Difference between revisions of "1958 AHSME Problems/Problem 2"

Latest revision as of 06:10, 3 October 2014

Problem

If $\frac {1}{x} - \frac {1}{y} = \frac {1}{z}$ , then $z$ equals:

$\textbf{(A)}\ y - x\qquad \textbf{(B)}\ x - y\qquad \textbf{(C)}\ \frac {y - x}{xy}\qquad \textbf{(D)}\ \frac {xy}{y - x}\qquad \textbf{(E)}\ \frac {xy}{x - y}$

Solution

$\frac{1}{x}-\frac{1}{y}=\frac{1}{z}$

$\frac{y}{xy}-\frac{x}{xy}=\frac{1}{z}$

$\frac{y-x}{xy}=\frac{1}{z}$

$\frac{1}{\frac{y-x}{xy}}=\frac{1}{\frac{1}{z}}$

$\frac{xy}{y-x}=z$

The answer is therefore $\boxed{\text{D}}$ .

1958 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 1	Followed by Problem 3
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All AHSME Problems and Solutions

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

@@ Line 17: / Line 17: @@
 <math> \frac{xy}{y-x}=z</math>
-The answer is therefore <math>mathbf{(D)}</math>.
+The answer is therefore <math>\boxed{\text{D}}</math>.
 ==See also==
-{{AHSME box|year=1958|num-b=1|num-a=3}}
+{{AHSME 50p box|year=1958|num-b=1|num-a=3}}
+{{MAA Notice}}

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Difference between revisions of "1958 AHSME Problems/Problem 2"

Latest revision as of 06:10, 3 October 2014

Problem

Solution

See also