MathDB

12

Part of 2003 AMC 10

Problems(2)

Random Point

Source:

1/2/2009
A point (x,y) (x,y) is randomly picked from inside the rectangle with vertices (0,0) (0,0), (4,0) (4,0), (4,1) (4,1), and (0,1) (0,1). What is the probability that x<y x<y? <spanclass=′latex−bold′>(A)</span> 18<spanclass=′latex−bold′>(B)</span> 14<spanclass=′latex−bold′>(C)</span> 38<spanclass=′latex−bold′>(D)</span> 12<spanclass=′latex−bold′>(E)</span> 34 <span class='latex-bold'>(A)</span>\ \frac{1}{8} \qquad <span class='latex-bold'>(B)</span>\ \frac{1}{4} \qquad <span class='latex-bold'>(C)</span>\ \frac{3}{8} \qquad <span class='latex-bold'>(D)</span>\ \frac{1}{2} \qquad <span class='latex-bold'>(E)</span>\ \frac{3}{4}
geometryrectangleprobabilityanalytic geometry
Friends' Investments

Source:

1/9/2009
Al, Betty, and Clare split $1000 \$1000 among them to be invested in different ways. Each begins with a different amount. At the end of one year they have a total of $1500 \$1500. Betty and Clare have both doubled their money, whereas Al has managed to lose $100 \$100. What was Al’s original portion? <spanclass=′latex−bold′>(A)</span> $250<spanclass=′latex−bold′>(B)</span> $350<spanclass=′latex−bold′>(C)</span> $400<spanclass=′latex−bold′>(D)</span> $450<spanclass=′latex−bold′>(E)</span> $500 <span class='latex-bold'>(A)</span>\ \$ 250 \qquad <span class='latex-bold'>(B)</span>\ \$ 350 \qquad <span class='latex-bold'>(C)</span>\ \$ 400 \qquad <span class='latex-bold'>(D)</span>\ \$ 450 \qquad <span class='latex-bold'>(E)</span>\ \$ 500