1976 AHSME Problems/Problem 1

Problem 1

If one minus the reciprocal of $(1-x)$ equals the reciprocal of $(1-x)$ , then $x$ equals

$\textbf{(A) }-2\qquad \textbf{(B) }-1\qquad \textbf{(C) }1/2\qquad \textbf{(D) }2\qquad \textbf{(E) }3$

Solution

The reciprocal of $(1-x)$ is $\frac{1}{1-x}$ , so our equation is $1-\frac{1}{1-x}=\frac{1}{1-x},$ which is equivalent to $\frac{1}{1-x}=\frac{1}{2}$ . So, $1-x=2$ and $x=-1\Rightarrow \textbf{(B)}$ .~MathJams

1976 AHSME (Problems • Answer Key • Resources)
Preceded by 1975 AHSME	Followed by 1977 AHSME
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
All AHSME Problems and Solutions

Page

Toolbox

Search

1976 AHSME Problems/Problem 1

Problem 1

Solution