MathDB

11

Part of 2004 AMC 10

Problems(2)

Problem: 2004 AMC 10 #11

Source:

2/1/2007
A company sells peanut butter in cylindrical jars. Marketing research suggests that using wider jars will increase sales. If the diameter of the jars is increased by 25% 25\% without altering the volume, by what percent must the height be decreased? <spanclass=′latex−bold′>(A)</span> 10<spanclass=′latex−bold′>(B)</span> 25<spanclass=′latex−bold′>(C)</span> 36<spanclass=′latex−bold′>(D)</span> 50<spanclass=′latex−bold′>(E)</span> 60 <span class='latex-bold'>(A)</span>\ 10 \qquad <span class='latex-bold'>(B)</span>\ 25 \qquad <span class='latex-bold'>(C)</span>\ 36 \qquad <span class='latex-bold'>(D)</span>\ 50 \qquad <span class='latex-bold'>(E)</span>\ 60
percentgeometry
Product and Sum of Numbers on Two Eight-Sided Dice

Source:

1/15/2009
Two eight-sided dice each have faces numbered 1 1 through 8 8. When the dice are rolled, each face has an equal probability of appearing on the top. What is the probability that the product of the two top numbers is greater than their sum? <spanclass=′latex−bold′>(A)</span> 12<spanclass=′latex−bold′>(B)</span> 4764<spanclass=′latex−bold′>(C)</span> 34<spanclass=′latex−bold′>(D)</span> 5564<spanclass=′latex−bold′>(E)</span> 78 <span class='latex-bold'>(A)</span>\ \frac{1}{2}\qquad <span class='latex-bold'>(B)</span>\ \frac{47}{64}\qquad <span class='latex-bold'>(C)</span>\ \frac{3}{4}\qquad <span class='latex-bold'>(D)</span>\ \frac{55}{64}\qquad <span class='latex-bold'>(E)</span>\ \frac{7}{8}
probability