Each employee of Company Z is an employee of either Division X or Division Y, but not both. If each division has some part-time employees, is the ratio of the number of full-time employees to the number of part-time employees greater for Division X than for Company Z ?

(1) The ratio of the number of full-time employees to the number of part-time employees is less for Division Y than for Company Z.

(2) More than half of the full-time employees of Company Z are employees of Division X, and more than half of the part-time employees of Company Z are employees of Division Y.

A contractor combined x tons of a gravel mixture that contained 10 percent gravel G, by weight, with y tons of a mixture that contained 2 percent gravel G, by weight, to produce z tons of a mixture that was 5 percent gravel G, by weight. What is the value of x ?

(1) y = 10

(2) z = 16

If 0 < x < 1, what is the median of the values x, \(x^{-1}, x^2\), √x, and \(x^3\)?

1/(a-b) < b-a

(1) a < b

(2) 1 < |a – b|

A used-car dealer sold one car at a profit of 25 percent of the dealer’s purchase price for that car and sold another car at a loss of 20 percent of the dealer’s purchase price for that car.  If the dealer sold each car for $20,000, what was the dealer’s total profit or loss, in dollars, for the two transactions combined?

Julia purchased a car on an installment plan.  She made a down payment of \$2,550 and then made n monthly payments of \$155 each. If Julia paid a total of \$9,060 for the car, how many monthly payments did she make?

During a 40-mile trip, Marla traveled at an average speed of x miles per hour for the first y miles of the trip and at an average speed of 1.25x miles per hour for the last 40 – y miles of the trip. The time that Marla took to travel the 40 miles was what percent of the time it would have taken her if she had traveled at an average speed of x miles per hour for the entire trip?

(1) x = 48

(2) y = 20

If p is a positive odd integer, what is the remainder when p is divided by 4 ?

(1) When p is divided by 8, the remainder is 5.

(2) p is the sum of the squares of two positive integers.

Jill, who lives in City C, plans to visit 3 different cities, M, L, and S.  She plans to visit each city exactly once and return to City C after the 3 visits.  She can visit the cities in any order.  In how many different orders can she visit the 3 cities?

Last year, a certain public transportation system sold an average (arithmetic mean) of 41,000 tickets per day on weekdays (Monday through Friday) and an average of 18,000 tickets per day on Saturday and Sunday.  Which of the following is closest to the total number of tickets sold last year?

A certain junior class has 1,000 students and a certain senior class has 800 students.  Among these students, there are 60 sibling pairs, each consisting of 1 junior and 1 senior.  If 1 student is to be selected at random from each class, what is the probability that the 2 students selected will be a sibling pair?

According to the directions on a can of frozen orange juice concentrate, 1 can of concentrate is to be mixed with 3 cans of water to make orange juice.  How many 12-ounce cans of the concentrate are required to prepare 200 6-ounce servings of orange juice?

Is \(√((x-3)^2)\) = 3-x

(1) x ≠ 3

(2) –x|x| > 0

A certain office supply store stocks 2 sizes of self-stick notepads, each in 4 colors:  blue, green, yellow, or pink.  The store packs the notepads in packages that contain either 3 notepads of the same size and the same color or 3 notepads of the same size and of 3 different colors.  If the order in which the colors are packed is not considered, how many different packages of the types described above are possible?

In the rectangular coordinate system shown above, does the line k (not shown) intersect quadrant II?

(1) The slope of k is -1/6

(2) The y-intercept of k is -6.

If R = 1 + 2xy + \((x^{2y})^{2}\), what is the value of xy?

(1) R = 0

(2) x > 0

The residents of Town X participated in a survey to determine the number of hours per week each resident spent watching television.  The distribution of the results of the survey had a mean of 21 hours and a standard deviation of 6 hours.  The number of hours that Pat, a resident of Town X, watched television last week was between 1 and 2 standard deviations below the mean.  Which of the following could be the number of hours that Pat watched television last week?

What is the remainder when the positive integer n is divided by 6 ?

(1) n is a multiple of 5.

(2) n is a multiple of 12.

If x and y are integers greater than 1, is x a multiple of y?

(1) \(3y^2\) + 7y = x.

(2) \(x^2\) – x is a multiple of y.

If m > 0 and n > 0, is (m+x)/(n+x) > m/n?

(1) m < n

(2) x > 0