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$$j$$ and $$k$$ are integers such that $$51 \leq j \lt k \leq 99$$.

Quantity A

The number of combinations of $$100$$ objects taken $$j$$ at a time

Quantity B

The number of combinations of $$100$$ objects taken $$k$$ at a time




A town library held a reading drive, in which 20 elementary school students were asked to record the number of books they read over the summer. Only whole numbers of books were recorded. The table above shows the results of the reading drive. The average (arithmetic mean) number of books read by the students was 2 books per student.

Which of the following statements individually provide(s) sufficient additional information to conclude that only one student read only 5 books?

Indicate all such statements.
If one item is to be randomly selected from the items whose manufacturing cost is greater than $140, what is the probability that the item selected will be one whose manufacturing time is greater than 60 minutes?
For each item, a manager calculates the ratio of the manufacturing cost to the manufacturing time. Which of the following is closest to the value of the greatest of these eleven ratios, in dollars per minute?
The manufacturing cost of the item that takes the most time to manufacture is approximately what percent greater than the cost of the item that takes the least time to manufacture?
The standard deviation of n numbers $$x_{1}$$, $$x_{2}$$, $$x_{3}$$,......, $$x_{n}$$, with mean $$\overline{x}$$ is equal to $$\sqrt{\frac{s}{n}}$$, where S is the sum of the squared differences $$(x_{i} - \overline{x})^{2}$$ for 1 ≤ i ≤ n.

List K consists of 5 different numbers. List L consists of 5 numbers and is formed by multiplying each number in K by 2. The standard deviation of the numbers in K is x and the standard deviation of the numbers in L is 2y.

Quantity A

x

Quantity B

y


How many different combinations of 5 cards can be chosen from a pack of 52 cards?
List A consists of 25 positive integers $$a_1$$, $$a_2$$, $$a_3$$,...,$$a_{25}$$ that are ordered from least to greatest. The median and the mode of the integers in A are both equal to 10. List B consists of 25 positive integers $$b_1$$, $$b_2$$, $$b_3$$,...,$$b_{25}$$ that are ordered from least to greatest. The median and the mode of the integers in B are both equal to 15. List C consists of the 25 sums $$a_i$$ +$$b_i$$, for all integers $$i$$ such that 1 ≤ $$i$$ ≤ 25. The mode of the integers in C is $$m$$.

Quantity A

The median of the integers in C

Quantity B

$$m$$


$$n$$ is a positive integer.

Quantity A

The remainder when $$3^{4n+2}+5$$ is divided by 10

Quantity B

4


Which of the following is equivalent to $$36^{-1}$$?
A lecture hall has 15 rows of seats. There are $$n-2$$ seats in the first row and $$n$$ seats in each of the other rows. If there are no other seats in the lecture hall and the total number of seats in the lecture hall is between 180 and 200, what is the total number of seats in the lecture hall?
A large pump and a small pump are available to fill a public fountain with 7,500 gallons of water. The pumps can be used alone or simultaneously. Working alone at their respective constant rates, the small pump would take 1.6 times as long as the large pump to fill the fountain. Working simultaneously at their respective constant rates, the two pumps would take 3 hours to fill the fountain. How long would the small pump take to fill the fountain, working alone at its constant rate?
A caterer has 20 liters of fruit punch that is 12 percent grape juice, by volume. How many liters of fruit punch that is 20 percent grape juice, by volume, must be added to the original 20 liters of fruit punch in order to create fruit punch that is 15 percent grape juice, by volume?

Quantity A

The expected value of X

Quantity B

The expected value of Y


Quantity A

$$x+y+z+u+v+w$$

Quantity B

$$360$$


A right circular cylindrical tank sitting on its base has a height of 6 feet and a volume of 54π cubic feet. What is the circumference, in feet, of the tank's base?


In the xy-plane shown, the x-axis represents an east-west road, the y -axis represents a north-south road, and the origin represents the intersection of the two roads. Point A and point B represent the centers of Town A and Town B, respectively, and the center of Town A is 5 kilometers north of the intersection. If the line through the origin and point B has slope $$\frac{3}{4}$$, which of the following is closest to the distance, in kilometers, between the centers of Town A and Town B?
If $$4y+6 \lt -18$$, which of the following is a possible value of $$y$$?
In 2009, the price of a certain stock increased by 25 percent from May 1 to June 1 and decreased by $$n$$ percent from June 1 to July 1. If the price of the stock on July 1 was greater than the price of the stock on May 1, which of the following could be the value of $$n$$?

Indicate all such values.
Four slips of paper are numbered 1, 2, 3, and 4, respectively and put into an empty box. If two of these slips of paper will be drawn out of the box at random and without replacement, what is the probability that the sum of the two numbers written on the slips of paper will be 3?

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