Difference between revisions of "2015 AMC 12A Problems/Problem 24"
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==Problem== | ==Problem== | ||
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| − | <math>\textbf{(A) } | + | Rational numbers <math>a</math> and <math>b</math> are chosen at random among all rational numbers in the interval <math>[0,2)</math> that can be written as fractions <math>\frac{n}{d}</math> where <math>n</math> and <math>d</math> are integers with <math>1 \le d \le 5</math>. What is the probability that |
| + | <cmath>(\text{cos}(a\pi)+i\text{sin}(b\pi))^4</cmath> | ||
| + | is a real number? | ||
| + | |||
| + | <math> \textbf{(A)}\ \frac{3}{5} \qquad\textbf{(B)}\ \frac{4}{25} \qquad\textbf{(C)}\ \frac{41}{200} \qquad\textbf{(D)}}\ \frac{6}{25} \qquad\textbf{(E)}\ \frac{13}{50}</math> | ||
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| + | ==Solution== | ||
| + | |||
| + | == See Also == | ||
| + | {{AMC12 box|year=2015|ab=A|num-b=23|num-a=25}} | ||
Revision as of 01:59, 5 February 2015
Problem
Rational numbers 
and 
are chosen at random among all rational numbers in the interval 
that can be written as fractions 
where 
and 
are integers with 
. What is the probability that
![\[(\text{cos}(a\pi)+i\text{sin}(b\pi))^4\]](http://latex.artofproblemsolving.com/8/8/7/887b74a71c3746ec5fd9fcee5cfd177bf7857b95.png)
is a real number?
$\textbf{(A)}\ \frac{3}{5} \qquad\textbf{(B)}\ \frac{4}{25} \qquad\textbf{(C)}\ \frac{41}{200} \qquad\textbf{(D)}}\ \frac{6}{25} \qquad\textbf{(E)}\ \frac{13}{50}$ (Error compiling LaTeX. Unknown error_msg)
Solution
See Also
| 2015 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 23 |
Followed by Problem 25 |
| 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 | |
