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Michael, Kim, Glenda, and Ian all own DVDs, and no DVD is owned by two or more of them. Michael owns $$\frac{1}{2}$$ of the number of DVDs that Kim owns. Glenda owns $$\frac{1}{3}$$ of the number of DVDs that Ian owns. If Kim and Ian own the same number of DVDs, what is the ratio of the total number of DVDs that Michael and Glenda own to the total number of DVDs that Kim and lan own?

Give your answer as a fraction.
A certain machine that produces copies of pictures has settings of 60 percent, 80 percent, 100 percent, 150 percent, and 200 percent, where each setting indicates the dimensions of the copy as a percent of the corresponding dimensions of the original picture. Which of the following combinations of settings could be used to make a second copy of a first copy of an original picture for which the dimensions of the second copy are 120 percent of the corresponding dimensions of the original picture?

Indicate all such combinations.
The closing price of a stock on a certain day was p dollars. For the next 8 consecutive trading days, the closing price changed as follows. For the 1st, 3rd, 5th, and 7th days, the closing price of the stock was 10 percent less than its closing price on the preceding day. For the 2nd, 4th, 6th, and 8th days, the closing price of the stock was 10 percent greater than its closing price on the preceding day. Which of the following represents the closing price, in dollars, of the stock on the 8th day?
A large pump and a small pump deliver water into a tank at their respective constant rates. Working simultaneously, the two pumps take 6 hours to fill the empty tank. If each pump worked alone, then the amount of time that it takes the large pump to fill the empty tank is $$\frac{2}{3}$$ of the amount of time that it takes the small pump to fill the empty tank. How many hours does it take the large pump, working alone, to fill the empty tank?
$$r=4+\frac{k}{d+500}$$

When a certain lending business loans an amount of $$d$$ dollars for one year, it charges interest equal to $$r$$ percent of the amount of the loan so that the interest rate $$r$$ and the amount $$d$$ are related by the formula shown, where $$k$$ is a constant. When the business loans 1,000 dollars for one year, the interest rate is 4.40 percent. When the business loaned an amount of money to Charles for one year, the interest rate was 4.12 percent. Approximately what was the total amount, including interest, that Charles had to repay the business for the loan?
At the beginning of a certain year, Jane opened a new savings account and a new money market account and deposited a total of $10,000 into the two accounts. The savings account and the money market account earned simple annual interest at the rates of 2 percent and 5 percent, respectively. There were no other transactions in the accounts. If the total amount of interest earned by the two accounts for the first 2 years after they were opened was $475, what was the amount that Jane deposited into the money market account?
Evan, lrene, and Juanita collected glass bottles for recycling. Evan collected twice as many bottles as lrene, and Juanita collected more bottles than the total number of bottles collected by Evan and lrene. lf Juanita collected 60 bottles, which of the following could be the number of bottles Evan collected?

Indicate all such numbers.


The table above shows four categories of methods of transportation to work, including the category None for people who work at home. For each category and for the years 2000 and 2010, the table shows the percent of workers in a certain city who used that method most of the time during the year. Based on the information given, which of the following statements must be true?

Indicate all such statements.
A shipment consists of x packages that weigh 10 pounds each and y packages that weigh 15 pounds each. Which of the following statements individually provide(s) sufficient additional information to determine the average (arithmetic mean) weight of the packages in the shipment?

Indicate all such statements.
Point $$P$$ and $$Q$$ lie on line segment $$AB$$, and P lies between points $$A$$ and $$Q$$. If $$\frac{AQ}{AP}$$=$$\frac{c}{d}$$ and $$\frac{BQ}{BP}$$=$$\frac{d}{c}$$, where $$c$$ and $$d$$ are positive numbers, which of the following is equal to $$\frac{PQ}{AB}$$?

Quantity A

The number of integers n, where 100 < n < 200, that are multiples of both 3 and 5

Quantity B

$$15$$
The price of s scarves is $$d$$ dollars. At this rate, what is the price of $$s+2,600$$ scarves, in dollars?
Which of the following values of $$x$$ is a solution of the equation shown? Indicate all such values.
Of all the applicants for jobs at a certain company last year, $$\frac{1}{3}$$ received a first interview. Of the applicants who received a first interview, $$\frac{1}{4}$$ received a second interview, The applicants who received no interview or only a first interview were not hired. Of the applicants who received a second interview, $$\frac{1}{5}$$ were hired and the rest were not hired. The applicants who received at least one interview and were not hired were what fraction of all the applicants for the jobs?
The pieces of art in a certain collection are classified as either ancient or modern. All pieces in the collection are 3 are on display in one of two wings of a museum, $$C$$ or $$D$$. Of the pieces in the collection on display in $$C$$, $$\frac{1}{3}$$ are ancient pieces, and of the pieces in the collection on display in $$D$$, $$\frac{1}{4}$$ are ancient pieces. The number of modern pieces on display in $$C$$ is equal to the number of modern pieces on display in $$D$$. Of all the ancient pieces in the collection, what fraction are on display in wing $$C$$?
A survey was given to a sample of residents in a certain town to determine the level of interest in creating a new park. Of those residents in the sample, 50 percent responded they were in favor of the park and 30 percent responded they were not in favor of the park. The remaining 20 percent of the sample did not respond to the survey. Which of the following statements individually provide(s) sufficient additional information to determine the number of residents in the sample? Indicate all such statements
The figure shows a normal distribution with mean m and standard deviation d, including approximate percents of the distribution corresponding to the six regions shown.

The discrete random variable V is approximately normally distributed with a mean of 500 and a standard deviation of 100. If 10,200 of the values of V are between 500 and 600, what is the best estimate of the number of values of V that are less than 400?
p is a prime number greater than 3.

Quantity A

The number of positive divisors of $$2p$$

Quantity B

The number of positive divisors of $$p^2$$
$$3^{-1}$$+$$3^{-2}$$+$$3^{-3}$$=
Container $$Q$$ contains exactly $$120$$ balls and container $$R$$ contains exactly $$6$$ balls. The balls in container $$Q$$ are numbered from $$1$$ to $$120$$, respectively, and the balls in container $$R$$ are numbered from $$1$$ to $$6$$, respectively. A ball is to be chosen at random from each of containers $$Q$$ and $$R$$.

Quantity A

The probability that the number of the ball chosen from container $$Q$$ will be divisible by $$2$$ or $$3$$

Quantity B

The probability that the number of the ball chosen from container $$R$$ will be divisible by $$2$$ or $$3$$

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