MathDB

2

Part of 2020 BMT Fall

Problems(5)

BMT Algebra #2 - Symmetric Sum of Roots

Source:

10/11/2020
Let aa and bb be the roots of the polynomial x2+2020x+cx^2+2020x+c. Given that ab+ba=98\frac{a}{b}+\frac{b}{a}=98, compute c\sqrt c.
Bmtalgebrapolynomialsum of roots
BMT 2020 Fall - Geometry 2

Source:

12/30/2021
Let OO be a circle with diameter AB=2AB = 2. Circles O1O_1 and O2O_2 have centers on AB‾\overline{AB} such that OO is tangent to O1O_1 at AA and to O2O_2 at BB, and O1O_1 and O2O_2 are externally tangent to each other. The minimum possible value of the sum of the areas of O1O_1 and O2O_2 can be written in the form mπn\frac{m\pi}{n} where mm and nn are relatively prime positive integers. Compute m+nm + n.
geometry
2020 BMT Team 2

Source:

1/9/2022
There are 3838 people in the California Baseball League (CBL). The CBL cannot start playing games until people are split into teams of exactly 99 people (with each person in exactly one team). Moreover, there must be an even number of teams. What is the fewest number of people who must join the CBL such that the CBL can start playing games? The CBL may not revoke membership of the 3838 people already in the CBL.
combinatorics
2020 BMT Individual 2

Source:

1/9/2022
Let mm be the answer to this question. What is the value of 2m−52m - 5?
algebra
2020 BMT Discrete #2

Source:

3/10/2024
Haydn picks two different integers between 11 and 100100, inclusive, uniformly at random. The probability that their product is divisible by 44 can be expressed in the form mn\frac{m}{n} , where mm and nn are relatively prime positive integers. Compute m+nm + n.
combinatoricsnumber theory