Difference between revisions of "2020 AMC 12B Problems/Problem 2"

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<cmath>\frac{100^2-7^2}{70^2-11^2} \cdot \frac{(70-11)(70+11)}{(100-7)(100+7)} = \frac{(100-7)(100+7)}{(70-11)(70+11)} \cdot \frac{(70-11)(70+11)}{(100-7)(100+7)}.</cmath>
 
<cmath>\frac{100^2-7^2}{70^2-11^2} \cdot \frac{(70-11)(70+11)}{(100-7)(100+7)} = \frac{(100-7)(100+7)}{(70-11)(70+11)} \cdot \frac{(70-11)(70+11)}{(100-7)(100+7)}.</cmath>
 
Cancelling all the terms, we get <math>\boxed{\textbf{(A) } 1}</math> as the answer.
 
Cancelling all the terms, we get <math>\boxed{\textbf{(A) } 1}</math> as the answer.
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== Video Solution (HOW TO CREATIVELY THINK!!!)==
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https://youtu.be/2z8MaCeqIKs
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 +
~Education, the Study of Everything
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== Video Solution ==
 
== Video Solution ==
 
https://youtu.be/WfTty8Fe5Fo
 
https://youtu.be/WfTty8Fe5Fo
 
~IceMatrix
 
  
 
== See Also ==
 
== See Also ==
 
{{AMC12 box|year=2020|ab=B|num-b=1|num-a=3}}
 
{{AMC12 box|year=2020|ab=B|num-b=1|num-a=3}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Latest revision as of 14:00, 8 June 2023

Problem

What is the value of the following expression?

\[\frac{100^2-7^2}{70^2-11^2} \cdot \frac{(70-11)(70+11)}{(100-7)(100+7)}\]

$\textbf{(A) } 1 \qquad \textbf{(B) } \frac{9951}{9950} \qquad \textbf{(C) } \frac{4780}{4779} \qquad \textbf{(D) } \frac{108}{107} \qquad \textbf{(E) } \frac{81}{80}$

Solution

Using difference of squares to factor the left term, we get \[\frac{100^2-7^2}{70^2-11^2} \cdot \frac{(70-11)(70+11)}{(100-7)(100+7)} = \frac{(100-7)(100+7)}{(70-11)(70+11)} \cdot \frac{(70-11)(70+11)}{(100-7)(100+7)}.\] Cancelling all the terms, we get $\boxed{\textbf{(A) } 1}$ as the answer.

Video Solution (HOW TO CREATIVELY THINK!!!)

https://youtu.be/2z8MaCeqIKs

~Education, the Study of Everything




Video Solution

https://youtu.be/WfTty8Fe5Fo

See Also

2020 AMC 12B (ProblemsAnswer KeyResources)
Preceded by
Problem 1
Followed by
Problem 3
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

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