MathDB

5

Part of 2021 MOAA

Problems(4)

Speed P5

Source:

10/16/2021
There are 12 students in Mr. DoBa's math class. On the final exam, the average score of the top 3 students was 8 more than the average score of the other students, and the average score of the entire class was 85. Compute the average score of the top 33 students.
Proposed by Yifan Kang
MOAA 2021speed
Accuracy P5

Source:

10/16/2021
If xx, yy, zz are nonnegative integers satisfying the equation below, then compute x+y+zx+y+z. (163)x×(2725)y×(54)z=256.\left(\frac{16}{3}\right)^x\times \left(\frac{27}{25}\right)^y\times \left(\frac{5}{4}\right)^z=256.
Proposed by Jeffrey Shi
MOAA 2021Accuracy
Team Round P5

Source:

10/16/2021
Two right triangles are placed next to each other to form a quadrilateral as shown. What is the perimeter of the quadrilateral?
[asy] size(4cm); fill((-5,0)--(0,12)--(0,6)--(8,0)--cycle, gray+opacity(0.3)); draw((0,0)--(0,12)--(-5,0)--cycle); draw((0,0)--(8,0)--(0,6)); label("5", (-2.5,0), S); label("13", (-2.5,6), dir(140)); label("6", (0,3), E); label("8", (4,0), S); [/asy] Proposed by Nathan Xiong
MOAA 2021team
Gunga P5

Source:

10/16/2021
Joshua rolls two dice and records the product of the numbers face up. The probability that this product is composite 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