Difference between revisions of "2020 AMC 12B Problems/Problem 2"
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− | ==Problem== | + | == Problem == |
+ | 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> | ||
+ | |||
+ | == Solution == | ||
+ | Using difference of squares to factor the left term, we get | ||
+ | <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. | ||
+ | |||
+ | == Video Solution (HOW TO CREATIVELY THINK!!!)== | ||
+ | https://youtu.be/2z8MaCeqIKs | ||
+ | |||
+ | ~Education, the Study of Everything | ||
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+ | |||
+ | |||
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− | == | + | == Video Solution == |
+ | https://youtu.be/WfTty8Fe5Fo | ||
+ | == 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 15:00, 8 June 2023
Contents
Problem
What is the value of the following expression?
Solution
Using difference of squares to factor the left term, we get
Cancelling all the terms, we get
as the answer.
Video Solution (HOW TO CREATIVELY THINK!!!)
~Education, the Study of Everything
Video Solution
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.