Three robots, Q, R, and L, which eject water independently and simultaneously, each at a characteristic, constant rate, can fill a pool in 10 minutes. How long does it take Robot Q, working alone at its constant rate, to fill that pool with water?

1. Machines R and L can fill the pool in 20 minutes.
2. Machines Q and L can fill the pool in 15 minutes.

The average (arithmetic mean) of the ages of three people, expressed as integers, is 60. What is the median age?

1. One of the ages is 55.
2. One of the ages is 60.

For any integers n and m, $\ddot{m}\left(n,m\right)$ and $\dot{m}\left(n,m\right)$ denote the minimum and the maximum of n and m, respectively. For example, $\ddot{m}\left(4,3\right)=3$ and $\dot{m}\left(4,3\right)=4$. For the integer m, what is the value of $\ddot{m}\left(100,m\right)$?

1. $m=\dot{m}\left(100,n\right)$ for some integer n.
2. $m=\dot{m}\left(100,m\right)$

Is n an integer?

1. $3n^2$ is an integer.
2. $\frac{\sqrt{n}}{3}$ is an integer.

To attend a conference, each attendee reserved a hotel room for either one night or two nights. How many of the attendees reserved a hotel room for two nights?

(1) 80 percent of the attendees reserved a hotel room for two nights.

(2) The attendees reserved a total of 153 nights at the hotel.

If m is an integer, is $m-\mathrm{<font\; color="\#FE8080">1</font>}$ even?

1. $m+3$ is an even integer.
2. $m-2$ is an odd integer.

Pat bought a new car for P dollars and sold it later for M dollars. The difference between the two sale prices was what percent of the initial price?

1. $M-P=10,000$
2. $\frac{P}{M}=\frac{3}{2}$

While on a straight road, Car C and Car D are traveling at different constant rates. If Car C is now 10 miles behind Car D, how many minutes from now will Car C be 20 miles behind Car D?

1. Car C is traveling at 30 miles per hour and Car D is traveling at 40 miles per hour.
2. Thirty minutes ago, Car C was 5 miles behind Car D.

The official height of a skyscraper is equal to the elevation of the roof plus the height of the spire atop the roof. The height of the spire on a certain skyscraper is what percent of the official height of the skyscraper?

(1) The height of the skyscraper's spire is 25 percent of the elevation of the roof.

(2) The official height of the skyscraper is 1,000 meters.

If Susan's team had 10 more people on it, it would have twice as many people as Phillip's team. Are there fewer people on Susan's team than on Phillip's?

1. Phillip's team has more than 5 people on it.
2. Susan's team has fewer than 10 people on it.

If  is an integer, is ?

A fishing boat receives $1.50 for each tuna it brings back to port and $1.80 for each mackerel. How many mackerels did it bring back to port yesterday?

1. Yesterday the number of tuna that the boat brought back was 5 less than twice the number of mackerel brought back.
2. Yesterday the boat received a total of $2,960 from tuna and mackerel brought back.

On a recent trip, Pat rode her bike 10 miles. What was Pat's average speed, in miles per hour, during the trip?

(1) Pat rode her bike 6 miles at an average speed of 12 miles per hour and then rode the remaining 4 miles at an average speed of 10 miles per hour.

(2) Pat rode her bike a total of 0.9 hour.

Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 10, 0.23, and 8.107 are three terminating decimals. If n and m are positive integers and the ratio $\frac{n}{m}$ is expressed as a decimal, is $\frac{n}{m}$ a terminating decimal?

1. n is a three-digit number divisible by 10.
2. $m=5$

If a company sold 20,000 units, and if the cost of the units was $100,000 plus 5 percent of the revenue obtained from sale of the units, did the company make a profit on the sale of the units?

1. The company's total revenue was greater than $112,000.
2. The revenue obtained from the sale of each unit was $6.

A total of $10,000 was invested for one year. Part of this amount earned simple annual interest at the rate of x percent per year, and the rest earned simple annual interest at the rate of y percent per year. If the total interest earned by the $10,000 for that year was $285, what is the value of x?

1. $x=\frac{12y}{11}$
2. The ratio of the amount of interest earned at the rate of x percent per year to the amount of interest earned at the rate of y percent per year was 8 to 11.

Each of the letters in the table above represents one of the numbers 3, 5, or 11, and each of these numbers occurs no more than once within any row or column, with the exception of 5, which may occur up to two times. What is the value of $d_2$?

1. $a_{\mathrm{<font\; color="\#FE8080">1</font>}}{c}_2=121$
2. $c_{\mathrm{<font\; color="\#FE8080">1</font>}}{d}_{\mathrm{<font\; color="\#FE8080">1</font>}}{a}_{2}e=375$

Angela and Maria each earn a different regular monthly salary. Each of them has a different percentage of that salary withheld every month by her employer. Is Angela's monthly salary after withholding greater than Maria's?

1. Angela's monthly salary after withholding is 20 percent less than her regular salary; Maria's monthly salary after withholding is 25 percent less than her regular salary.
2. Angela's monthly salary after withholding is $1000 less than her regular salary; Maria's monthly salary after withholding is $1200 less than her regular salary.

In a class of 200 students, 30 percent are enrolled in a finance course, and 40 percent are enrolled in an investments course. What percentage of the class is enrolled in neither a finance course nor an investments course?

1. 25 percent of the class is enrolled in an investments course but not in a finance course.
2. 15 percent of the class is enrolled in a finance course and also in an investments course.

In △$ABC$, if $AB=a$, $BC=b+\frac{\mathrm{<font\; color="\#FE8080">1</font>}}{2}$ , and $AC=b$, which of the three angles of △$ABC$ has the greatest degree measure?

1. $b=a+\frac{3}{2}$
2. $a=\frac{2}{3}$