MathDB

13

Part of 2022 AMC 10

Problems(2)

I can't believe it's not cheese!

Source: 2022 AMC 10A P13

11/11/2022
Let △ABC\triangle ABC be a scalene triangle. Point PP lies on BC‾\overline{BC} so that AP‾\overline{AP} bisects ∠BAC\angle BAC. The line through BB perpendicular to AP‾\overline{AP} intersects the line through AA parallel to BC‾\overline{BC} at point DD. Suppose BP=2BP = 2 and PC=3PC = 3. What is ADAD ?
<spanclass=′latex−bold′>(A)</span>8<spanclass=′latex−bold′>(B)</span>9<spanclass=′latex−bold′>(C)</span>10<spanclass=′latex−bold′>(D)</span>11<spanclass=′latex−bold′>(E)</span>12<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>11\qquad<span class='latex-bold'>(E) </span>12
2022 AMC 10A P132022 AMCAMC 10AMC2022 AMC 10aTrianglegeometry
twin primes?

Source: 2022 AMC 10B P13

11/17/2022
The positive difference between a pair of primes is equal to 22, and the positive difference between the cubes of the two primes is 3110631106. What is the sum of the digits of the least prime that is greater than those two primes?
<spanclass=′latex−bold′>(A)</span>8<spanclass=′latex−bold′>(B)</span>10<spanclass=′latex−bold′>(C)</span>11<spanclass=′latex−bold′>(D)</span>13<spanclass=′latex−bold′>(E)</span>16<span class='latex-bold'>(A) </span> 8 \qquad <span class='latex-bold'>(B) </span> 10 \qquad <span class='latex-bold'>(C) </span> 11 \qquad <span class='latex-bold'>(D) </span> 13 \qquad <span class='latex-bold'>(E) </span> 16
AMCAMC 102022 AMC 10B2022 AMCprimesdifference of cubes