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If the length of each side of a regular hexagon is 6, what is the area of the regular hexagon?
Working alone at their respective constant rates, an outlet pump can empty a certain tank of water in 7 hours when the tank is initially full, and an inlet pump can fill the tank in 10 hours when the tank is initially empty. Beginning with a full tank, both pumps work simultaneously at their respective constant rates for 1 hour before the inlet pump is shut off. How many more hours would it take the outlet pump working alone to empty the tank?


In the figure, the line l and the x-axis are tangent to the circle at points P and S, respectively, and the line segment QS passed through center R of the circle. What is the slope of l?


The graph shows for each movie category the percent of a sample of middle school students who had watched at least one movie in that category within the last year. If 87 percent of the students in the sample had watched at least one movie in the comedy category and at least one movie in the drama category, what percent of the students in the sample had not watched any movies in either of these two categories?


In square PRSU shown, Q and T are midpoints of sides PR and SU, respectively, and the length of QS is √5. What is the area of quadrilateral PQST?

_____
For each set of three distinct nonzero digits, consider the sum of all positive three-digit integers that can be formed by the digits. For example, for the three digits 1, 2, and 3, the sum of all positive three-digit integers that can be formed by the digits is 123 + 132 + 213 + 231 + 312 + 321 = 1,332. How many different integers are equal to such a sum?


In the figure shown, what is the product of the lengths of line segments RU and RT?
x > y > 0

Quantity A

$$\frac{x}{y}+\frac{y}{x}$$

Quantity B

2


Of the students at a certain university, 40 percent are graduate students, and the rest are undergraduate students. If 15 percent of the graduate students and 30 percent of the undergraduate students are pursuing an engineering degree, what percent of the students pursuing an engineering degree are graduate students?


In the figure shown, WXYZ represents a flat garden with an area of 140 square meters. Edge WX of the garden has length 10 meters, and edge XY has n meters.

Quantity A

n

Quantity B

10


a is an integer.

$$2^{a}$$ < 7!

Quantity A

The greatest possible value of a

Quantity B

11


List L consists of positive integers. The median of the integers in L is m. The least integer in L is less than m, and the greatest integer in L is greater than m.

Quantity A

The number of integers in L that are less than or equal to m

Quantity B

Twice the number of integers in L that are greater than m


Five children, Alex, Beth, Carl, Dan, and Ellen, stand side by side in a line, in ascending order of height where all five heights are different. Carl is the second tallest and he is taller than Beth but shorter than Dan. Alex has the same number of children standing to his left and to his right, and neither Dan nor Ellen are standing next to Alex. Which of the following shows the five children listed in order from shortest to tallest?
A sales representative for a photography company makes a base salary of $30,000 per year. In addition he earns a commission of $500 for each of the first 20 photograph packages he sells in a year and $1000 for each photograph package he sells in a year after the first 20. Each year he spends $4,000 on work-related travel. The sales representatives` income before taxes is his base salary plus commission, minus the amount he spends on work-related travel. How many photograph packages must he sell in a year so that his income before taxes is equal to $50,000?

_____photograph packages


In triangle BCD shown, which of the following is closest to the sum of the lengths of the three interior line segments?
The standard deviation of n numbers $$x_{1}$$, $$x_{2}$$, $$x_{3}$$,......, $$x_{n}$$, with mean x is equal to $$\sqrt{\frac{s}{n}}$$, where S is the sum of the squared differences, $$(x_{i}- x)^{2}$$ for 1 ≤ i ≤ n.

List S: 3, 4, 7, 9, 10, 15

For which of the following lists is the standard deviation of the numbers in the list equal to 4 times the standard deivation of the numbers in lists?

Indicate all such lists.
A certain list contains exactly five numbers. The median of the numbers in the list is 7, the mode (most frequently occurring number) of the numbers in the list is 4, and the average (arithmetic mean) of the greatest and second greatest numbers in the list is 20. What is the average of the numbers in this list?
Last year a certain school offered three different math classes for juniors: algebra, geometry, and statistics. Of a total of 24 students enrolled in these math classes, 12 students were enrolled in algebra, 8 students were enrolled in geometry, and 6 students were enrolled in both algebra and geometry. If no student who was enrolled in statistics was enrolled in algebra or geometry, how many students were enrolled in statistics?_____ _____students
A list consists of 12 consecutive even integers and 12 consecutive odd integers such that the greatest even integer is 11 more than the greatest odd integer. What is the range of the integers in the list?

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