Tie 1

Part of 2020 BMT Fall

Problems(4)

2020 BMT Algebra Tiebreakers 1

Source:

Find the sum of the squares of all values of

x

\log_2 (x + 3) + \log_2 (2 - x) = 2

BMT 2020 Fall - Geometry Tiebreaker 1

Source:

Given a regular hexagon, a circle is drawn circumscribing it and another circle is drawn inscribing it. The ratio of the area of the larger circle to the area of the smaller circle can be written in the form

\frac{m}{n}

, where m and n are relatively prime positive integers. Compute

m + n

sum of exterior angles of triangle and 12-gon 2020 BMT Individual Tiebreakers 1

Source:

An exterior angle is the supplementary angle to an interior angle in a polygon. What is the sum of the exterior angles of a triangle and dodecagon (

12

-gon), in degrees?

2020 BMT Discrete Tiebreaker #1

Source:

Compute the smallest positive integer

n

\frac{n}{2}

is a perfect square and

\frac{n}{3}

is a perfect cube.