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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




David bought $$n$$ stamps that cost $0.32 each. He paid with bills worth $1.00 each and received $0.08.

Quantity A

$$n$$

Quantity B

9


If -8 ≤ h ≤ 10 and h+m=-4, what is the least possible value of mh?
At a certain dealership, $$\frac{2}{5}$$ of the trucks have four-wheel drive, and $$\frac{1}{3}$$ of the vehicles that have four-wheel drive are trucks. Of the vehicles that are trucks or have four-wheel drive, what fraction are trucks that have four-wheel drive?

Give your answer as a fraction.

Circle A has radius 4.
Circle B has radius 3.

Quantity A

$$x$$

Quantity B

$$y$$B


$$d$$ is the greatest common divisor of 36 and 60, $$m$$ is the least common multiple of 36 and 60.

Quantity A

$$\frac{36}{d}$$

Quantity B

$$\frac{m}{60}$$



x=y

BD∥AE

Quantity A

The area of △ACE

Quantity B

The area of △BDF




The tick marks shown on the number line are evenly spaced. Points D and E have coordinates of $$4^{10}$$ and $$4^{11}$$, respectively. The point that has a coordinate of $$4^{9}$$ is?
$$2 \lt x \lt 5$$

$$\frac{1}{10} \lt y \lt \frac{1}{5}$$

Quantity A

$$x+y$$

Quantity B

$$\frac{1}{x}$$+$$\frac{1}{y}$$


If x and y are integers, and 1 < -x < 4, 2 < y < 5, what is the least possible value of xy?
From a class of 8 students, of which 5 students are female, a president and a vice president are to be chosen at random. If a student cannot be both the president and the vice president, what is the probability that the president and the vice president will both be female?
Give your answer as a fraction.
Sequence $$S$$: $$a_{1}, a_{2}, a_{3},......,a_{n}$$........

In sequence $$S$$, $$a_{1}$$ is an integer and $$a_{n}=2a_{n-1}$$ for all integers n greater than 1. If no term of sequence S is a multiple of 100, which of the following could be the value of $$a_{1}$$?

Indicate all such values.
$$n$$ and $$k$$ are integers, $$n > k > 1$$

Quantity A

$$(n-k)!$$

Quantity B

$$n!-k!$$


Four different toys need to be assigned to three kids such that each kid receives at least one toy. In how many ways can these toys be distributed?
x and y are prime numbers

x+y is odd

x < y

Quantity A

x

Quantity B

3


|x| ≤ 6 and |y| ≤ 4

x and y are integers, where x≠0. M is the greatest possible value of |$$\frac{y}{x}$$|.

Quantity A

M

Quantity B

1


N copies of a certain health magazine cost a total of $64.

R copies of a certain news magazine cost a total of $80.

Quantity A

The ratio of the cost of 1 of the health magazines to the cost of 1 of the news magazines

Quantity B

$$\frac{4}{5}$$


$$|2x+7| < 13$$

Quantity A

$$x^{2}$$

Quantity B

9


Three printers, $$X_1$$, $$X_2$$ and $$X_3$$, work only at their respective constant rates. Working together,$$X_1$$, $$X_2$$ and $$X_3$$ can complete a certain job in 9 hours; working together, $$X_2$$ and $$X_3$$ can complete the same job in 12 hours. Working alone, how many hours will it take $$X_1$$ to complete the job?


The three squares share a common vertex, as shown.

Quantity A

a+b

Quantity B

90°




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