: Solution to Problem 18 2018-05-21T15:03:10Z <p>Solution to Problem 18</p> <p><b>New page</b></p><div>== Problem ==<br /> <br /> The yearly changes in the population census of a town for four consecutive years are, <br /> respectively, 25% increase, 25% increase, 25% decrease, 25% decrease. <br /> The net change over the four years, to the nearest percent, is:<br /> <br /> &lt;math&gt;\textbf{(A)}\ -12 \qquad<br /> \textbf{(B)}\ -1 \qquad<br /> \textbf{(C)}\ 0 \qquad<br /> \textbf{(D)}\ 1\qquad<br /> \textbf{(E)}\ 12 &lt;/math&gt;<br /> <br /> ==Solution==<br /> A 25% increase means the new population is &lt;math&gt;\frac{5}{4}&lt;/math&gt; of the original population. A 25% decrease means the new population is &lt;math&gt;\frac{3}{4}&lt;/math&gt; of the original population.<br /> <br /> Thus, after four years, the population is &lt;math&gt;1 \cdot \frac{5}{4} \cdot \frac{5}{4} \cdot \frac{3}{4} \cdot \frac{3}{4} = \frac{225}{256}&lt;/math&gt; times the original population.<br /> <br /> Thus, the net change is -12%, so the answer is &lt;math&gt;\boxed{\textbf{(A)}}&lt;/math&gt;.<br /> <br /> ==See Also==<br /> {{AHSME 40p box|year=1961|num-b=17|num-a=19}}<br /> <br /> {{MAA Notice}}</div> Rockmanex3