### Problem Solving Practice Questions

A code is to be made by arranging 7 letters. Three of the letters used will be the letter A, two of the letters used will be the letter B, one of the letters used will be the letter C, and one of the letters used will be the letter D. If there is only one way to present each letter, how many different codes are possible?

If a rectangular billboard has an area of 104 square feet and a perimeter of 42 feet, what is the length of each of the shorter sides?

If x is an integer and 2.134 x 10^{x} is less than 210,000, what is the greatest possible value for x?

John spent 40 percent of his earnings last month on rent and 30 percent less than what he spent on rent to purchase a new dishwasher. What percent of last month's earnings did John have left over?

If negative integers *k* and *p* are NOT both even, which of the following must be odd?

Peter read P books last year, and Nikki read N books last year. If Peter read 35 more books than Nikki last year, which of the following reflects the relationship?

If 2 is the remainder when *m* is divided by 5, what is the remainder when 3*m* is divided by 5?

If 2 + ^{2}/_{x} = 3 - ^{3}/_{x} , then x =

To fill and art exhibit, the students in an art course are assigned to create one epiece of artwork each in the following distribution: ^{1}⁄_{3} are sculptures, ^{1}⁄_{8} are oil paintings, ^{1}⁄_{2} are watercolors and the remaining 10 pieces are mosaics. How many students are in the art class?