MathDB

10

Part of 2011 AMC 10

Problems(2)

Find the cost of pencils

Source: 2011 AMC A Problem 10

6/25/2011
A majority of the 30 students in Ms. Deameanor'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\$17.71. What was the cost of a pencil in cents?
<spanclass=′latex−bold′>(A)</span> 7<spanclass=′latex−bold′>(B)</span> 11<spanclass=′latex−bold′>(C)</span> 17<spanclass=′latex−bold′>(D)</span> 23<spanclass=′latex−bold′>(E)</span> 77<span class='latex-bold'>(A)</span>\,7 \qquad<span class='latex-bold'>(B)</span>\,11 \qquad<span class='latex-bold'>(C)</span>\,17 \qquad<span class='latex-bold'>(D)</span>\,23 \qquad<span class='latex-bold'>(E)</span>\,77
AMC
Ratio of elements in a set

Source: AMC 10 2011 b Problem 10

2/24/2011
Consider the set of numbers {1,10,102,103,...1010}\{1,10,10^2,10^3, ... 10^{10} \}. The ratio of the largest element of the set to the sum of the other ten elements of the set is closest to which integer?
<spanclass=′latex−bold′>(A)</span> 1<spanclass=′latex−bold′>(B)</span> 9<spanclass=′latex−bold′>(C)</span> 10<spanclass=′latex−bold′>(D)</span> 11<spanclass=′latex−bold′>(E)</span> 101 <span class='latex-bold'>(A)</span>\ 1 \qquad <span class='latex-bold'>(B)</span>\ 9 \qquad <span class='latex-bold'>(C)</span>\ 10 \qquad <span class='latex-bold'>(D)</span>\ 11 \qquad <span class='latex-bold'>(E)</span>\ 101
ratioAMC