1953 AHSME Problems/Problem 19

Revision as of 20:48, 1 April 2017 by Xiej (talk | contribs) (Created page with "==Problem 19== In the expression <math>xy^2</math>, the values of <math>x</math> and <math>y</math> are each decreased <math>25</math> %; the value of the expression is: <m...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem 19

In the expression $xy^2$, the values of $x$ and $y$ are each decreased $25$ %; the value of the expression is:

$\textbf{(A)}\ \text{decreased } 50\% \qquad \textbf{(B)}\ \text{decreased }75\%\\  \textbf{(C)}\ \text{decreased }\frac{37}{64}\text{ of its value}\qquad \textbf{(D)}\ \text{decreased }\frac{27}{64}\text{ of its value}\\ \textbf{(E)}\ \text{none of these}$

Solution

$xy^2$

$(\frac{3x}{4})(\frac{3y}{4})^2$

$(\frac{3}{4})^3xy^2$

$\frac{27}{64}xy^2$

$xy^2-\frac{27}{64}xy^2 = \frac{37}{64}xy^2 \implies \textbf{(C)}$

See Also

1953 AHSC (ProblemsAnswer KeyResources)
Preceded by
Problem 18
Followed by
Problem 20
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 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
All AHSME Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png