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题目内容
If $$k$$ and $$n$$ are integers and if $$k-n$$ is an odd integer, which of the following must be an odd integer?
Two different integers, $$x$$ and $$y$$, are to be selected at random from the set of positive integers less than $$100$$.

Quantity A

The probability that both $$x$$ and $$y$$ will be even

Quantity B

The probability that $$x+y$$ will be even
When the integer $$n$$ is divided by $$21$$, the remainder is $$12$$. Which of the following must be a divisor of $$n$$?
Set $$S$$ consists of all integers greater than $$7$$ and less than $$60$$ such that when each of the integers is divided by $$7$$, the remainder is $$3$$. How many integers are in $$S$$?
$$x$$ is an integer

Quantity A

$$(-1)^{(x-1)}$$

Quantity B

$$(-1)^{(x+1)}$$
$$k$$, $$x$$, and $$y$$ are positive integers, and $$x=2k+6$$.

Quantity A

$$(-1)^{xy}$$

Quantity B

$$0$$
$$n$$ is a positive integer.

Quantity A

$$(-1)^{(2n-1)}$$

Quantity B

$$(-1)^{2(n-1)}$$
$$m$$ and $$n$$ are positive integers.
$$m-n=4$$

Quantity A

$$(-1)^m$$

Quantity B

$$(-1)^n$$
$$k$$ is a positive even integer.

Quantity A

$$(-1)^{(2k-3)}$$

Quantity B

$$(-1)^{(3k+7)}$$
$$x$$ and $$y$$ are positive integers. One of these integers is odd and the other is even.

Quantity A

$$(-1)^{(x+1)}$$

Quantity B

$$(-1)^y$$
$$x$$ is a prime number between $$1$$ and $$10$$, and $$y$$ is a prime number greater than $$10$$.

Quantity A

$$(-1)^{(x+y)}$$

Quantity B

$$(-1)^{xy}$$
Which of the following statements are true for all integers $$a$$ and $$b$$?
Indicate all such statements.
$$3n+1$$ is an even number.

Quantity A

$$(-1)^{(n+1)}$$

Quantity B

$$1$$

Quantity A

$$(-2)^{14}(-3)^{15}$$

Quantity B

$$(-2)^{15}(-3)^{14}$$
Set $$X$$ consists of all integers of the form $$(-n)^{(50-n)}$$, where $$n$$ is an integer and $$1 \leq n \leq 50$$.

Quantity A

The number of positive integers in $$X$$

Quantity B

The number of negative integers in $$X$$
Which of the following numbers are positive?
Indicate all such numbers.
Which of the following numbers is positive?
$$n$$ is a positive odd integer.
$$a=\frac{n+1}{2}$$
$$b=\frac{n-1}{2}$$

Quantity A

$$(-2)^a$$

Quantity B

$$(-2)^b$$
$$x$$ is a negative integer.

Quantity A

$$(2x-1)^{2x-1}$$

Quantity B

$$0$$
$$1, 2, 3,……., r$$
$$1, 2, 3,……., r+1$$
The first sequence consists of $$r$$ consecutive integers, where $$r$$ is an even integer. The second sequence consists of $$r + 1$$ consecutive integers.

Quantity A

The percent of the integers in the first sequence that are even

Quantity B

The percent of the integers in the second sequence that are even

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