MathDB

8

Part of 2022 MIG

Problems(2)

2022 A Individual #8

Source:

4/28/2022
Write a list of the first 1010 positive integers in increasing order. Erase any number adjacent to a prime; if two primes are adjacent, do not erase either prime. Apply this process twice. How many positive integers remain in the list?
<spanclass=′latex−bold′>(A)</span>2<spanclass=′latex−bold′>(B)</span>3<spanclass=′latex−bold′>(C)</span>4<spanclass=′latex−bold′>(D)</span>5<spanclass=′latex−bold′>(E)</span>6<span class='latex-bold'>(A) </span>2\qquad<span class='latex-bold'>(B) </span>3\qquad<span class='latex-bold'>(C) </span>4\qquad<span class='latex-bold'>(D) </span>5\qquad<span class='latex-bold'>(E) </span>6
2022 A Individual
2022 B Individual #8

Source:

4/30/2022
Let ABCABC be a triangle and DD be a point on segment BCBC. If △ABD\triangle ABD is equilateral and ∠ACB=14∘\angle ACB = 14^{\circ}, what is ∠DAC\angle{DAC}?
<spanclass=′latex−bold′>(A)</span>26∘<spanclass=′latex−bold′>(B)</span>34∘<spanclass=′latex−bold′>(C)</span>46∘<spanclass=′latex−bold′>(D)</span>50∘<spanclass=′latex−bold′>(E)</span>54∘<span class='latex-bold'>(A) </span>26^{\circ}\qquad<span class='latex-bold'>(B) </span>34^{\circ}\qquad<span class='latex-bold'>(C) </span>46^{\circ}\qquad<span class='latex-bold'>(D) </span>50^{\circ}\qquad<span class='latex-bold'>(E) </span>54^{\circ}
2022 B Individualgeometry