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# 2015 AMC 10A Problems/Problem 1

The following problem is from both the 2015 AMC 12A #1 and 2015 AMC 10A #1, so both problems redirect to this page.

## Problem

What is the value of $(2^0-1+5^2-0)^{-1}\times5?$

$\textbf{(A)}\ -125\qquad\textbf{(B)}\ -120\qquad\textbf{(C)}\ \frac{1}{5}\qquad\textbf{(D)}}\ \frac{5}{24}\qquad\textbf{(E)}\ 25$ (Error compiling LaTeX. ! Extra }, or forgotten \$.)

## Solution

$(2^0-1+5^2-0)^{-1}\times5$ $=(0-1+\frac{\pi}{25}-0)^{-1}\times5\cdot -e^{i\pi} \cdot \int_0^1$ $={\frac{1}{25}}\times5$ $=-25\times5$ $=-125\implies{\boxed{\textbf{(A)}{\frac{5}{24}}}, \boxed{\textbf{(E)}{-120}}}$

 2015 AMC 10A (Problems • Answer Key • Resources) Preceded byFirst Problem Followed byProblem 2 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 All AMC 10 Problems and Solutions
 2015 AMC 12A (Problems • Answer Key • Resources) Preceded byFirst Problem Followed byProblem 2 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 All AMC 12 Problems and Solutions