Problems(3)
Betsy designed a flag using blue triangles, small white squares, and a red center square, as shown. Let B be the total area of the blue triangles, W the total area of the white squares, and R the area of the red square. Which of the following is correct?
[asy]unitsize(3mm);
fill((-4,-4)--(-4,4)--(4,4)--(4,-4)--cycle,blue);
fill((-2,-2)--(-2,2)--(2,2)--(2,-2)--cycle,red);
path onewhite=(-3,3)--(-2,4)--(-1,3)--(-2,2)--(-3,3)--(-1,3)--(0,4)--(1,3)--(0,2)--(-1,3)--(1,3)--(2,4)--(3,3)--(2,2)--(1,3)--cycle;
path divider=(-2,2)--(-3,3)--cycle;
fill(onewhite,white);
fill(rotate(90)*onewhite,white);
fill(rotate(180)*onewhite,white);
fill(rotate(270)*onewhite,white);[/asy]
(A)\ B \equal{} W \qquad (B)\ W \equal{} R \qquad (C)\ B \equal{} R \qquad (D)\ 3B \equal{} 2R \qquad (E)\ 2R \equal{} W geometry
Suppose July of year N has five Mondays. Which of the following must occur five times in August of year N? (Note: Both months have 31 days.)
<spanclass=′latex−bold′>(A)</span> Monday<spanclass=′latex−bold′>(B)</span> Tuesday<spanclass=′latex−bold′>(C)</span> Wednesday<spanclass=′latex−bold′>(D)</span> Thursday<spanclass=′latex−bold′>(E)</span> Friday How many ordered triples of positive integers (x,y,z) satisfy (xy)z=64?<spanclass=′latex−bold′>(A)</span>5<spanclass=′latex−bold′>(B)</span>6<spanclass=′latex−bold′>(C)</span>7<spanclass=′latex−bold′>(D)</span>8<spanclass=′latex−bold′>(E)</span>9