If x is positive and x > y, which of the following must be positive?

I. x²y−xy²

II. x³−x²y

III. x³−xy²

­If x is positive and the distance between -7 and 0 is equal to the distance between x and 0, what is the value of x?

­A certain country with a total population of 50 million is divided into six regions J, K, L, M, N and P, ranked from the most populated to the least populated, with some of the populations possibly equal. If 21 percent of the total population of the country is in region M and if the population of region P is 2 million, what is the greatest possible population of region N?

The equation |2x - 3| = x - 5 has how many solutions for x?

Last year a credit card company gave each of its cardholders a rebate on the amount charged during the year. The rebate was 1 percent of the portion of the amount charged in excess of $2,000 but less than or equal to $5,000, and 2 percent of the portion of the amount charged in excess of $5,000. If a cardholder received a total rebate equal to 1.3 percent of the amount charged, how much did the cardholder charge on the card?

Rs. 16,820 is divided between Seeta and Geeta who are 27 and 25 years old, respectively. Their money is invested at 5% per annum compound interest in such a way that both receive equal money at the age of 40 years. Find the share of each out of Rs. 16,820.

Which of the following describe(s) two quantities that vary inversely?

I. The price per gallon of a certain home heating oil and the number of gallons that can be purchased for $600.

II. The revenue from the sale of tickets costing $6 each and the number of tickets sold.

III. The average rate at which a car is driven on a certain 60-mile trip and the amount of time required for the trip.

From a committee of 25 legislators, n members formed a task force. Each member of the task force sent a report to each committee member who was not on the task force. If a letter was sent in response to each report, which of the following represents the combined number of reports and letters sent?

At a certain resort, each of the 39 food service employees is trained to work in a minimum of 1 restaurant and a maximum of 3 restaurants. The 3 restaurants are the family buffet, the dining room, and the snack bar. Exactly 19 employees are trained to work in the family buffet, 18 are trained to work in the dining room, and 12 are trained to work in the snack bar. If 4 employees are trained to work in exactly 2 restaurants, how many employees are trained to work in all 3 restaurants?

If Sn is the sum of first n terms of a certain sequence and S_n = n (n² + 1) for all positive integers. What is the 4th term of the sequence?