Problems(2)
A base-10 three-digit number n is selected at random. Which of the following is closest to the probability that the base-9 representation and the base-11 representation of n are both three-digit numerals?
<spanclass=′latex−bold′>(A)</span> 0.3<spanclass=′latex−bold′>(B)</span> 0.4<spanclass=′latex−bold′>(C)</span> 0.5<spanclass=′latex−bold′>(D)</span> 0.6<spanclass=′latex−bold′>(E)</span> 0.7 probability
In rectangle ABCD, AB\equal{}5 and BC\equal{}3. Points F and G are on CD so that DF\equal{}1 and GC\equal{}2. Lines AF and BG intersect at E. Find the area of △AEB.
[asy]unitsize(6mm);
defaultpen(linewidth(.8pt)+fontsize(8pt));pair A=(0,0), B=(5,0), C=(5,3), D=(0,3), F=(1,3), G=(3,3);
pair E=extension(A,F,B,G);
draw(A--B--C--D--A--E--B);label("A",A,SW);
label("B",B,SE);
label("C",C,NE);
label("D",D,NW);
label("E",E,N);
label("F",F,SE);
label("G",G,SW);
label("B",B,SE);label("1",midpoint(D--F),N);
label("2",midpoint(G--C),N);
label("3",midpoint(B--C),E);
label("3",midpoint(A--D),W);
label("5",midpoint(A--B),S);[/asy]<spanclass=′latex−bold′>(A)</span> 10<spanclass=′latex−bold′>(B)</span> 221<spanclass=′latex−bold′>(C)</span> 12<spanclass=′latex−bold′>(D)</span> 225<spanclass=′latex−bold′>(E)</span> 15 geometryrectangleratio