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题目内容
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 wit 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


In the survey of employees shown, none cited all three reasons for leaving, but 15 percent cited two of the three reasons. What percent of the employees surveyed cited none of the three reasons in the table?


Quantity A

The number of doctors surveyed who said that drug Q was effective and did not say that drug R was effective

Quantity B

210


The interior of the figure shown is divided into two squares and three triangles.

Quantity A

The measure of angle x

Quantity B

56


In quadrilateral ABCD, AB=BC=BD and the measure of angle ABC is 60 degrees What is the measure of angle ADC?


The original two sides and hypotenuse of a triangle are x, y, and z, respectively.

Quantity A

The hypotenuse of the triangle after x and y are turned into x+1 and y+1

Quantity B

z+1


BC=DC

Quantity A

x

Quantity B

y


The relative frequency distributions of the values in data set A and the values in data set B are shown in the two histograms, respectively, where each interval contains values that are greater than or equal to the left endpoint and less than the right endpoint. The number of values in A is $$\frac{1}{2}$$ of the number of values in B. If data set C consists of the values in A and the values in B, which of the following histograms shows the relative frequency distribution of the values in C?

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