The area of a square garden is A square feet and the perimeter is P feet. If A = 2P + 9, what is the perimeter of the garden, in feet?

If x is an even integer and y is an odd integer, which of the following is even?

In a certain senior class, 72 percent of the male students and 80 percent of the female students have applied to college.
What fraction of the students in the senior class are male?

(1) There are 840 students in the senior class.

(2) 75 percent of the students in the senior class have applied to college.

If a and b are nonzero numbers on the number line, is 0 between a and b?

(1) The distance between 0 and a is greater than the distance between 0 and b.

(2) The sum of the distances between 0 and a and between 0 and b is greater than the distance between 0 and the sum a + b .

Each of the numbers w, x, y, and z is equal to either 0 or 1. What is the value of w + x + y + z ?

(1) w/2 + w/4 + y/8 + z/16 = 11/16

(2) w/3 + x/9 + y/27 + z/81 = 31/81

A grocer stacked oranges in a pile. The bottom layer was rectangular with 3 rows of 5 oranges each. In the second layer from the bottom, each orange rested on 4 oranges from the bottom layer, and in the third layer, each orange rested on 4 oranges from the second layer. Which of the following is the maximum number of oranges that could have been in the third layer?

If n is a positive integer and r is the remainder when \(n^2\) – 1 is divided by 8, what is the value of r?

(1) n is odd.

(2) n is not divisible by 8

In the xy-plane, line k passes through the point (1,1) and line m passes through the point (1,-1). Are lines k and m
perpendicular to each other?

(1) Lines k and m intersect at the point (1,-1).

(2) Line k intersects the x-axis at the point (1,0).

In the figure shown, point O is the center of the semicircle and points B, C, and D lie on the semicircle. If the length of line segment AB is equal to the length of line segment OC, what is the degree measure of angle BAO?

(1) The degree measure of angle COD is 60.

(2) The degree measure of angle BCO is 40.

The lunch menu at a certain restaurant contains 4 different entrees and 5 different side dishes. If a meal consists of 1 entree and 2 different side dishes, how many different meal combinations could be chosen from this menu?

If x is an integer, which of the following must be an odd integer?

A farm used two harvesting machines, H and K, to harvest 100 acres of wheat.  Harvesting machine H, working alone at its constant rate, harvested 40 acres of wheat in 8 hours.  Then harvesting machine K was brought in, and harvesting machines H and K, working together at their respective constant rates, harvested the remaining acres of wheat in 5 hours.  Harvesting machine K harvested how many acres of wheat per hour?

In 1995 Division A of Company X had 4,850 customers. If there were 86 service errors in Division A that year, what was
the service-error rate, in number of service errors per 100 customers, for Division B of Company X in 1995?

(1) In 1995 the overall service-error rate for Divisions A and B combined was 1.5 service errors per 100 customers.

(2) In 1995 Division B had 9,350 customers, none of whom were customers of Division A.

In the xy-coordinate plane, line m and line k intersect at the point (4, 3). Is the product of their slopes negative?

(1) The product of the x-intercepts of lines m and k is positive.

(2) The product of the y-intercepts of lines m and k is negative.

At a certain supplier, a machine of type A costs $20,000 and a machine of type B costs $50,000. Each machine can be purchased by making a 20 percent down payment and repaying the remainder of the cost and the finance charges over a period of time. If the finance charges are equal to 40 percent of the remainder of the cost, how much less would 2 machines of type A cost than 1 machine of type B under this arrangement?

In a certain group of 10 members, 4 members teach only French and the rest teach only Spanish or German. If the group is to choose a 3-member committee, which must have at least 1 member who teaches French, how many different committees can be chosen?

To determine her state income tax last year, Elena computed 5 percent of her gross income, rounded the resulting figure down to the nearest $100, and subtracted $50 for each dependent that she claimed. If Elena’s gross income was $34,500 and she claimed 2 dependents, how much did she determine her state income tax to be?

For any triangle T in the xy-coordinate plane, the center of T is defined to be the point whose x-coordinate is the average (arithmetic mean) of the x-coordinates of the vertices of T and whose y-coordinate is the average of the y-coordinates of the vertices of T. If a certain triangle has vertices at the points (0,0) and (6,0) and center at the point (3,2), what are the coordinates of the remaining vertex?

If 500 is the multiple of 100 that is closest to x and 400 is the multiple of 100 that is closest to y, which multiple of 100 is closest to x + y?

(1) x < 500

(2) y < 400

All the clients that Company X had at the beginning of last year remained with the company for the whole year. If
Company X acquired new clients during the year, what was the ratio of the number of clients that Company X had at the end
of last year to the number of clients that it had at the beginning of last year?

(1) The ratio of the number of clients that Company X had at the beginning of last year to the number of new clients that it acquired during the year was 12 to 1.

(2) Company X had 144 clients at the beginning of last year.