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题目内容
0 < a < b < c < d < e

List X: a, b, c, d, e

List Y: -2a, -2b, -2c, -2d, -2e

Quantity A

The standard deviation of the numbers in list X

Quantity B

The standard deviation of the numbers in list Y
$$B_n=\frac{n}{n+1}$$ for all integers $$n$$ > 1.

$$C_n=B_n + B_{n-1}$$ for all integers $$n$$ > 2.

The integer $$k$$ is greater than 2.

Quantity A

$$C_k$$

Quantity B

$$\frac{2k^2-1}{k+k}$$
Working continuously for a total of 120 hours, a machine first assembled $$x$$ units of product A and then assembled $$y$$ units of product B. where $$x$$ and $$y$$ are positive integers. It took the machine 3 hours to assemble each unit of product A and 5 hours to assemble each unit of product B. Which of the following could be the total number of units of product A and product B that the machine assembled in the 120 hours?

Indicate all such numbers.

Quantity A

The number of integers between 10,000 and 25,000 that are multiples of 14

Quantity B

The number of integers between 10,000 and 26,000 that are multiples of 15
In a probability experiment, R and S are independent events such that 0 < P(R) < $$\frac{1}{2}$$ and 0 < P(S) < 1.

Quantity A

The probability that S will occur given that R has occurred

Quantity B

P(R)
Of the 60 people in a room, $$\frac{2}{3}$$ are women and $$\frac{2}{5}$$ are vegetarian. What is the greatest possible number of people in the room who are women that are not vegetarian?
If the perimeter of an isosceles right triangle is ($$1+\sqrt{2}$$), what is the area of the triangular region?
The least and greatest values in data set $$X$$ are $$j$$ and $$k$$. respectively, and the least and greatest values in data set $$Y$$ are $$p$$ and $$r$$, respectively, where $$j < k < p < r$$. The least value in data set $$Z$$ is the average (arithmetic mean) of $$j$$ and $$k$$, and the greatest value in data set $$Z$$ is the average of $$p$$ and $$r$$.

Quantity A

The average of the range of the values in data set $$X$$ and the range of the values in data set $$Y$$

Quantity B

The range of the values in data set $$Z$$
$$\frac{2}{\sqrt{3}+\sqrt{1}}$$, $$\frac{2}{\sqrt{5}+\sqrt{3}}$$, $$\frac{2}{\sqrt{7}+\sqrt{5}}$$, .............., $$\frac{2}{\sqrt{121}+\sqrt{119}}$$

Consider the sequence above, where the $$k^{th}$$ term is equal to $$\frac{2}{\sqrt{2k+1}+\sqrt{2k-1}}$$ for each integer $$k$$ from 1 to 60. What is the sum of the 60 terms of the sequence?
$$x$$ and $$y$$ are positive integers.

$$xy$$ is divisible by $$24$$.

$$\frac{x}{2}$$ is an odd integer.

Quantity A

The remainder when $$y$$ is divided by $$4$$

Quantity B

$$1$$
A gardener is planning a vegetable garden that will be enclosed by a fence.The garden will be rectangular with an area of 24 square meters, and each side of the garden will be a whole number of meters in length. Fence posts will be placed so that there is a post at each corner, the centers of the posts are along the perimeter of the garden, and the distance between the centers of adjacent posts is 1 meter. Which of the following CANNOT be the total number of fence posts in the plan?
How many integers between 360 and 630 are there such that they have odd number of divisors?

Quantity A

The remainder when $$35^{12}+63^{17}$$ is divided by 14

Quantity B

3
What is the remainder when $$8^{43}$$ is divided by $$7$$?
If wooden logs are stacked in layers so that the bottom layer has n logs, the top layer has 1 log, and each layer except for the bottom layer has 1 log less than the layer immediately below it, then the total number of logs in the stack is equal to $$\frac{n(n+1)}{2}$$. If 62 logs are to be stacked in this manner, perhaps with some logs left over, what is the least number of logs that could be left over?
List $$S$$ consists of $$n$$ different positive values, where $$n$$ is greater than 1. List T consists of the squares of the $$n$$ values in $$S$$.

Quantity A

The square of the range of the values in $$S$$

Quantity B

The range of the values in $$T$$


A data set consists of 200 values, all of which are integers. The data set is summarized by the boxplot shown. Based on the boxplot, which of the following statements must be true?
Sets R, S, and T are nonempty, and each has the same number of elements. The sets R∩S, R∩T, and S∩T are nonempty, and each has the same number of elements. The set R∩S∩T is empty. Set V consists of all the elements in R that are not in S.

Quantity A

3 times the number of elements in V

Quantity B

The number of elements in the set R∪S∪T

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