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题目内容
k is a positive integer.

Quantity A

The remainder when $$4^k$$ is divided by 11

Quantity B

8
In the xy-plane, the vertices of triangle $$T_n$$, are defined as the points $$(n, 0), (3n+1, 0)$$,and $$(n, 2n^2+2n)$$ for all positive integers n. The perimeter of triangle $$T_5$$ is how much greater than the perimeter of triangle $$T_4$$ ?
In a candy factory, quality-control tests were conducted on six 1,000-piece batches of candy. The numbers of pieces of candy that were rejected in these batches were 4, 3, 8, 6, 3, and 12, respectively. If the median of these numbers is used topredict the number of rejections in each 1,000-piece batch of candy produced by this factory, what is the total number of rejections predicted for 20 such batches?
From a set of 15 questions, a student must select exactly 12 questions to answer. How many different selections of 12 questions are possible if the order in which the questions are selected does not matter?
$$a=-2, b=-3$$, and $$c=0$$

Quantity A

$$a^3b+ac$$

Quantity B

18
$$4^{x-1} > 500$$

Quantity A

x

Quantity B

5
|x|+6 < |y|+7

Quantity A

x

Quantity B

y
Trapezoid RSTU has bases RU and ST. Base RU of trapezoid RSTU is a side of triangie RXU.The height of triangle RXU that corresponds to side RU is greater than the height of trapezoid RSTU that corresponds to bases RU and ST.

Quantity A

The area of the triangle RXT

Quantity B

The area of the trapezoid RSTU
a and b are integers such that 0 < a < b

Quantity A

$$a^2+b^2$$

Quantity B

$$\frac{1}{2} (a+b)^2$$
How many four-digit positive integers are there such that the digits are distinct and have a sum greater than or equal to 29?
The letters R, W, S, T, M, and P are to be arranged from left to right in a sequence such that each of the 6 letters occurs exactly once. For example, PMRSTW is one such sequence. Of all possible sequences of this type, how many have S as the left-most letter and T as the right-most letter?
How many different 3-digit numbers can be formed using the digits 1, 2, 3, 4, and 5 if all the digits in each number must be different?
The cast of a certain play has 2 male characters and 2 female characters. The director of the play will select the 2 male characters from 6 male actors and the 2 female characters from 8 female actors. How many different sets of 4 actors, consisting of 2 male actors and 2 female actors, are there that can be selected by the director?
How many six-digit positive integers are greater than 535,000 and consist of the digits 1, 2, 3, 5, 7, 9, where each digit occurs only once?
How many different five-digit positive integers can be formed in which each of the digits 1, 2, 3, 6, and 7 is used exactly once?
A product testing company will test 7 different fax machines by linking every possible pair and transmitting first from one machine to the other and then transmitting in the opposite direction. Thus, 2 transmissions will occur in testing each pair. If each transmission takes 10 minutes, how many minutes of transmission time will it take to test all of the machines?
How many different four-digit integers contain each of the four digits 3, 4, 5, and 6 exactly once?
Of the 12 members of a certain club, one is to be selected to serve as president, and another is to be selected to serve as secretary. How many different choices of president and secretary can be selected from the 12 members of the club?
Six students are competing in a contest that will result in a list of three winners:one first-place winner, one second-place winner, and one third-place winner. How many different lists of three winners are possible?
On a certain farm, the same set of 5 different chores is to be completed each day, but the order in which the chores are completed changes from day to day.The integer x represents the greatest possible number of consecutive days that can occur before an ordering of the chores must be repeated.

Quantity A

x

Quantity B

100

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