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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 $1,000 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 list S?

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?
The sum of two numbers divided by 2, gives a result of 24 and their difference divided by 2 gives a result of 17. The product of these two numbers is divisible by which of the following?
Four people, including Ito and Kenji, are to be assigned to 3 offices. Two of the offices can accommodate only 1 person and the other office can accommodate 2 persons. If Ito and Kenji cannot be assigned to the same office,how many different assignments of the 4 people to the offices are possible?
A marine biologist recorded the lengths of 115 fish. The median of the recorded lengths is 60 centimeters. Which of the following statements must be true?

Indicate all such statements.
In a distribution of 1,300 different positive numbers, 65.1 is at the 54th percentile and 63.8 is at the 4th percentile. Approximately how many of the numbers in the distribution are greater than 65.1?
When driving a car at a constant speed of 50 miles per hour the driver decided to apply the brake. How many feet did the car travel during the $$\frac{3}{4}$$ second that elapsed between the time the driver decided to apply the brake and the time the driver actually started to apply the brake? (1 mile=5,280 feet)

_____feet
In the xy-plane (not shown), a right triangle has its right angle at the origin and has its hypotenuse along the line $$y=7x-1$$. If none of the sides of the triangle are vertical, what is the product of the slopes of the three sides of the triangle?


Each ● in the table above represents an entry that is the product of the corresponding row and column values. What is the least positive entry of the 45 entries represented in the table?
For one toss of a certain coin, the probability that the outcome will be heads is $$\frac{1}{2}$$. If this coin is tossed 4 times, what is the probability that the outcome will be heads at least 3 times?
Set T is the set of all numbers of the form $$\frac{1}{n(n-1)}$$, where n is an integer and 2 < n < 5.

Quantity A

The sum of all the numbers in T

Quantity B

$$\frac{1}{4}$$
When the positive integer p is divided by 7, the remainder is 3. When p is divided by 6, the remainder is 4. Which of the following could be the value of p?

Indicate all such values.
In the xy-plane, which of the following could be the graph of y=kx+b, where k < b < -1?
In company X, 60 percent of the employees are female. 80 percent of the female employees are college graduates, and half of the female college graduates are new employees.

Quantity A

The percent of the employees in Company X who are not female, not college graduates, and not new employees

Quantity B

8%
In the xy-plane , the graph of the function $$y=x^{3} (x^{2}-3)(x+3)$$ intersects the x-axis at k different points.

Quantity A

k

Quantity B

3

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