Difference between revisions of "2020 AMC 10A Problems/Problem 3"
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Note that <math>a-3</math> is <math>-1</math> times <math>3-a</math>. Likewise, <math>b-4</math> is <math>-1</math> times <math>4-b</math> and <math>c-5</math> is <math>-1</math> times <math>5-c</math>. Therefore, the product of the given fraction equals <math>(-1)(-1)(-1)=\boxed{\textbf{(A)}-1}</math>. | Note that <math>a-3</math> is <math>-1</math> times <math>3-a</math>. Likewise, <math>b-4</math> is <math>-1</math> times <math>4-b</math> and <math>c-5</math> is <math>-1</math> times <math>5-c</math>. Therefore, the product of the given fraction equals <math>(-1)(-1)(-1)=\boxed{\textbf{(A)}-1}</math>. | ||
Revision as of 14:25, 22 December 2020
Contents
Problem
Assuming ,
, and
, what is the value in simplest form of the following expression?
Solutions
Solution 1
Note that is
times
. Likewise,
is
times
and
is
times
. Therefore, the product of the given fraction equals
.
Solution 2
Substituting values for , we see that if each of them satify the inequalities above, the value goes to be
.
Therefore, the product of the given fraction equals
.
Solution 3
It is known that for
. We use this fact to cancel out the terms.
~CoolJupiter
Video Solution 1
~IceMatrix
Video Solution
Education, The Study of Everything
Video Solution 2
https://www.youtube.com/watch?v=7-3sl1pSojc
~bobthefam
Video Solution 3
~savannahsolver
See Also
2020 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 2 |
Followed by Problem 4 | |
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.