2010 AMC 12B Problems/Problem 3

The following problem is from both the 2010 AMC 12B #3 and 2010 AMC 10B #8, so both problems redirect to this page.

Problem 3

A ticket to a school play cost $x$ dollars, where $x$ is a whole number. A group of 9_th graders buys tickets costing a total of $ $48$ , and a group of 10_th graders buys tickets costing a total of $ $64$ . How many values for $x$ are possible?

$\textbf{(A)}\ 1 \qquad \textbf{(B)}\ 2 \qquad \textbf{(C)}\ 3 \qquad \textbf{(D)}\ 4 \qquad \textbf{(E)}\ 5$

Solution

We find the greatest common factor of $48$ and $64$ to be $16$ . The number of factors of $16$ is $5$ which is the answer $(E)$ .

Video Solution

https://youtu.be/I3yihAO87CE?t=179

~IceMatrix

2010 AMC 12B (Problems • Answer Key • Resources)
Preceded by Problem 2	Followed by Problem 4
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All AMC 12 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

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2010 AMC 12B Problems/Problem 3

Contents

Problem 3

Solution

Video Solution

See also