2011 AMC 12A Problems/Problem 7

Revision as of 18:55, 10 February 2011 by Motoe123 (talk | contribs) (Solution)

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, 11 cents per pencil, and each student bought 7 pencils. $\Rightarrow$

See also

2011 AMC 12A (ProblemsAnswer KeyResources)
Preceded by
Problem 6
Followed by
Problem 8
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All AMC 12 Problems and Solutions
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