Difference between revisions of "2015 AMC 10A Problems/Problem 1"

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What is the value of <math>(2^0-1+5^2-0)^{-1}\times5?</math>
 
What is the value of <math>(2^0-1+5^2-0)^{-1}\times5?</math>
  
<math> \textbf{(A)}\ -125\qquad\textbf{(B)}\ -120\qquad\textbf{(C)}\ \frac{1}{5}\qquad\textbf{(D)}}\ \frac{5}{24}\qquad\textbf{(E)}\ 25</math>
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<math> \textbf{(A)}\ -125\qquad\textbf{(B)}\ -120\qquad\textbf{(C)}\ \frac{1}{5}\qquad\textbf{(D)}\ \frac{5}{24}\qquad\textbf{(E)}\ 25</math>
  
 
==Solution==
 
==Solution==
<math>(2^0-1+5^2-0)^{-1}\times5</math>
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<math>(2^0-1+5^2-0)^{-1}\times5 = (1-1+25-0)^{-1} \times 5 = 25^{-1} \times 5 = \frac{1}{25} \times 5 = \boxed{\textbf{(C) } \, \frac{1}{5}}</math>.
<math>=(1-1+{25}-0)^{-1}\times5</math>
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<math>={\frac{1}{25}}\times5</math>
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Bash it out.
<math>=-25\times5</math>
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<math>=-125\implies{\boxed{\textbf{(C)}{\frac{1}{5}}}</math>
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==Video Solution==
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https://youtu.be/UdENmDoPGHU
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 +
~savannahsolver
  
 
==See Also==
 
==See Also==

Latest revision as of 18:00, 16 June 2020

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 $(2^0-1+5^2-0)^{-1}\times5?$

$\textbf{(A)}\ -125\qquad\textbf{(B)}\ -120\qquad\textbf{(C)}\ \frac{1}{5}\qquad\textbf{(D)}\ \frac{5}{24}\qquad\textbf{(E)}\ 25$

Solution

$(2^0-1+5^2-0)^{-1}\times5 = (1-1+25-0)^{-1} \times 5 = 25^{-1} \times 5 = \frac{1}{25} \times 5 = \boxed{\textbf{(C) } \, \frac{1}{5}}$.

Bash it out.

Video Solution

https://youtu.be/UdENmDoPGHU

~savannahsolver

See Also

2015 AMC 10A (ProblemsAnswer KeyResources)
Preceded by
First Problem
Followed by
Problem 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 (ProblemsAnswer KeyResources)
Preceded by
First Problem
Followed by
Problem 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

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

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