MathDB

9

Part of 2012 AMC 10

Problems(2)

Odd Dice

Source: 2012 AMC10A Problem #9

2/8/2012
A pair of six-sided fair dice are labeled so that one die has only even numbers (two each of 22, 44, and 66), and the other die has only odd numbers (two each of 11, 33, and 55). The pair of dice is rolled. What is the probability that the sum of the numbers on top of the two dice is 77?
<spanclass=′latex−bold′>(A)</span> 16<spanclass=′latex−bold′>(B)</span> 15<spanclass=′latex−bold′>(C)</span> 14<spanclass=′latex−bold′>(D)</span> 13<spanclass=′latex−bold′>(E)</span> 12 <span class='latex-bold'>(A)</span>\ \dfrac{1}{6} \qquad<span class='latex-bold'>(B)</span>\ \dfrac{1}{5} \qquad<span class='latex-bold'>(C)</span>\ \dfrac{1}{4} \qquad<span class='latex-bold'>(D)</span>\ \dfrac{1}{3} \qquad<span class='latex-bold'>(E)</span>\ \dfrac{1}{2}
probabilityAMC
Minimum Even Integers

Source: 2012 AMC 12 #5

2/23/2012
Two integers have a sum of 2626. When two more integers are added to the first two integers the sum is 4141. Finally when two more integers are added to the sum of the previous four integers the sum is 5757. What is the minimum number of even integers among the 66 integers?
<spanclass=′latex−bold′>(A)</span> 1<spanclass=′latex−bold′>(B)</span> 2<spanclass=′latex−bold′>(C)</span> 3<spanclass=′latex−bold′>(D)</span> 4<spanclass=′latex−bold′>(E)</span> 5{{ <span class='latex-bold'>(A)</span>\ 1\qquad<span class='latex-bold'>(B)</span>\ 2\qquad<span class='latex-bold'>(C)</span>\ 3\qquad<span class='latex-bold'>(D)</span>\ 4}\qquad<span class='latex-bold'>(E)</span>\ 5}
AMC 10AMC