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题目内容
If $$x=k^2n^3p$$ and $$y=k^3np^2$$, where $$k$$, $$n$$, and $$p$$ are different prime numbers, which of the following is the least common multiple of $$x$$ and $$y$$?
A bank offers two types of reward programs for its credit card customers, where a certain percent of the amount of each purchase made using the credit card is paid back to the customer. The first program has no annual fee and pays back 1 percent of the amount of each purchase. The second program has an annual fee of $200 and pays back 1.6 percent of the amount of each travel purchase and 1.1 percent of the amount of each of the other purchases. A customer's annual reward is equal to the total amount paid back to thecustomer annually minus the annual fee. If the amount of all purchases made by a customer using the credit card during a year is $50,000, what is the amount of travel purchases for which the customer's annual reward under the first program will be equal to the customer' s annual reward under the second program?
Each of two pumps delivers water into a tank at a constant rate of 30 liters per minute, and a third pump removes water from the tank at a constant rate of 15 liters per minute. If the three pumps start working simultaneously when the tank is filled to half of its capacity and continue working until the tank is full, it will take 12 minutes to fill the tank. What is the capacity, in liters, of the tank?
Triangle T is a right isosceles triangle. If the length of at least one side of triangle T is $$6\sqrt{2}$$, which of the following values could be the area of triangle T?

Indicate all such values.
n > 1

When the integer n is divided by 6, the remainder is 1, and when n is divided by 8, the remainder is also 1.

Quantity A

The least possible value of n

Quantity B

49


The table shows the frequency distribution of the values in a list, where n is a positive integer such that n ≤ 100.

Quantity A

The average (arithmetic mean) of the values in the list

Quantity B

3.45


Which of the following is closest to the ratio of the expenditures for household operation services to the expenditures for nondurable goods?
If the results of this survey accurately reflect the distribution of car ownership in a population of 1.2 million families, approximately how many of the families would most likely have exactly 3 motor vehicles?

Quantity A

$$x$$

Quantity B

$$y$$
At the end of 1989, 10 million employees in the United States had their paychecks deposited electronically in their bank accounts. By the end of 1996, that number had increased to 50 million. If during the last year of the period from the end of 1989 through the end of 1996, the number of employees who had their paychecks deposited electronically increased by 10 million, what was the average (arithmetic mean) increase per year for the first 6 years in the period?
For all values of $$a$$ and $$b$$, $$(a+b)^3 =a^3+3a^2b+3ab^2+b^3$$.

Quantity A

$$(c-d)^3+3(c-d)^2d+3(c-d)d^2+d^3$$

Quantity B

$$c^3$$
What is the greatest possible area of a rectangular region whose perimeter is 60?
Examinees who received a score of 6 or more passed the test. Which of the following is closest to the average (arithmetic mean) score of the examinees who passed the test?
What was the median score?
Which of the following is closest to the percent of the examinees who received scores that were within 1.0 standard deviation of the mean?

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