MathDB

10

Part of 2012 AMC 10

Problems(2)

An Arithmetic Sequence of Sectors

Source: 2012 AMC 12A Problem #7 and AMC 10A Problem #10

2/8/2012
Mary divides a circle into 1212 sectors. The central angles of these sectors, measured in degrees, are all integers and they form an arithmetic sequence. What is the degree measure of the smallest possible sector angle?
<spanclass=′latex−bold′>(A)</span> 5<spanclass=′latex−bold′>(B)</span> 6<spanclass=′latex−bold′>(C)</span> 8<spanclass=′latex−bold′>(D)</span> 10<spanclass=′latex−bold′>(E)</span> 12 <span class='latex-bold'>(A)</span>\ 5\qquad<span class='latex-bold'>(B)</span>\ 6\qquad<span class='latex-bold'>(C)</span>\ 8\qquad<span class='latex-bold'>(D)</span>\ 10\qquad<span class='latex-bold'>(E)</span>\ 12
AMC
Counting Ordered Pairs

Source: 2012 AMC10B Problem #10

2/23/2012
How many ordered pairs of positive integers (M,N)(M,N) staisfy the equation M6=6N\frac{M}{6}=\frac{6}{N}?
<spanclass=′latex−bold′>(A)</span> 6<spanclass=′latex−bold′>(B)</span> 7<spanclass=′latex−bold′>(C)</span> 8<spanclass=′latex−bold′>(D)</span> 9<spanclass=′latex−bold′>(E)</span> 10 <span class='latex-bold'>(A)</span>\ 6\qquad<span class='latex-bold'>(B)</span>\ 7\qquad<span class='latex-bold'>(C)</span>\ 8\qquad<span class='latex-bold'>(D)</span>\ 9\qquad<span class='latex-bold'>(E)</span>\ 10
AMC