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题目列表

题目内容
A large cube consists of 216 small identical cubes. What is the number of small cubes that do not have a face that is part of a face of the large cube?
Angle A measures r degrees. The complement of angle A measures 90-r degrees, and the supplement of angle A measures 180-r degrees. If the measure of angle A is greater than the measure of its complement and less than one-half the measure of its supplement, which of the following gives all possible values of r?

x=y

BD∥AE

Quantity A

The area of △ACE

Quantity B

The area of △BDF

The figure shown consists of a rectangle with length 14 and width 6, together with three isosceles right triangles. What is the area of the entire figure?
Passwords for a certain computer consist of 5 symbols typed on a computer keyboard. Each password consists of one @ symbol, two # symbols, and two $ symbols, typed in any order. For example, @#$$# and $#$#@ are two different passwords for the computer. What is the total number of different passwords for the computer?
A certain factory has 8 identical machines that process a certain chemical product at the same constant rate. If it takes 40 hours for 5 of the machines, working simultaneously at their constant rate, to process a totaI of one ton of the product, how many hours does it take the 8 machines, working simultaneously at their constant rate, to process a total of one ton of the product?

_____hours
In the xy-plane, points (-4, 0) and point (4, 0) lie on a circle C.

Quantity A

The radius of circle C

Quantity B

4
Which of the following values of x satisfies the equation $$\frac{x}{2}=n!$$ for some positive integer n?

The figure above shows a rectangle and five circles. Each circle is tangent to the other circles and to the sides of the rectangle that it touches. If the diameter of each circle is 4, what is the area of the rectangle?


The boxplot above summarizes a list of 240 numbers. Which of the following statements must be true?

Indicate all such expressions.
In each round of a certain game, either 1, 3, 7, or 10 points are awarded to the winner of the round. Which of the following CANNOT be the total number of points awarded to the winner of three rounds?
For each value $$x$$ in a list of values with mean $$m$$, the absolute deviation of x from the mean is defined as $$|x-m|$$.

A certain online course is offered once a month at a university. The number of people who register for the course each month is at least 5 and at most 30. For the past 6 months, the mean number of people who registered for the course per month was 20. For the numbers of people who registered for the course monthly for the past 6 months, which of the following values could be the sum of the absolute deviations from the mean?

Indicate all such values.
Let $$\frac{1}{3}$$+$$\frac{1}{5}$$+$$\frac{1}{7}$$+$$\frac{1}{9}$$+$$\frac{1}{11}$$=$$\frac{m}{(3)(5)(7)(9)(11)}$$, where m is a positive integer. What is the remainder when m is divided by 5?
If $$y=1-\frac{1}{x}$$, where $$x$$ is a nonzero integer, which of the following could be the value of $$y$$?

Indicate all such values.
The reciprocal of n equals 8 times the square of n.

Quantity A

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

Quantity B

2
If k and n are each positive integers between 12 and 30, then $$\frac{5+k}{7+n}$$will be equal to $$\frac{5}{7}$$for how many pairs of (k, n)?
In a certain election, $$\frac{3}{5}$$ of the voters in District K and $$\frac{1}{2}$$ of the voters in District P voted for the candidate Miguel Garcia. If 4 times as many people voted in District K as voted in District P, what percent of the voters in both districts combined voted for Miguel Garcia?
The population of City X in 1999 was r percent greater than it was in 1990, and the average income per person in 1999 was i percent greater than it was in 1990. The percent increase in the total income of the entire population from 1990 to 1999 would have been greatest for which of the following values of r and i?
By draining 40 gallons of water from a tank, the amount of water in the tank was decreased from $$\frac{1}{5}$$ of the tank 's full capacity to $$\frac{2}{11}$$ of the tanks full capacity. Water was then added to the tank until the tank was full. How many gallons of water were added to the tank?
A certain charity is conducting a fund-raiser. For the first $9,000 raised by the charity, Company B will contribute $1 for every $3 collected by the charity. For any amount over $9,000 raised by the charity, Company B will contribute $2 for every $5 collected by the charity. How much money must the charity raise in order to reach a total of $68,000, including the contribution from Company B?

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