MathDB

18

Part of 2022 MIG

Problems(2)

2022 A Individual #18

Source:

4/28/2022
If the six-digit number 2‾ 0‾ 2‾ 1‾ a‾ b‾\underline{2}\, \underline{0}\, \underline{2} \, \underline{1} \, \underline{a} \, \underline{b} is divisible by 99, what is the greatest possible value of a⋅ba \cdot b?
<spanclass=′latex−bold′>(A)</span>18<spanclass=′latex−bold′>(B)</span>20<spanclass=′latex−bold′>(C)</span>36<spanclass=′latex−bold′>(D)</span>40<spanclass=′latex−bold′>(E)</span>42<span class='latex-bold'>(A) </span>18\qquad<span class='latex-bold'>(B) </span>20\qquad<span class='latex-bold'>(C) </span>36\qquad<span class='latex-bold'>(D) </span>40\qquad<span class='latex-bold'>(E) </span>42
2022 A Individual
2022 B Individual #18

Source:

4/30/2022
Two equilateral triangles are glued, and their opposite vertices are connected. If the larger equilateral triangle has an area of 225225 and the smaller equilateral triangle has an area of 100100, what is the area of the shaded region? [asy] size(4cm); draw((0,0)--(3,0)--(3/2,3sqrt(3)/2)--(0,0)); draw((0,0)--(2,0)--(1,-sqrt(3))--(0,0)); draw((1,-sqrt(3))--(3/2,3sqrt(3)/2)); filldraw((0,0)--(6/5,0)--(3/2,3sqrt(3)/2)--cycle, gray); [/asy]
<spanclass=′latex−bold′>(A)</span>60<spanclass=′latex−bold′>(B)</span>90<spanclass=′latex−bold′>(C)</span>96<spanclass=′latex−bold′>(D)</span>108<spanclass=′latex−bold′>(E)</span>120<span class='latex-bold'>(A) </span>60\qquad<span class='latex-bold'>(B) </span>90\qquad<span class='latex-bold'>(C) </span>96\qquad<span class='latex-bold'>(D) </span>108\qquad<span class='latex-bold'>(E) </span>120
2022 B Individualgeometry