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题目内容
$$n$$ 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
The least of five consecutive odd integers is $$x-3$$.

Quantity A

The greatest of the five integers

Quantity B

$$x+3$$
For each positive integer $$n$$, set $$A_n$$ consists of n consecutive even integers. What is the range of the integers in set $$A_100$$?

Quantity A

The range of nine consecutive odd integers

Quantity B

$$16$$
The positive integer $$x$$ is the product of $$3$$ different prime numbers.
The positive integer $$y$$ is the product of $$4$$ different prime numbers.

Quantity A

$$x$$

Quantity B

$$y$$
Two positive integers are twin primes if each is prime and their difference is $$2$$. Which of the following pairs of integers is NOT a pair of twin primes?

Quantity A

The greatest prime number that is less than $$91$$

Quantity B

The least prime number that is greater than $$84$$
Pat has $$7$$ identical pieces of paper. One or more of the pieces are cut into $$7$$parts each, then one or more of the smaller pieces are cut into $$7$$ parts each again. Which of the following could be the total number of pieces of paper after these cuts have been made?
How many two-digit positive integers are equal to the product of two different prime numbers greater than $$0$$?
A total of $$77$$ coins are to be divided equally among n people, where $$n \gt 1$$.

Quantity A

$$n^2$$

Quantity B

$$81$$
$$x$$, $$y$$, and $$z$$ are integers such that $$1 \lt x \lt y \lt z$$ and $$xyz=105$$.

Quantity A

$$x+z$$

Quantity B

$$2y$$
A total of $$143$$ players arrived on the first day of football practice. The coaches divided them into n groups, each with the same number of players, where $$n \gt 1$$.

Quantity A

$$n^2$$

Quantity B

$$125$$
$$N$$ is the least 3-digit positive integer for which the product of its digits is equal to $$24$$.

Quantity A

$$N$$

Quantity B

$$234$$
$$1575=3^m \times 5^n \times 7^p$$, where $$m$$, $$n$$, and $$p$$ are positive integers.

Quantity A

$$m+n+p$$

Quantity B

$$5$$

Quantity A

The number of distinct prime factors of $$1,001^{1,001}$$

Quantity B

The number of distinct prime factors of $$210^{210}$$
What is the number of distinct prime factors of $$n$$?
$$n=13!+15!$$

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