Difference between revisions of "1986 AHSME Problems/Problem 20"

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==Solution==
 
==Solution==
  
We see that <math>x</math> is multiplied by <math>\frac{100+p}{100}</math> when it is increased by <math>p%</math>. Therefore, <math>y</math> is multiplied by <math>\frac{100}{100+p}</math>, and so it is decreased by <math>\frac{p}{100+p}</math> times itself. Therefore, it is decreased by <math>\frac{100p}{100+p}%</math>, and so the answer is <math>\boxed{E}</math>.
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We see that <math>x</math> is multiplied by <math>\frac{100+p}{100}</math> when it is increased by <math>p</math>%. Therefore, <math>y</math> is multiplied by <math>\frac{100}{100+p}</math>, and so it is decreased by <math>\frac{p}{100+p}</math> times itself. Therefore, it is decreased by <math>\frac{100p}{100+p}</math>%, and so the answer is <math>\boxed{E}</math>.
  
 
== See also ==
 
== See also ==

Latest revision as of 18:50, 9 October 2017

Problem

Suppose $x$ and $y$ are inversely proportional and positive. If $x$ increases by $p\%$, then $y$ decreases by

$\textbf{(A)}\ p\%\qquad \textbf{(B)}\ \frac{p}{1+p}\%\qquad \textbf{(C)}\ \frac{100}{p}\%\qquad \textbf{(D)}\ \frac{p}{100+p}\%\qquad \textbf{(E)}\ \frac{100p}{100+p}\%$

Solution

We see that $x$ is multiplied by $\frac{100+p}{100}$ when it is increased by $p$%. Therefore, $y$ is multiplied by $\frac{100}{100+p}$, and so it is decreased by $\frac{p}{100+p}$ times itself. Therefore, it is decreased by $\frac{100p}{100+p}$%, and so the answer is $\boxed{E}$.

See also

1986 AHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 19
Followed by
Problem 21
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 26 27 28 29 30
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