Difference between revisions of "2011 AMC 12A Problems/Problem 7"

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Revision as of 21:51, 3 July 2013

Problem

A majority of the $30$ students in Ms. Demeanor's class bought pencils at the school bookstore. Each of these students bought the same number of pencils, and this number was greater than $1$. The cost of a pencil in cents was greater than the number of pencils each student bought, and the total cost of all the pencils was $17.71$. What was the cost of a pencil in cents?

$\textbf{(A)}\ 7 \qquad \textbf{(B)}\ 11 \qquad \textbf{(C)}\ 17 \qquad \textbf{(D)}\ 23 \qquad \textbf{(E)}\ 77$

Solution

\[1771 = 7 \times 11 \times 23\]

The only factor of $1771$ between $16$ and $30$ ($16$ because it has to be a majority of her students) is $23$. Therefore, we can conclude that there are $23$ students, pencils cost $11$ cents, and each student bought $7$ pencils. Thus the answer is $\boxed{B}$

See also

2011 AMC 12A (ProblemsAnswer KeyResources)
Preceded by
Problem 6
Followed by
Problem 8
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

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