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In square ABCD, point P is the midpoint of side BC and point Q is the midpoint of side AD. Point E (not shown) is located on line l and triangle BCE is equilateral.

Quantity A

The length of PQ

Quantity B

The length of PE





Data sets X and Y each consist of 4 values, as shown in the table. If the range of dataset X is 21, what is the range of dataset Y?


The table shows the number of pages in each of 5 textbooks. What is the greatest possible value of x for which the average (arithmetic mean) number of pages of the 5 textbooks is equal to the median number of pages of the 5 textbooks?
Which of the following could be the value of x to make sure that $$x^{3}-x$$ is divisible by 10?

Indicate all such values.
The ratio of A to B is 1:4 before a chemical reaction,   $$\frac{1}{4}$$of A was transformed into B, while at the same time,  $$\frac{1}{4}$$ of B was transformed into A, then what is the ratio of A to B after the reaction.

Give your answer as a fraction.
$$y > 1,001$$

Quantity A

$$\sqrt[3]{y}$$

Quantity B

$$\frac{y}{100}$$




The leg of isosceles triangle A is 8, while the leg of isosceles triangle B is 10.

Quantity A

The area of isosceles triangle A

Quantity B

The area of isosceles triangle B




The figure above shows five congruent circles each with radius 2 such that each of the five circles is tangent to two other congruent circles and to a smaller inner circle. The perimeter of the figure is composed of 5 line segments of length x and 5 circular arcs of length y. What is the perimeter of the figure?
k is a positive integer greater than 1

Quantity A

The remainder when $$k^{2}$$-k is divided by 2

Quantity B

0




Angle A measures r degrees. The complement of angle A measures 90-r degrees, and the supplement of angle A measures 180-r degrees. If the measure of angle A is greater than the measure of its complement and less than one-half the measure of its supplement, which of the following gives all possible values of r?

x=y

BD∥AE

Quantity A

The area of △ACE

Quantity B

The area of △BDF



The figure shown consists of a rectangle with length 14 and width 6, together with three isosceles right triangles. What is the area of the entire figure?
A caterer has 20 liters of fruit punch that is 12 percent grape juice, by volume. How many liters of fruit punch that is 20 percent grape juice, by volume, must be added to the original 20 liters of fruit punch in order to create fruit punch that is 15 percent grape juice, by volume?

_____liters
$$a=\frac{x}{x+y+z}$$ , $$b=\frac{y}{x+y+z}$$ , $$c=\frac{z}{x+y+z}$$


Quantity A

The average of a, b and c

Quantity B

$$\frac{1}{2}$$


The operation ▼ is defined by $$ n^{▼}=(n-1)^{2} $$ for all numbers n.

Quantity A

$$ \frac{(a+1)^{▼}}{a^{2}}$$

Quantity B

1


If a set S has a total of 6 subsets that consist of 2 members each, then S consists of how many members?
40 DVDs (17 are about psychology, 14 are about biology, and 9 are about history) need to be arranged in a bookshelf such that the 9 history-related DVDs are, on the whole, arranged in chronological order. In how many ways can these DVDs be arranged?
If one number is chosen at random from the first 1,000 positive integers, what is the probability that the number chosen has at least one digit with the number 6?
Give your answer as a fraction.
x and y are integers, 0 < x < y, and $$x^{2}+y^{2} $$ is even. Which of the following integers must be even?

Indicate all that are true.

Quantity A

The number of positive factors of 87

Quantity B

The number of positive factors of 97


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