Problem Solving

If z ≠ 0 and z + 1 − 2 z 2 z = w z , then w =

For the positive numbers, n, n + 1, n + 2, n + 4, and n + 8, the mean is how much greater than the median?

Each person who attended a company meeting was either a stockholder in the company, an employee of the company or both. If 62 percent of these who attended the meeting were stockholders and 47 percent were employees. What percent were stockholders, who were not employees?

For a party, three solid cheese balls with diameters of 2 inches, 4 inches, and 6 inches, respectively, were combined to form a single cheese ball. What was the approximate diameter, in inches, of the new cheese ball?

Cheryl purchased 5 identical hollow pine doors and 6 identical solid oak doors for the house she is building. The regular price of each solid oak door was twice the regular price of each hollow pine door. However, Cheryl was given a discount of 25% off the regular price of each solid oak door. If the regular price of each hollow pine door was $40, what was the total price of all 11 doors?

Which of the following statements must be true about the average (arithmetic mean) and the median of 5 consecutive integers?

In the figure shown, if the area of the shaded region is 3 times the area of the smaller circular region, then the circumference of the larger circle is how many times the circumference of the smaller circle?

A bicycle store purchased two bicycles, one for $250andtheotherfor$375, and sold both bicycles at a total gross profit of $250.Ifthestoresoldoneofthebicyclesfor$450, which of the following could be the store's gross profit from the sale of the other bicycle?

Greg assembles units of a certain product at a factory. Each day he is paid $2.00perunitforthefirst40unitsthatheassemblesand$2.50 for each additional unit that he assembles that day. If Greg assembled at least 30 units on each of two days and was paid a total of $180.00 for assembling units on the two days, what is the greatest possible number of units that he could have assembled on one of the two days?

Carol purchased one basket of fruit consisting of 4 Apples and 2 Oranges and another basket of fruit consisting of 3 Apples and 5 Oranges. Carol is to select one piece of fruit at random from each of the two baskets. What is the probability that one of the two pieces of fruit selected will be an apple and the other will be an orange?

If (1 – 1.25)N = 1, then N =

If (1 3 + 1 4 + 1 5 + 1 6) = r (1 9 + 1 12 + 1 15 + 1 18) , then r =

A worker carries jugs of liquid soap from a production line to a packing area, carrying 4 jugs per trip. If the jugs are packed into cartons that hold 7 jugs each, how many jugs are needed to fill the last partially filled carton after the worker has made 17 trips?

The number line shown contains three points R, S, and T, whose coordinates have absolute values r, s, and t, respectively. Which of the following equals the average (arithmetic mean) of the coordinates of the points R, S, and T ?

In a certain sequence of 8 numbers, each number after the first is 1 more than the previous number. If the first number is −5, how many of the numbers in the sequence are positive?

The symbol ∆ denotes one of the four arithmetic operations:addition,subtraction,multiplication,or division,If 6∆3≤ 3 ,which of the following must be true ?

Judy bought a quantity of pens in packages of 5 for $0.80perpackage.Shesoldallofthepensinpackagesof3for$0.60 per package. If Judy's profit from the pens was $8.00, how many pens did she buy and sell?

The annual budget of a certain college is to be shown on a circle graph. If the size of each sector of the graph is to be proportional to the amount of the budget it represents , how many degrees of the circle should be used to represent an item that is 15 percent of the budget?

If k^2 = m^2, which of the following must be true?

A certain restaurant that regularly advertises through the mail has 1,040 cover letters and 3,000 coupons in stock. In its next mailing, each envelope will contain 1 cover letter and 2 coupons. If all of the cover letters in stock are used, how many coupons will remain in stock after this mailing?