MathDB

4

Part of 2012 AMC 10

Problems(2)

Smallest Possible Measure of an Angle

Source: 2012 AMC10A Problem #4

2/8/2012
Let ∠ABC=24∘\angle ABC=24^\circ and ∠ABD=20∘\angle ABD =20^\circ. What is the smallest possible degree measure for ∠CBD\angle CBD?
<spanclass=′latex−bold′>(A)</span> 0<spanclass=′latex−bold′>(B)</span> 2<spanclass=′latex−bold′>(C)</span> 4<spanclass=′latex−bold′>(D)</span> 6<spanclass=′latex−bold′>(E)</span> 12 <span class='latex-bold'>(A)</span>\ 0 \qquad<span class='latex-bold'>(B)</span>\ 2 \qquad<span class='latex-bold'>(C)</span>\ 4 \qquad<span class='latex-bold'>(D)</span>\ 6 \qquad<span class='latex-bold'>(E)</span>\ 12
AMC
Placing Marbles Into Bags

Source: 2012 AMC 10B Problem #4

2/23/2012
When Ringo places his marbles into bags with 66 marbles per bag, he has 44 marbles left over. When Paul does the same with his marbles, he has 33 marbles left over. Ringo and Paul pool their marbles and place them into as many bags as possible, with 66 marbles per bag. How many marbles will be left over?
<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
modular arithmeticAMC