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Of the paperbacks in a private library, 5 percent are biographies. If 3 percent of all the books in the library are paperbacks that are biographies, what percecnt of all the books in the library are paperbacks?
If S is the set of positive integers that are multiples of 6, and T is the set of positive integers that are multiples of 8, how many integers between 1 and 100 are in both sets S and T?
Looking back on a project that they had approached with both great________ and considerable aspirations, they were amused to recognize that neither the fears nor the hopes had been at all realistic.
The passage suggests that Taruskin would probably agree with which of the following criticisms regarding the partisans of the early music movement?
x and y are different positive integers

$$x^{2}y$$=180

Quantity A

x

Quantity B

y


A box contains small toys, and each toy is worth either $3 or $6. If a toy is selected at random from the box, the probability that the selected toy will be worth $6 is 0.25. Which of the following could be the total value of all the toys in the box?

Indicate all such values.
A total of $96,000 was invested for one month in a new money market account that paid simple annual interest at the rate of $$r$$ percent. If the investment earned $960 in interest for the month, what is the value of $$r$$?
A pound of tea makes 210 cups of tea, and a pound of coffee makes 40 cups of coffee. If, on the average, a restaurant serves 12 times as many cups of coffee as tea, what is the ratio of pounds of tea to pounds of coffee used at the restaurant?

Quantity A

The ones digit of $$208^{208}$$

Quantity B

7


In the xy-plane , the graph of the function $$y=x^{3} (x^{2}-3)(x+3)$$ intersects the x-axis at k different points.

Quantity A

k

Quantity B

3


If a > 1, which of the following could be the value of $$(1+\frac{1}{a})^{-1}$$?

Indicate all such values.
$$0 < a < b < c$$

Quantity A

The standard deviation of the seven numbers $$-c, -b, -a, 0, a, b, c$$

Quantity B

The standard deviation of the seven numbers $$-c^{2}, -b^{2}, -a^{2}, 0, a^{2}, b^{2}, c^{2}$$




Quantity A

The standard deviation of data set Ⅰ

Quantity B

The standard deviation of data set Ⅱ


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?

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