Difference between revisions of "1985 AJHSME Problem 9"
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<math>\text{(A)}\ \frac {1}{10} \qquad \text{(B)}\ \frac {1}{9} \qquad \text{(C)}\ \frac {1}{2} \qquad \text{(D)}\ \frac {10}{11} \qquad \text{(E)}\ \frac {11}{2}</math> | <math>\text{(A)}\ \frac {1}{10} \qquad \text{(B)}\ \frac {1}{9} \qquad \text{(C)}\ \frac {1}{2} \qquad \text{(D)}\ \frac {10}{11} \qquad \text{(E)}\ \frac {11}{2}</math> | ||
| − | == In-depth Solution by | + | == In-depth Solution by BoundlessBrain!== |
https://youtu.be/yBrLXnjasgg | https://youtu.be/yBrLXnjasgg | ||
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<cmath>\frac{1}{2} \cdot \frac{2}{3} \dots \frac{9}{10}.</cmath> | <cmath>\frac{1}{2} \cdot \frac{2}{3} \dots \frac{9}{10}.</cmath> | ||
Numerators and denominators cancel to yield the answer: <math>\boxed{\text{(A)} \frac{1}{10}}.</math> | Numerators and denominators cancel to yield the answer: <math>\boxed{\text{(A)} \frac{1}{10}}.</math> | ||
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| + | == Solution 2 (Brute Force) == | ||
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| + | Multiply the numerators and denominators | ||
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| + | The expression is <math>\frac{362880}{3628800}</math> which is <math>\frac{1}{10}</math> or <math>\boxed{\textbf{(A)}\frac{1}{10}}</math> | ||
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| + | <math>\textbf{Note: Do not use unless no other method found}</math> | ||
Latest revision as of 07:29, 6 October 2024
Problem
The product of the 9 factors 
In-depth Solution by BoundlessBrain!
Solution
This product simplifies to:
![\[\frac{1}{2} \cdot \frac{2}{3} \dots \frac{9}{10}.\]](http://latex.artofproblemsolving.com/c/d/f/cdf3e4229337b6e0cb5e4e4d010c70f59ef5a685.png)
Numerators and denominators cancel to yield the answer: 
Solution 2 (Brute Force)
Multiply the numerators and denominators
The expression is 
which is 
or 
