Difference between revisions of "2020 AMC 12B Problems/Problem 2"
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What is the value of the following expression? | What is the value of the following expression? | ||
| − | <cmath>\frac{100^2-7^2}{70^2-11^2} \cdot \frac{(70-11)(70+11)}{(100-7)(100+7)}</cmath><math>\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} </math> | + | <cmath>\frac{100^2-7^2}{70^2-11^2} \cdot \frac{(70-11)(70+11)}{(100-7)(100+7)}</cmath> |
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| + | <math>\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} </math> | ||
== Solution == | == Solution == | ||
Revision as of 13:28, 19 January 2021
Contents
Problem
What is the value of the following expression?
![\[\frac{100^2-7^2}{70^2-11^2} \cdot \frac{(70-11)(70+11)}{(100-7)(100+7)}\]](http://latex.artofproblemsolving.com/5/f/4/5f4f7b3d646f920fd9ef3f767aad765860768b41.png)
Solution
Using difference of squares to factor the left term, we get
![\[\frac{100^2-7^2}{70^2-11^2} \cdot \frac{(70-11)(70+11)}{(100-7)(100+7)} =\]](http://latex.artofproblemsolving.com/b/9/b/b9bfcc5c19805ee0e129d431b33d0bed28354834.png)
![\[\frac{(100-7)(100+7)}{(70-11)(70+11)} \cdot \frac{(70-11)(70+11)}{(100-7)(100+7)}\]](http://latex.artofproblemsolving.com/b/4/4/b444697a7e198c859f5a04efac8eb60127101d77.png)
Cancelling all the terms, we get 
as the answer.
Video Solution
~IceMatrix
See Also
| 2020 AMC 12B (Problems • Answer Key • Resources) | |
| 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 | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
