MathDB

16

Part of 2022 MIG

Problems(2)

2022 A Individual #16

Source:

4/28/2022
Let PP be a point on side AB‾\overline{AB} of equilateral triangle ABCABC. If BP=6BP = 6 and CP=9CP = 9, what is the length of ABAB?
<spanclass=′latex−bold′>(A)</span>25<spanclass=′latex−bold′>(B)</span>3+6<spanclass=′latex−bold′>(C)</span>35<spanclass=′latex−bold′>(D)</span>36+3<spanclass=′latex−bold′>(E)</span>62<span class='latex-bold'>(A) </span>2\sqrt5\qquad<span class='latex-bold'>(B) </span>3+\sqrt6\qquad<span class='latex-bold'>(C) </span>3\sqrt5\qquad<span class='latex-bold'>(D) </span>3\sqrt6 + 3\qquad<span class='latex-bold'>(E) </span>6\sqrt2
2022 A Individualgeometry
2022 B Individual #16

Source:

4/30/2022
An ant climbs either two inches or three inches each day. In how many ways can the ant climb twelve inches, if the order of its climbing sequence matters? <spanclass=′latex−bold′>(A)</span>8<spanclass=′latex−bold′>(B)</span>9<spanclass=′latex−bold′>(C)</span>10<spanclass=′latex−bold′>(D)</span>12<spanclass=′latex−bold′>(E)</span>14<span class='latex-bold'>(A) </span>8\qquad<span class='latex-bold'>(B) </span>9\qquad<span class='latex-bold'>(C) </span>10\qquad<span class='latex-bold'>(D) </span>12\qquad<span class='latex-bold'>(E) </span>14
2022 B Individual