\(2 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8\) =

For a certain race, 3 teams were allowed to enter 3 members each. A team earned 6 – n points whenever one of its members finished in nth place, where 1 <= n <= 5. There were no ties, disqualifications, or withdrawals. If no team earned more than 6 points, what is the least possible score a team could have earned?

What is the value of \(a^4 – b^4\)?

(1) \(a^2 – b^2\) = 16

(2) a + b = 8

A rectangular region has a fence along three sides and a wall along the fourth side. The fenced side opposite the wall is twice the length of each of the other two fenced sides. If the area of the rectangular region is 128 square feet, what is the total length of the fence, in feet?

List S and list T each contain 5 positive integers, and for each list the average (arithmetic mean) of the integers in the list is 40. If the integers 30, 40, and 50 are in both lists, is the standard deviation of the integers in list S greater than the standard deviation of the integers in list T?

(1) The integer 25 is in list S.

(2) The integer 45 is in list T.

In the rectangular coordinate system, are the points (r, s) and (u, v) equidistant from the origin?

(1) r + s = 1

(2) u = 1 – r and v = 1 – s.

In May, Xiang sold 15 used cars. For these 15 cars, the range of the selling prices was $15,000 and the lowest selling price was $4,500. In June, Xiang sold 10 used cars. For these 10 cars, the range of the selling prices was $16,500 and the lowest selling price was $6,100. What was the range of the selling prices of the 25 used cars sold by Xiang in May and June?

How much time did it take a certain car to travel 400 kilometers?

(1) The car traveled the first 200 kilometers in 2.5 hours.

(2) If the car’s average speed had been 20 kilometers per hour greater than it was, it would have traveled the 400
kilometers in 1 hour less time than it did.

A certain store found that last year the average (arithmetic mean) monthly sales from January through October was $120,000. In November and December, the monthly sales were 3 and 5 times, respectively, the average for the other 10 months. What was the store’s average monthly sales last year?

For each hour of production, a certain factory requires 1 assembly line worker for every 25 units to be produced in that hour. The factory also requires 12 managers regardless of the number of units to be produced. Which of the following expressions represents the total number of assembly line workers and managers that this factory requires to produce 50N units in one hour, where N is a positive integer?

Do more than 50 percent of the children in a certain group have brown hair?

(1) 70 percent of the boys in the group have brown hair.

(2) 30 percent of the children in the group are girls with brown hair.

If n is a positive integer, which of the following must be an even integer?

If (400)(6,000) = (240)(\(100^x\)), what is the value of x ?

A television network sells advertising time on a certain program at the rate of $10,000 per minute. If the program is shown once a day for 5 days a week, what is the cost of advertising on this program for 3 weeks at 30 seconds per day?

A stamping machine produces 100 gaskets per hour. When this machine works with a newer machine, the two machines, working simultaneously and independently at their respective constant rates, produce a total of 2,000 gaskets in 8 hours. How many gaskets does the newer machine produce per hour?

Robin split a total of $24,000 between two investments, X and Y. If investment Y earns 7 percent simple annual interest,
how much of the total did Robin put into investment Y?

(1) Each investment earns the same dollar amount of interest annually.

(2) Investment X earns 5 percent simple annual interest.

In a certain year the United Nations’ total expenditures were $1.6 billion. Of this amount, 67.8 percent was paid by the 6
highest-contributing countries, and the balance was paid by the remaining 153 countries. Was Country X among the 6
highest-contributing countries?

(1) 56 percent of the total expenditures was paid by the 4 highest-contributing countries, each of which paid more than
Country X.

(2) Country X paid 4.8 percent of the total expenditures.

If v and w are different integers, does v = 0?

(1) vw= \(v^2\)

(2) w = 2

Some of the students enrolled at College T are part-time students and the rest are full-time students. By what percent did
the number of full-time students enrolled at College T increase from the fall of 1999 to the fall of 2000?

(1) There were 50 more full-time students enrolled at College T in the fall of 2000 than in the fall of 1999.

(2) The total number of students enrolled at College T increased by 5 percent from the fall of 1999 to the fall of 2000.

Is √\((x-5)^2\) = 5 – x

(1) -x|x| > 0

(2) 5 – x > 0