Problem Solving

Which of the following has a value less than 1?

R is the set of positive odd integers less than 50, and S is the set of the squares of the integers in R. How many elements does the intersection of R and S contain ?

In N is a positive integer less than 200, and 14N/60 is an integer, then N has how many different positive prime factors?

If the product of the integers w, x, y and z is 770, and if 1 < w < x < y < z, what is the value of w + z?

In a acertain company, the ratio of the numer of manager to the number of production-line workers is 5 to 72. If 8 additional Production-line workers were to be hired, the ratio of the number of managers to the number of production-line workers would be 5 to 74. How many managers does the company have?

At the rate of m meters per s seconds, how many meters does a cyclist travel in x minutes?

In the circle above, PQ is parallel to diameter OR, and OR has length 18. What is the length of minor arc PQ?

What is the decimal equivalent of (1/5) 5 ?

The temperatures in degrees Celsius recorded at 6 in the morning in various parts of a certain country were 10, 5, -2, -1, -5, and 15. What is the median of these temperatures?

If 1 2 + 1 3 + 1 4 = 13 x , which of the following must be an integer? I. x 8 II. x 12 III. x 24

Which of the following ratios is most nearly equal to the ratio 1 + 5 √ 1 + 5 to 2?

The average (arithmetic mean) of 6,8, and 10 equals the average of 7,9 and

The average salary of 15 people in the shipping department at a certain firm is $20,000.Thesalaryof5oftheemployeesis$25,000 each and the salary of 4 of the employees is $16,000 each. What is the average salary of the remaining employees?

(2 √ + 1) (2 √ − 1) (3 √ + 1) (3 √ − 1) = (2 + 1) (2 − 1) (3 + 1) (3 − 1) =

If the sum of n consecutive integers is 0, which of the following must be true? I. n is an even number II. n is an odd number III. The average (arithmetic mean) of the n integers is 0

In a nationwide poll, N people were interviewed. If 1/4 of them answered "yes" to question 1, and of those, 1/3 answered "yes" to question 2, which of the following expressions represents the number of people interviewed who did NOT answer "yes" to both questions?

If x^2 = 2y^3 and 2y = 4, what is the value of x^2 + y?

In the formula V = 1/(2r)^3, if r is halved, then V is multiplied by

If 4x + 3y = -2 and 3x + 6 = 0, what is the value of y?

A retail appliance store priced a video recorder at 20 percent above the wholesale cost of $200. If a store employee applied the 10 percent employee discount to the retail price to buy the recorder, how much did the employee pay for the recorder?