MathDB

6

Part of 2011 AMC 10

Problems(2)

Smallest possible number of elements in union of a,b

Source: 2011 AMC a Problem 6

6/25/2011
Set AA has 20 elements, and set BB has 15 elements. What is the smallest possible number of elements in A∪BA \cup B , the union of AA and BB ?
<spanclass=′latex−bold′>(A)</span> 5<spanclass=′latex−bold′>(B)</span> 15<spanclass=′latex−bold′>(C)</span> 20<spanclass=′latex−bold′>(D)</span> 35<spanclass=′latex−bold′>(E)</span> 300 <span class='latex-bold'>(A)</span>\ 5 \qquad<span class='latex-bold'>(B)</span>\ 15 \qquad<span class='latex-bold'>(C)</span>\ 20\qquad<span class='latex-bold'>(D)</span>\ 35\qquad<span class='latex-bold'>(E)</span>\ 300
AMC
Casper sharing Halloween candies

Source: AMC 10 2011 b Problem 6

2/24/2011
On Halloween Casper ate 13\frac{1}{3} of his candies and then gave 22 candies to his brother. The next day he ate 13\frac{1}{3} of his remaining candies and then gave 44 candies to his sister. On the third day he ate his final 88 candies. How many candies did Casper have at the beginning?
<spanclass=′latex−bold′>(A)</span> 30<spanclass=′latex−bold′>(B)</span> 39<spanclass=′latex−bold′>(C)</span> 48<spanclass=′latex−bold′>(D)</span> 57<spanclass=′latex−bold′>(E)</span> 66 <span class='latex-bold'>(A)</span>\ 30 \qquad <span class='latex-bold'>(B)</span>\ 39 \qquad <span class='latex-bold'>(C)</span>\ 48 \qquad <span class='latex-bold'>(D)</span>\ 57 \qquad <span class='latex-bold'>(E)</span>\ 66
AMC