Problems of the Week 2/7

Please review the solutions to the previous week's set. Then, move onto this one. In the meantime, be looking at the marathon problems.

1. Laws in certain states require a 60% approval rate from voters before issues are “passed”. If 1,140 people voted in favor of the law, and this represents 57% of the total number of voters, how many voters were there in this election?

2. Two congruent cones with radius 12cm and height 12cm are enclosed within a cylinder. The base of each cone is a base of the cylinder, and the height of the cylinder is 24cm. What is the number of cubic centimeters in the volume of the cylinder not occupied by the cones? Express your answer in terms of π.

3. The sum of three different prime numbers is 40. Find the product of the largest two of the primes.

4. Shauna did a number trick with Zach. She told him to pick an even number, double it, add 48, divide by 4, subtract 7, multiply by 2, and subtract his original number. She then told him the result he should have attained. What was it?

5. A positive three digit integer is divided by a positive two digit integer, yielding an integer quotient and zero remainder. What is the smallest possible integer quotient?

Have fun, guys!