1. The diameter of circle A is the radius of circle B. What is the ratio of the area of circle B to the area of circle A? Your answer should be a simplified fraction.
2. Grace rolls 2 standard six-sided dice and records the sum of the 2 numbers showing. Then she rolls the dice again and records the second sum. How many times must she keep rolling the dice to ensure that she will repeat at least one sum from a previous roll?
3. Reagan has a bag that contains 120 pieces of candy. Reagan shares her candy by giving Brooke 3/4 of 2/3 of her candy. Brooke shares her candy with Will by giving Will 3/4 of 2/3 of her candy. If 2/3 of Will's candies are red, how many of his pieces are red?
4. The planet Thor is inhabited by a race of highly intelligent one-toed quadrupeds with elephant-like trunks. So, with four toes and a trunk, they have adopted the five base for their number system. With that in mind, convert the Pento number 1234 into its decimal equivalent.
5. Nathan, Gus, and Cutler agreed to weed Ruffing's garden. Nathan, with all his swag, will weed 1/5 more than Gus, and 1/3 more than Cutler? What fraction of the garden will Gus weed?
6. Find two numbers so that the square of the first plus the second, added to the square of the second plus the first equals 238.