2011 AMC 12A Problems/Problem 7

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 $\boxed{B}$

2011 AMC 12A (Problems • Answer Key • Resources)
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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2011 AMC 12A Problems/Problem 7

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