Express  $74_{10}$  as a base six number.

(a)  

2020!  $\div$  2019! = 

(a)  

In a survey of 100 students who watch movies, 24 watch Frozen, 42 watch Avengers, and seven watch both. How many of the students surveyed watch neither movie?

(a)  

When the sum of the reciprocals of two distinct positive integers is divided by the sum of the two integers, the result is 1/49. What is the sum of the two integers?

(a)  

How many liters of a 20% alcohol solution must be added to 90 liters of a 50% alcohol solution to form a 45% solution?

(a)  

The real numbers x, y, and z satisfy the equations  $x+2y+3z=950$  and  $3x+2y+z=1450$  . What is the sum of x,y and z?

(a)  

If two numbers are randomly chosen without replacement from {3,4,5,6}, what is the probability that their sum will be 9? Express your answer as a common fraction.

(a)  

I have a pet Tigger who climbs stairs either one or three steps at a time. Our staircase has 11 steps. How many different ways can Tigger climb the stairs?

(a)  

How many diagonals does a convex polygon with 20 sides have?

(a)  

 If n is a positive integer, what is the smallest value of n for which  $\sqrt{\frac{27n}{7}}$ is an integer?

(a)  

PACE wishes to donate a sum of money to each of its 3 favorite charities. The total donation is to be divided among the charities in a ratio of 7:5:3.. If the total donation is $15,000, what is the difference between the largest and the smallest donation?

(a)  

Three friends have a total of 10 identical pencils, and each one has at least two pencils. In how many ways can this happen

(a)  

If the radius of a circle is increased by 10%, by what percent is the area increased?

(a)  

Tim can cut a log into 3 pieces in 24 minutes. At that rate, how long will it take him to cut another log into 6 pieces?

(a)  

If 200% of x is equal to 50% of y and y=16, what is the value of x?

(a)  

What is the sum of the arithmetic sequence -2, -1, 0, 1, 2, 3, ..., 33?

(a)