1970 AHSME Problems/Problem 3

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Problem

If $x=1+2^p$ and $y=1+2^{-p}$, then $y$ in terms of $x$ is

$\text{(A) } \frac{x+1}{x-1}\quad \text{(B) } \frac{x+2}{x-1}\quad \text{(C) } \frac{x}{x-1}\quad \text{(D) } 2-x\quad \text{(E) } \frac{x-1}{x}$

Solution

Since we want the $y$ expression in terms of $x$, let's convert the $y$ expression. We can convert it to $1+ \frac{1}{2^p} \Rightarrow \frac{2^p+1}{2^p} \Rightarrow \frac{x}{x-1} \Rightarrow$ $\fbox{C}$

See also

1970 AHSC (ProblemsAnswer KeyResources)
Preceded by
Problem 2
Followed by
Problem 4
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