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题目内容
A group of people plan to pay $240 for a facility and split the bill. If 2 of them drop the plan, then the rest of them need to pay $4 more each. How much do they need to pay each at first?
The equation $$x^{3}$$ - $$x^{2}$$-2x=0 has three different roots.

Quantity A

The product of the three roots

Quantity B

-2

Quantity A

The number of integers n such that -9 < 2n+1 < 15

Quantity B

11
For which of the following values of x is the inequality $$\frac{(x-4)^{4}(x+5)^{6}}{(x-2)^{10}}$$ ≤ 0 satisfied?

Indicate all such values.
Which of the following inequalities is equivalent to 3 ≤ x ≤ 4?
$$x \gt 0$$, $$y \gt 0$$, $$x^{2}+y^{2} \leq1$$

Which of the following must be true?

Indicate all such statements.
List L consists of the numbers $$1-\frac{1}{k}$$ for all integers $$k$$ from $$1$$ to $$100$$, inclusive. List M consists of the number $$1$$ and the numbers $$1-\frac{1}{k}$$ for all integers $$k$$ from $$1$$ to $$100$$, inclusive.

Quantity A

The average (arithmetic mean) of the numbers in list L

Quantity B

The average (arithmetic mean) of the numbers in list M
a and b are integers

Quantity A

$$\frac{a^{10}}{b^{10}}$$

Quantity B

$$\frac{a^{10}+5^{15}}{b^{10}+5^{15}}$$
A saltwater solution contains $$25$$ percent salt by weight. To $$1$$ kilogram of this solution, $$x$$ grams of salt and $$4x$$ grams of water are added , where $$x \gt 0$$.

Quantity A

The percent of salt in the resulting solution

Quantity B

$$25%$$
A mixture of brown sugar and cinnamon in a bowl contains 20 percent cinnamon, by weight. To this mixture x ounces of cinnamon and 5x ounces of brown sugar will be added (x > 0).

Quantity A

The percent of cinnamon, by weight, in the bowl after the cinnamon and brown sugar are added

Quantity B

20%
If x is an integer, then what is the least possible value of $$3^{x}$$ + $$3^{-x}$$ ?
x is a positive integer.

g > 0

Quantity A

$$g^{x}$$+$$\frac{1}{g^{x}}$$

Quantity B

1
The volume of a rectangular solid is 60, and the area of one of its faces is 11.

Quantity A

The surface area of the solid

Quantity B

100
If the sum of two numbers is $$9$$, what is the greatest possible value of the product of the two numbers?
$$\frac{1}{a}$$ +$$\frac{1}{b}$$ =$$\frac{1}{c}$$ , a+b=40, a, b and c are all positive numbers, which of the following could be the value of c?

Indicate all such numbers
The measure of each interior angle of a regular polygon with n sides is between 110° and 130°.

Quantity A

n

Quantity B

8
Jayden, Kenny and Laina are paid hourly wages at their jobs. Jayden`s hourly wage is between $8.00 and $9.00, Kenny`s hourly wage is $5.00 less than 2 times Jayden`s hourly wage, and Laina`s hourly wage is $1.00 more than Jayden`s hourly wage. Which of the following shows Jayden, Kenny, and Laina listed in order according to their hourly wages, from least to greatest?
When the total cost of 90 dollars for the rental of a van was evenly divided among n passengers, the cost to each passenger was less than 23 dollars.

Quantity A

n

Quantity B

5
A company has assets worth $150,000 and liabilities worth $70,000, giving it an asset-to-liability ratio of approximately 2.1. The company will borrow x dollars, and the amount borrowed will be added to both the assets and the liabilities. If the asset-to-liability ratio is to be greater than 1.2 after the money is borrowed, which of the following could be the value of x?

Indicate all such values.
P(x)=$$x^{17}$$ - $$x^{18}$$

Quantity A

P($$\frac{8}{7}$$)

Quantity B

P($$\frac{7}{8}$$)

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