AMC 12A Fall 2021 (Problem 19)
Let be the least real number greater than such that , where the arguments are in degrees. What is rounded up to the closest integer?
Case 1:
By Toolkit 21 — Quadratic Formula,
When , the solutions are and .
Therefore, the least solution greater than in this case occurs when :
By Toolkit 21 — Quadratic Formula,
When , the solutions are and .
Therefore, the least solution greater than in this case occurs when :
By Hints 2 and 3, the least possible value is
Since
we have
Therefore, rounded to the nearest integer is .
Since
we have
Therefore, rounded to the nearest integer is .
(B)