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题目内容
The width and the length of a rectangular piece of plywood are 4 feet and 8 feet, respectively. Along one edge of the plywood, a strip $$x$$ inches wide and 8 feet long is removed. Then, along an edge perpendicular to the 8-foot edge, a strip $$x$$ inches wide is removed. For what value of $$x$$ will the remaining rectangular piece have width and length in the ratio of 2 to 5? (1 foot = 12 inches)
Working simultaneously at their respective constant rates, pump $$P$$ and pump $$S$$ together pumped out $$\frac{2}{3}$$ of the water in a full tank in 1 hour 20 minutes. Pump $$P$$ then stopped working, and pump $$S$$, working alone at its constant rate, pumped out the rest of the water in the tank in 50 minutes. How many hours would it have taken pump $$P$$, working alone at its constant rate, to pump out all the water in the full tank?
A furniture store purchased sofas for a wholesale price of $400 each and sold most of them for a retail price of $560 each. In a summer sale, the retail price of the last few sofas was reduced by $$x$$ dollars, and they were sold at this reduced price. The store's profit from selling the last sofa was more than 15 percent of its wholesale price. Which of the following could be the value of $$ x$$ ?

Indicate all such values.
If $$0 \lt |x|-2x \lt 3$$, which of the following is true?
If $$r$$ and $$s$$ are integers such that $$2 \leq r \lt s \leq 7$$，what is the greatest possible value of $$\frac{r+s}{rs}$$？
$325, $418, $722, $818, $955, $1,092

The six amounts listed are the reported commissions eamed by 6 salespeople during April. Two of the reported amounts are in error; one is $120 greater than the actual amount and one is $120 less.

Quantity A

The standard deviation of the six reported commissions

Quantity B

The standard deviation of the six actual commissions
Theo owns $$\frac{1}{3}$$ of the number of pairs of shoes that Samantha owns, and Richard owns twice as many pairs as Samantha. If Richard owns fewer than 30 pairs of shoes, which of the following could be the number of pairs he owns?

Indicate all such numbers.
If the surface area of a cube is 96, what is its volume?
In a poll, 50 percent of those polled said they would vote for Candidate M, and 80 percent said they were in favor of proposition 3.

Quantity A

The percent of those polled who said they would not vote for Candidate M and were not in favor of proposition 3

Quantity B

$$25%$$
A list of data values was divided into three smaller lists, where list A contains one-half of the data values, list B contains one-fifth of the data values, and list C contains the rest. The average (arithmetic mean) of the data values in list A is 12, the average of the data values in list B is 15, and the average of the data values in list $$C$$ is 6. What is the average of all of the data values in the original list?
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.
$$n$$ is a positive integer and $$k=10,000n$$.

Quantity A

The sum of the digits of $$n$$

Quantity B

The sum of the digits of $$k$$
The pieces of art in a certain collection are classified as either ancient or modern. All pieces in the collection 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?
Nancy has a job where she is paid at a regular hourly rate for the first 40 hours that she works each week. For each hour that Nancy works each week in excess of the first 40 hours, she is paid 1.5 times her regular hourly rate. Nancy worked 35 hours during the first week of last month and 50 hours during the second week of last month. If Nancy was paid $270.00 more during the second week than during the first week, what is her regular hourly rate?
When asked what their major staffing issues were, 42 percent of the companies in a survey said "finding competent staff" and 18 percent of the companies in the survey said “training staff." If 15 percent of the companies in the survey said that both of the issues were major staffing issues, what percent of the companies in the survey said that neither of the two issues was a major staffing issue?
If $$x$$, $$y$$, and z are integers greater than $$1$$ and $$xyz=231$$, what is the value of $$x+y+z$$?
A student is to be selected at random from a certain class. The probability that the student will be a female is $$p$$, the probability that the student will be under the age of $$19$$ is $$r$$, and the probability that the student will be a female and under the age of $$19$$ is $$0.3$$. Which of the following could be the values of $$p$$ and $$r$$? Indicate all such values.
The number of feet in the perimeter of a rectangular game board is equal to the number of square feet in the area of the game board.

Quantity A

The width of the game board

Quantity B

2 feet
In Vermont the number of acres of forest area in 1992 was $$76.5$$ percent of the total number of acres of land area. Which of the following is closest to the number of millions of acres of land area in Vermont?

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