MathDB

15

Part of 2008 AMC 10

Problems(2)

Han, Ian, and Jan

Source: AMC 10 2008A Problem 15

2/22/2008
Yesterday Han drove 1 1 hour longer than Ian at an average speed 5 5 miles per hour faster than Ian. Jan drove 2 2 hours longer than Ian at an average speed 10 10 miles per hour faster than Ian. Han drove 70 70 miles more than Ian. How many more miles did Jan drive than Ian? <spanclass=′latex−bold′>(A)</span> 120<spanclass=′latex−bold′>(B)</span> 130<spanclass=′latex−bold′>(C)</span> 140<spanclass=′latex−bold′>(D)</span> 150<spanclass=′latex−bold′>(E)</span> 160 <span class='latex-bold'>(A)</span>\ 120 \qquad <span class='latex-bold'>(B)</span>\ 130 \qquad <span class='latex-bold'>(C)</span>\ 140 \qquad <span class='latex-bold'>(D)</span>\ 150 \qquad <span class='latex-bold'>(E)</span>\ 160
AMC
Integer Right Triangles

Source: AMC 10 2008B Problem 15

3/1/2008
How many right triangles have integer leg lengths a a and b b and a hypotenuse of length b\plus{}1, where b<100 b<100? <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
algebradifference of squaresspecial factorizationsAMC