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题目内容
$$n$$ is a positive two-digit integer.

Quantity A

The greatest prime factor of $$n$$

Quantity B

The greatest prime factor of $$2n+1$$
$$n=(2^a)(3^a)$$, where $$a$$ is a positive integer.

Quantity A

The number of different positive factors of $$n$$

Quantity B

$$a^2$$
A manager oversees 7 employees, including 1 new employee, assigning one or more of them to work on various tasks. The manager will assign 2 employees to work together on a certain task. Of all 21 possible pairs of employees that the manager can choose from the 7 employees to work on the task, the number of pairs that will not include the new employee is how many greater than the number of pairs that will include the new employee?
The remainder is 1 when the integer $$n$$ is divided by 5.

Quantity A

The remainder when the integer $$2n$$ is divided by 5

Quantity B

3
A group consisting of 4 adults and 3 children wil occupy 7 adjacent seats in one row of a theater, one person per seat. How many different arrangements of the 7 people are possible such that no two adults and no two children sit next to each
Let $$p$$ be theproduct of the integers from 1 to 200. What is the exponent of the prime number 7 in the prime factorization of $$p$$?
Let A be the set of integers between 1and 100 that, when divided by 5, have a remainder of 2. Let B be the set of integers between 1 and 100 that, when divided by 6, have a remainder of 1. How many integers are in the set A∩B?


The figure shows a circle with center O and radius $$r$$. If the length of line segment AB is $$\sqrt{2}r$$, what is the area of the shaded region?
The circumference of circle P is 9, and the circumference of circle T is 36.

Quantity A

The ratio of the radius of circle P to the radius of circle T

Quantity B

$$\frac{1}{2}$$

Quantity A

The greatest integer $$n$$ such that $$360^n$$ is a factor of $$2^{37}3^{25}2^{41}$$

Quantity B

11


The circles with centers P and O have radii 6 and 2, respectively, and are tangent to each other. Line $$l$$ is tangent to the circles at points A and B, as shown. What is the length of line segment AB ?

Quantity A

$$(0.001)^{2,000}$$

Quantity B

$$(10)^{-4,000}$$
How many six-digit positive integers have three digits that are 1s, one digit that is 2, one digit that is 3, and one digit that is 4?
The function g is defined by g(x) =x+1 for all numbers x.

Quantity A

$$g(-1)$$

Quantity B

1
How many five-digit positive integers have four of the digits the same and the other digit different?
The fraction $$\frac{22}{7}$$ is equivalent to the repeating decimal $$3.\overline{142857}$$, and the first 10 digits of the number π are 3.141592653. By how much does $$\frac{22}{7}(10^7)$$ exceed $$π(10^7)$$?

Give your answer to the nearest integer.
For each value x in a list of values with mean m, the absolute deviation of * from the mean is defined as |x-m|.

The absolute deviations from the mean of the five numbers in list L are 0, 1, 2, 3, and 6. If k is an integer greater than 1, the numbers in which of the following lists have the same absolute deviations from the mean as the numbers in L ?

Indicate all such lists.
In a list of consecutive integers the least integer is -15 and the greatest is 87. How many integers are in the list?


According to the data in the graph, approximately what is the average (arithmetic mean) annual decrease from 1980 to 1995 in the list price of a Brand X microcomputer?

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