MathDB

7

Part of 2021 MOAA

Problems(4)

Speed P7

Source:

10/16/2021
If positive real numbers x,y,zx,y,z satisfy the following system of equations, compute x+y+zx+y+z.
xy+yz=30xy+yz = 30 yz+zx=36yz+zx = 36 zx+xy=42zx+xy = 42
Proposed by Nathan Xiong
MOAA 2021speed
Accuracy P7

Source:

10/16/2021
Jeffrey rolls fair three six-sided dice and records their results. The probability that the mean of these three numbers is greater than the median of these three numbers can be expressed as mn\frac{m}{n} for relatively prime positive integers mm and nn. Compute m+nm+n.
Proposed by Nathan Xiong
MOAA 2021Accuracy
Team Round P7

Source:

10/16/2021
Compute the number of ordered pairs (a,b)(a,b) of positive integers satisfying ab=2100a^b=2^{100}.
Proposed by Nathan Xiong
MOAA 2021team
Gunga P7

Source:

10/16/2021
Andover has a special weather forecast this week. On Monday, there is a 12\frac{1}{2} chance of rain. On Tuesday, there is a 13\frac{1}{3} chance of rain. This pattern continues all the way to Sunday, when there is a 18\frac{1}{8} chance of rain. The probability that it doesn't rain in Andover all week can be expressed as mn\frac{m}{n} for relatively prime positive integers mm and nn. Compute m+nm+n.
Proposed by Nathan Xiong
MOAA 2021Gunga