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题目内容
$$n \neq 0$$ and $$n \neq -1$$

Quantity A

$$\frac{n+n^2}{n^3+n^4}$$

Quantity B

$$\frac{1}{n^2}$$

In the figure, each edge of the cube has length 1. What is the area of the rectangular region $$ABCD$$?
A rectangular solid has length $$l$$, width $$w$$, and height $$h$$, where $$l + w + h = 24$$.
Which of the following statements individually provide(s) sufficient additional information to determine the surface area of the solid?
Indicate all such statements.
Line $$l$$ passes through the center of circle $$R$$ and intersects circle $$R$$ at points $$P$$ and $$Q$$. Line $$k$$ is perpendicular to line $$l$$ and intersects circle $$R$$ at points $$M$$ and $$N$$.

Quantity A

The length of arc $$MPN$$

Quantity B

The length of arc $$MQN$$

A plot of land is to be divided into three smaller lots, as shown in the figure above. If the total length of the sides of the three lots along Main Street is 360 feet, what is the length, in feet, of the side of lot $$A$$ that is along Main Street?
If $$y=x^2-2x+3$$, for what values of $$x$$ is the value of $$y$$ positive?
$$x^2+x-6=0$$

Quantity A

\frac{1}{1+3^x}

Quantity B

\frac{1}{1+5^x}
In a certain board game a player must throw two dice for a sum of 8 to end the game. If there is an equal likelihood of getting any one of the numbers 1 through 6 on each of the dice thrown, what is the probability that the player will end the game on the next throw?
The probability that event $$A$$ will occur is 0.40 and the probability that event $$B$$ will occur is 0.30. If the two events are independent, what is the probability that at least one of the events will occur?
A science book, a philosophy book, a geometry book, and a trigonometry book are to be arranged next to each other on a shelf. There are $$n$$ possible arrangements of the 4 books such that the geometry book and the trigonometry book are next to each other.

Quantity A

$$n$$

Quantity B

$$10$$
$$P=23^{25}$$-23

In the equation above, what is the units digit of $$P$$?


The graph above shows the annual sales, in thousands of dollars, for a certain product sold at three different stores for the years 2011 to 2015. Of the following sales, which had the greatest percent increase?
$$n$$ is a positive integer.

Quantity A

$$(n+2)!-n!$$

Quantity B

$$(n+1)!$$
A piece of string one meter long was cut in half; then one half was discarded and the remaining half was cut in half. This pattern of cutting and discarding was continued until a piece of string of less than 0.04 meter was obtained. What is the number of cuts that were made?
$$a_1, a_2, a_3,……a_n,……..$$
In the sequence above, $$a_1=5$$ and $$a_{n+1}=- a_n$$ for all positive integers $$n$$.

Quantity A

$$a_{15}$$

Quantity B

$$a_{27}$$
$$a_1, a_2, a_3, ......, a_n, ......$$
In the sequence of numbers shown, $$a_1=13^3$$, and $$a_n=a_{n-1}+13^3$$ for each integer $$n$$ greater than 1. If $$a_k=13^4$$ , what is the value of $$k$$?
In a group of 250 people who take classes at a community center, 75 people take drawing classes and 65 people take music classes. Which of the following could be the number of people in the group who take neither drawing classes nor music classes?
Indicate all such numbers.
Set $$A$$ and set $$B$$ each have 20 elements.
Which of the following statements individually provide(s) sufficient additional information to determine the number of elements in the intersection of $$A$$ and $$B$$?
Indicate all such statements.

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