Difference between revisions of "2020 AMC 10A Problems/Problem 3"
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| + | ==Problem 3== | ||
| + | Assuming <math>a\neq3</math>, <math>b\neq4</math>, and <math>c\neq5</math>, what is the value in simplest form of the following expression? | ||
| + | <cmath>\frac{a-3}{5-c} \cdot \frac{b-4}{3-a} \cdot \frac{c-5}{4-b}</cmath> | ||
| + | <math>\textbf{(A) } -1 \qquad \textbf{(B) } 1 \qquad \textbf{(C) } \frac{abc}{60} \qquad \textbf{(D) } \frac{1}{abc} - \frac{1}{60} \qquad \textbf{(E) } \frac{1}{60} - \frac{1}{abc}</math> | ||
| + | |||
| + | == Solution == | ||
| + | |||
| + | 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{\text{(A) }-1}</math>. | ||
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==See Also== | ==See Also== | ||
{{AMC10 box|year=2020|ab=A|num-b=2|num-a=4}} | {{AMC10 box|year=2020|ab=A|num-b=2|num-a=4}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 22:06, 31 January 2020
Problem 3
Assuming 
, 
, and 
, what is the value in simplest form of the following expression?
![\[\frac{a-3}{5-c} \cdot \frac{b-4}{3-a} \cdot \frac{c-5}{4-b}\]](http://latex.artofproblemsolving.com/9/2/6/926ff7e4cb0ce3392334f8215dd3aa4c51438f15.png)
Solution
Note that 
is 
times 
. Likewise, 
is times 
and 
is times 
. Therefore, the product of the given fraction equals 
.
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. 
