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Two metal cans are right circular cylinders of different sizes. The interior base of can A has an area of 5π square inches, and the height of the oil in can A is 6 inches. The interior base of can B has an area of 10π square inches, and the height of the oil in can B is 2 inches. Oil is to be moved from can A to can B so that the height of the oil will be the same in both cans. Which of the following is closest to what will be the new height of the oil, in inches?
A certain type of code is a list of 4 identical asterisks and 2 identical dots in any order. For example, **•*•* is one such code.

Quantity A

The number of possible codes of this type

Quantity B

15


$$0 < x^y < 1$$

$$y$$ is an integer

Quantity A

$$y$$

Quantity B

0


Machines A, B, and C produce widgets at their respective constant rates. Machine A produces $$n$$ widgets in $$x$$ hours, machine B produces $$n$$ widgets in $$2x$$ hours, and machine C produces $$n$$ widgets in $$3x$$ hours. In terms of $$x$$, how many hours does it take the three machines, working simultaneously at their respective constant rates to produce $$n$$ widgets?
A bus traveled $$m$$ miles in $$h$$ hours at an average speed of $$r$$ miles per hour. If the number of hours traveled by the bus had been 20 percent greater and the average speed had been 20 percent less, then the distance traveled by the bus would have been what percent less?

_____%
$$P$$ and $$Q$$ are regular polygons with $$n$$ sides and $$n+1$$ sides, respectively.

Quantity A

The median of the $$2n+1$$ measures of the interior angles of $$P$$ and $$Q$$

Quantity B

$$(\frac{n-1}{n+1})180°$$


Pam, Steve,and Adrian each had a party. The number of people at Pam's party was 6 more than the number of people at Steve's party. The number of people at Steve's party was 8 fewer than the number of people at Adrian's party. No one attended more than one of the three parties. If the total number of people at the three parties was 89, what was the number of people at Adrian's party?
A certain triangle has sides of lengths 5, 12, and $$x$$. Which of the following could be the value of x?

Indicate all such values.
At a certain location, the high temperatures for the past seven days, in degrees Fahrenheit, were 76, 66, 61, 54, 59, x, and 70. Which of the following values could be the median of the high temperatures, in degrees Fahrenheit?

Indicate all such values.


Square GBDF is inscribed in the isosceles right triangle ACE.

Quantity A

The area of triangular region ABG

Quantity B

$$\frac{1}{4}$$ of the area of triangular region ACE


The author suggests that according to historical demographers, the birth rate in early-modern German cities
Of the 29 students in a class, 15 students study French, fewer than 16 students study Spanish, and 5 students study neither French nor Spanish. Which of the following could be the number of students in the class who study both French and Spanish?

Indicate all such numbers.
The prizes for a certain contest are in 5 sealed envelopes: 2 containing cash and the other 3 containing gift certificates. If 2 envelopes are to be randomly selected from the 5 envelopes, one at a time without replacement, what is the probability that at least one of the envelopes selected will contain a cash prize?
On a radio call-in show, the 6th caller and every 6th caller thereafter were given a T-shirt. Also, the 15th caller and every 15th caller thereafter were given movie tickets. A total of 78 people called the show, all at different times. How many of the callers were given neither a T-shirt nor movie tickets?

_____callers


Points P, R, and S are on the circle with cener O. The measure of angle ROS is 92°.

Quantity A

x

Quantity B

y


How many distinct solutions does the equation $$|1-|x-215||=1$$ have?
$$\frac{51!-50!}{50!-49!}$$=
Of the people surveyed about the effectiveness of various treatments for insomnia, 65 percent reported that prescription drugs were effective and 48 percent reported that exercise was effective. If 22 percent of those surveyed reported that prescription drugs were effective but did not report that exercise was effective,what percent of those surveyed reported that exercise was effective but did not report that prescription drugs were effective?
Which of the following can be inferred about the "Oldowan artifacts" mentioned in the passage?
The author mentions Kombewa "flake tools" most likely in order to argue that

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