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2008 AMC 8 Problems/Problem 24: Difference between revisions

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<!-- don't remove the following tag, for PoTW on the Wiki front page--><onlyinclude>Ten tiles numbered <math>1</math> through <math>10</math> are turned face down. One tile is turned up at random, and a die is rolled. What is the probability that the product of the numbers on the tile and the die will be a square?<!-- don't remove the following tag, for PoTW on the Wiki front page--></onlyinclude>
<!-- don't remove the following tag, for PoTW on the Wiki front page--><onlyinclude>Ten tiles numbered <math>1</math> through <math>10</math> are turned face down. One tile is turned up at random, and a die is rolled. What is the probability that the product of the numbers on the tile and the die will be a square?<!-- don't remove the following tag, for PoTW on the Wiki front page--></onlyinclude>


<math>\textbf{(A)}\ \frac{1}{10}\qquad
<math>\textbf{(A)}\ \frac{1}{10}\qquad\textbf{(B)}\ \frac{1}{6}\qquad\textbf{(C)}\ \frac{11}{60}\qquad\textbf{(D)}\ \frac{1}{5}\qquad\textbf{(E)}\ \frac{7}{30}</math>
\textbf{(B)}\ \frac{1}{6}\qquad
\textbf{(C)}\ \frac{11}{60}\qquad
\textbf{(D)}\ \frac{1}{5}\qquad
\textbf{(E)}\ \frac{7}{30}</math>


==Solution==
==Solution==

Revision as of 21:20, 11 February 2020

Problem

Ten tiles numbered $1$ through $10$ are turned face down. One tile is turned up at random, and a die is rolled. What is the probability that the product of the numbers on the tile and the die will be a square?

$\textbf{(A)}\ \frac{1}{10}\qquad\textbf{(B)}\ \frac{1}{6}\qquad\textbf{(C)}\ \frac{11}{60}\qquad\textbf{(D)}\ \frac{1}{5}\qquad\textbf{(E)}\ \frac{7}{30}$

Solution

The numbers can at most multiply to be $60$. The squares less than $60$ are $1,4,9,16,25,36,$ and $49$. The possible pairs are $(1,1),(1,4),(2,2),(4,1),(3,3),(9,1),(4,4),(8,2),(5,5),(6,6),$ and $(9,4)$. There are $11$ choices and $60$ possibilities giving a probability of $\boxed{\textbf{(C)}\ \frac{11}{60}}$.

See Also

2008 AMC 8 (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 AJHSME/AMC 8 Problems and Solutions

These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. Error creating thumbnail: File missing

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