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题目内容
$$7^{n}$$ is a positive integer whose units digit is 9. Which of the following can be the value of n?

Indicate all such numbers.
How many different positive 7-digit integers begin with 555 and end with 22?
x is an integer greater than 1.

$$N=(15)^{x}(4)^{x-1}$$?

Quantity A

The tens digit of N

Quantity B

0
If $$\sqrt{108}$$ =a*$$\sqrt{b}$$, where a and b are positive integers.

Quantity A

The number of the possible values of a+b

Quantity B

3
$$x=(8q)^{n}$$, where q and n are integers greater than 5 and q is odd.

Quantity A

The ratio of the number of odd positive factors of x to the number of even positive factor of x

Quantity B

$$\frac{1}{3n}$$


The boxplot shown summarizes the numbers in a certain list, where all the numbers are positive integers. Based on the boxplot, which of the following statements are true?

Indicate all such statements.
The harmonic mean of two positive numbers is the reciprocal of the average (arithmetic mean) of their reciprocals. The harmonic mean of 10 and 20 is closest to which of the following?
N is a positive 3-digit integer with hundreds digit x and units digit y. Which of the following must be a factor of N–100x–y ?
What is the units digit of ($$4^{32}$$ - $$3^{32}$$)?
As a result of a chemical reaction between compounds A and B. $$\frac{1}{4}$$ of each compound was transformed into an equal amount of the other compound, while the remaining $$\frac{3}{4}$$ of each compound was not transformed. If the amount of B was initially 4 times the amount of A. what was the ratio of the amount of A to the amount of B after the reaction?
If c < b < a < 0, which of the following is equal to |a-b-c|-|b+c|?
All the chairs in a certain cargo have the same weight, and all the tables in the cargo have the same weight. There are 6 times as many chairs as there are tables. The weight of each table is 9 times the weight of each chair. If the total weight of the tables is 1,200 kilograms, then the total combined weight of the chairs and tables is how many kilograms?


Each morning Betty walks from intersection P to intersection R, always walking along streets shown in the figure above and always going east or north. If she varies her walks as much as possible, taking every different path in turn before repeating the sequence of paths, on how many mornings in 48 consecutive mornings will Betty walk through intersection Q?
Pumps A ,B ,and C pump water at their respective constant rates. Working simultaneously, A and B can fill an empty pool in 6 hours. Working simultaneously, B and C can fill the empty pool in 5 hours. Working simultaneously, A and C can fill the empty pool in 4 hours. Working simultaneously, A ,B , and C can fill the empty pool in approximately how many hours?
When a driver got on the expressway, she set the cruise control at 55 miles per hour for the first 2 hours and at 65 miles per hour for the remaining 2.2 hours of the trip. When she returned, she traveled the same distance along the expressway and averaged 50 miles per hour for the return trip. How many more minutes was she on the expressway returning than going?
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 box contains 30 marbles of which 6 are red, 7 are blue, 8 are yellow, and the rest are green. Marbles are selected randomly from the box one at a time without replacement. The selection process stops as soon as 2 marbles of different colors have been selected. What is the greatest number of selections that might be needed in order to stop the process?
If n and 1.25n are positive integers, which of the following could be the units digit of n?

Indicate all such digits.
$$x^{2}-y^{2}$$=25

x-y=5

Quantity A

x+y

Quantity B

5
The standard deviation of n numbers $$x_{1}$$, $$x_{2}$$, $$x_{3}$$,......, $$x_{n}$$, with mean x is equal to $$\sqrt{\frac{s}{n}}$$, where S is the sum of the squared differences, $$(x_{i}- x)^{2}$$ for 1 ≤ i ≤ n.

c,c,c,2c,4c,4c,5c,6c

In the list of 8 numbers shown, c > 0. Which of the following is closest to the standard deviation of the 8 numbers?

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