MathDB

BMT 2022 Fall Algebra P2

Source:

5/5/2023

The equation

4^x -5 \cdot 2^{x+1} +16 = 0

has two integer solutions for

x.

Find their sum.

algebraeasy

BMT 2022 Fall Discrete P2

Source:

5/6/2023

Compute the number of positive integer divisors of

100000

which do not contain the digit

0.

number theory

BMT 2022 Geometry #2 / General #15

Source:

8/12/2023

Sohom constructs a square

BERK

of side length

10

. Darlnim adds points

T

,

O

,

W

, and

N

, which are the midpoints of

\overline{BE}

,

\overline{ER}

,

\overline{RK}

, and

\overline{KB}

, respectively. Lastly, Sylvia constructs square

CALI

whose edges contain the vertices of

BERK

, such that

\overline{CA}

is parallel to

\overline{BO}

. Compute the area of

CALI

. https://cdn.artofproblemsolving.com/attachments/0/9/0fda0c273bb73b85f3b1bc73661126630152b3.png

geometry

BMT 2022 Guts #2

Source:

8/31/2023

A bag has

3

white and

7

black marbles. Arjun picks out one marble without replacement and then a second. What is the probability that Arjun chooses exactly

1

white and

1

black marble?

combinatorics

2