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题目内容
Let $$q$$ be a prime number less than $$100$$. When $$q$$ is divided by $$5$$, the remainder is $$2$$. When $$q$$ is divided by $$7$$, the remainder is $$6$$, what is the remainder when $$q$$ is divided by $$8$$?
For all positive even integers $$n$$, $$n」$$ represents the product of all even integers from 2 to $$n$$, inclusive. For example, $$12」=12\times10\times8\times6\times4\times2$$. What is the greatest prime factor of $$20」+22」$$?
How many positive integers less than or equal to 603 are multiples of 2 or multiples of 3 or both?
How many integers from 1 to 1000, inclusive, have the same remainder when divided by 2, 3, 5, 7?
How many integers between 100 and 1,000 are multiples of 7?
If the sum of two numbers is 10, what is the greatest possible value of the product of the two numbers?
The sum of three different positive integers is 11.

Which two of the following statements together provide sufficient information to determine the three integers?

Indicate two such statements.
Z=$$123^{4}$$-$$123^{3}$$+$$123^{2}$$-123

What is the remainder when Z is divided by 122?
Which of the following numbers satisfy their sum of reciprocals is either less than $$\frac{1}{3}$$ or greater than $$\frac{1}{2}$$ ?

Indicate all such numbers.
x≠0, y≠0

|x|+|y|=|x+y|

Which of the following statements must be true?

Indicate all such statements.
Carolyn took out a one-year loan for $15,000 at 8 percent simple annual interest. She repaid the total amount, including the interest, by making 12 equal monthly payments on the last day of each month beginning in January. At the beginning of which of the following months did Carolyn have less than $10,000 of the total amount left to the repaid?

Indicate ALL such months.
For 7 soccer ball teams, each of them has to play with all the other teams. However, to decide which team wins, every two teams have to play 3 rounds and the team that win for the most times will ultimately win. How many rounds of game do all teams have to play in total?
There are n positive integers. The sum of the numbers is greater than 48, while the arithmetic average of the numbers is 1.2. What is the least value of n?
If $$1 \lt r \lt s \lt t$$, which of the following is closest in value to the product $$rst$$?
x≠0

Quantity A

$$ax^{4}$$

Quantity B

$$(ax)^{4}$$
$$n$$ is a positive integer.

Quantity A

$$\frac{1}{3^{n}}$$

Quantity B

$$3(\frac{1}{4^{n}})$$
If $$x \geq 0$$, $$y \geq 0$$, and $$x^{2}$$+$$y^{2}$$=$$1$$, which of the following statements must be true?

Indicate all such statements.
The ratio of the lengths of sides of a certain triangle is 3 : 5 : 7.

Quantity A

Degree of the greatest angle of this triangle

Quantity B

85°
The lengths of the sides of triangle $$RST$$ are $$3$$, $$4$$, and $$y$$. Which of the following inequalities specifies those values of $$y$$ for which each angle measure of triangle $$RST$$ is less than $$90°$$?
d≠0

Quantity A

The area of a square region with sides of length d

Quantity B

The area of a circular region with diameter d

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