MathDB

16

Part of 2023 AMC 12/AHSME

Problems(2)

RIP perfect score :/

Source: 2023 AMC 12A #16

11/9/2023
Consider the set of complex numbers zz satisfying ∣1+z+z2∣=4|1+z+z^{2}|=4. The maximum value of the imaginary part of zz can be written in the form mn\tfrac{\sqrt{m}}{n}, where mm and nn are relatively prime positive integers. What is m+nm+n?
<spanclass=′latex−bold′>(A)</span> 20<spanclass=′latex−bold′>(B)</span> 21<spanclass=′latex−bold′>(C)</span> 22<spanclass=′latex−bold′>(D)</span> 23<spanclass=′latex−bold′>(E)</span> 24<span class='latex-bold'>(A)</span>~20\qquad<span class='latex-bold'>(B)</span>~21\qquad<span class='latex-bold'>(C)</span>~22\qquad<span class='latex-bold'>(D)</span>~23\qquad<span class='latex-bold'>(E)</span>~24
AMCAMC 122023 AMC2023 AMC 12A
Triple Chicken McNugget

Source: 2023 AMC 12B #16

11/15/2023
In Coinland, there are three types of coins, each worth 6,6, 10,10, and 15.15. What is the sum of the digits of the maximum amount of money that is impossible to have?
<spanclass=′latex−bold′>(A)</span>11<spanclass=′latex−bold′>(B)</span>6<spanclass=′latex−bold′>(C)</span>8<spanclass=′latex−bold′>(D)</span>9<spanclass=′latex−bold′>(E)</span>10<span class='latex-bold'>(A) </span>11\qquad<span class='latex-bold'>(B) </span>6\qquad<span class='latex-bold'>(C) </span>8\qquad<span class='latex-bold'>(D) </span>9\qquad<span class='latex-bold'>(E) </span>10 (I forgot the order)
AMCAMC 12number theoryChicken McNugget Theorem2023 AMC2023 AMC 12B