February 2021

If $\left| 3t - 5 \right| \gt 4$, which of the following is correct?

A group of musicians is composed of three drummers, four pianists, and seven guitarists. How many ways can a trio are formed with 1 pianist, 1 drummer, and 1 guitarist?

The shipment of items is divided into two portions. If the difference between the portions is one-third of their average, what is the ratio of the larger portion to the smaller portion?

Mario’s hat is four more than Alex’s hat and one-half that of Gabriel’s hat. If the total number of hats is 24, how many hats does Alex have?

Albert can do a work in 1 hour, Bryan can do it in 2 hours, and Carl can do it in 4 hours. Working together from start, how long can they do the work?

If 8 men can cut 22 trees in a day, how many trees can 20 men cut in a day?

If a car can travel x km in y hours, how many hours can it travel a distance of z km?

The polynomial $x^3 + 4x^2 - 3x + 8$ is divided by $x - 5$. What is the remainder?

What is the coefficient of the term involving $x^{-3}$ in the expansion of $\left( 2x + \dfrac{2}{x} \right)^5$?

Given the following equations:
 

$$ab = 1/8 \qquad ac = 3 \qquad bc = 6$$
 

Find the value of b.