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题目内容
For each value $$x$$ in a list of values with mean $$m$$, the absolute deviation of $$x$$ from the mean is defined as $$|x-m|$$.

A certain online course is offered once a month at a university. The number of people who register for the course each month is at least $$5$$ and at most $$30$$. For the past $$6$$ months, the mean number of people who registered for the course per month was $$20$$. For the numbers of people who registered for the course monthly for the past $$6$$ months, which of the following values could be the sum of the absolute deviations from the mean?

Indicate all such values.
There are 34 different tasks assigned for 7 students (each student has at least one task). Student A is assigned more tasks than any another students, while student B is assigned fewer tasks than any other students. What is the least possible difference between the number of tasks assigned to student A and student B ?
A certain truck takes $$10$$ trips to transport $$2,000$$ cartons from warehouse A to warehouse B. For each trip except the $$10^{th}$$ trip, the truck is loaded to its full carrying capacity of $$x$$ cartons. On the $$10^{th}$$ trip, the truck is loaded with the remaining cartons.

Quantity A

$$x$$

Quantity B

$$210$$
The sum of ten different positive integers is 101. What is the greatest possible value of the maximum among the integers?
Dr. Bradley treated a different number of patients on each of the 5 working days last week, and the least number of patients treated on any of the days was 20. No patient was treated on more than one day.

Quantity A

The least possible total number of patients that Dr. Bradley treated on the 5 working days last week

Quantity B

110
If $$a^{2}$$+$$b^{2}$$=$$c^{2}$$, and a, b, c are all integers. Which of the following CANNOT be the value of a+b+c?
In a two-digit integer n, the tens digit is 1, the units digit is to be determined, while the tens digit of the square of n is 2.

Quantity A

The hundreds digit of the square of n

Quantity B

2
If set S consists of the squares of the integers from -5 to 5, inclusive, how many elements are in set S?
$$3 \lt x^{2} \lt 27$$

$$6 \lt y^{2} \lt 69$$

Quantity A

The least possible value of the product $$xy$$, where $$x$$ and $$y$$ are integers satisfying the inequalities

Quantity B

$$-40$$
w, x, y and z are integers

w < x and y < z

Quantity A

wy

Quantity B

xz
0 < x < 1

-1 < y < 0

Which of the following must be true?

Indicate all such statements.
k, m, and p are integers.

If k and m are negative integers, which of the following must be negative integers?

Indicate all such integers.
$$a_1$$, $$a_2$$, $$a_3$$,......$$a_{99}$$

In the sequence shown, each term after the first is 1 greater than the preceding term. If the sum of all the 99 terms of the sequence is 99, then what is the value of the first term of the sequence?
The product of five consecutive integers is not 0.

Which of the following statements individually provide(s) sufficient additional information to determine all these integers are negative?

Indicate all such statements.
n=1234567891011.........499500

The digits of the integer n above are the digits of the integers from 1 to 500 written in consecutive order. How many digits does n have?
List L consists of an odd number of consecutive integers. The median of the integers in L is 3. Which of the following statements must be true?

Indicate all such statements.
$$q$$, $$r$$ and $$s$$ are consecutive positive integers and $$q \lt r \lt s$$.

Quantity A

$$\frac{qs}{r}$$

Quantity B

$$r-\frac{1}{r}$$

Quantity A

The number of odd integers between $$\sqrt{12}$$ and $$12^{2}$$

Quantity B

70
If $$x=2y+1$$, and $$y=2w$$, where $$w$$, $$x$$, and $$y$$ are integers, which of the following must be an odd integer?
If r, s, t, and u are positive integers such that (r+s)(t+u) is an odd integer and (r+s+t)(s+t+u) is an odd integer, which of the following statements must be true?

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