MathDB

2

Part of 2008 AMC 10

Problems(2)

Square in a Rectangle

Source: AMC 10 2008A Problem 2

2/22/2008
A square is drawn inside a rectangle. The ratio of the width of the rectangle to a side of the square is 2:1 2: 1. The ratio of the rectangle's length to its width is 2:1 2: 1. What percent of the rectangle's area is inside the square? <spanclass=latexbold>(A)</span> 12.5<spanclass=latexbold>(B)</span> 25<spanclass=latexbold>(C)</span> 50<spanclass=latexbold>(D)</span> 75<spanclass=latexbold>(E)</span> 87.5 <span class='latex-bold'>(A)</span>\ 12.5 \qquad <span class='latex-bold'>(B)</span>\ 25 \qquad <span class='latex-bold'>(C)</span>\ 50 \qquad <span class='latex-bold'>(D)</span>\ 75 \qquad <span class='latex-bold'>(E)</span>\ 87.5
geometryrectangleratiopercentAMC
Calendar

Source: AMC 12 2008B Problem 2

2/28/2008
A 4×4 4\times 4 block of calendar dates is shown. The order of the numbers in the second row is to be reversed. Then the order of the numbers in the fourth row is to be reversed. Finally, the numbers on each diagonal are to be added. What will be the positive difference between the two diagonal sums? \setlength{\unitlength}{5mm} \begin{picture}(4,4)(0,0) \multiput(0,0)(0,1){5}{\line(1,0){4}} \multiput(0,0)(1,0){5}{\line(0,1){4}} \put(0,3){\makebox(1,1){\footnotesize{1}}} \put(1,3){\makebox(1,1){\footnotesize{2}}} \put(2,3){\makebox(1,1){\footnotesize{3}}} \put(3,3){\makebox(1,1){\footnotesize{4}}} \put(0,2){\makebox(1,1){\footnotesize{8}}} \put(1,2){\makebox(1,1){\footnotesize{9}}} \put(2,2){\makebox(1,1){\footnotesize{10}}} \put(3,2){\makebox(1,1){\footnotesize{11}}} \put(0,1){\makebox(1,1){\footnotesize{15}}} \put(1,1){\makebox(1,1){\footnotesize{16}}} \put(2,1){\makebox(1,1){\footnotesize{17}}} \put(3,1){\makebox(1,1){\footnotesize{18}}} \put(0,0){\makebox(1,1){\footnotesize{22}}} \put(1,0){\makebox(1,1){\footnotesize{23}}} \put(2,0){\makebox(1,1){\footnotesize{24}}} \put(3,0){\makebox(1,1){\footnotesize{25}}} \end{picture} <spanclass=latexbold>(A)</span> 2<spanclass=latexbold>(B)</span> 4<spanclass=latexbold>(C)</span> 6<spanclass=latexbold>(D)</span> 8<spanclass=latexbold>(E)</span> 10 <span class='latex-bold'>(A)</span>\ 2 \qquad <span class='latex-bold'>(B)</span>\ 4 \qquad <span class='latex-bold'>(C)</span>\ 6 \qquad <span class='latex-bold'>(D)</span>\ 8 \qquad <span class='latex-bold'>(E)</span>\ 10
AMC