During a particular period, water enters a partially filled reservoir at a constant rate through a mountain stream. At the same time, water is pumped out of the reservoir at a constant rate through an outlet pipe. At what rate, in gallons per minute, is the amount of water in the reservoir increasing?

(1) The amount of water initially in the reservoir is 1800 gallons.

(2) Water enters the reservoir at a rate of 8 gallons per minute and is pumped out at a rate of 20 gallons every 3 minutes.

In the figure above, points A, B, C, D, E, and F lie on a line perpendicular to the square's sides. If point A lies on the square, point B lies on the circle, point C bisects AF, point D is the center of the circle, point E bisects DF, and point F lies on the circle and on the square, what is the difference in area between the square and the circle?

1. $AB=6$ and $BC=4$.
2. $AB=6$ and $EF=3.5$.

Pam has unopened packages of corn and of rice, which she has purchased for $17 and $13 per package, respectively. How many packages of corn does she have?

(1) Pam has $282 worth of packages of corn and of rice.

(2) Pam has twice as many packages of corn as she has of rice.

If Chris saved $400 of his earnings last month, how much did Chris earn last month?

(1) Chris spent  of his earnings last month on rent and saved $\frac{}{}$of the remainder.

(2) Last month, Chris paid three times as much in loan payments as he saved. 

l, 17.2, 12.2, 7.2, 22.2 What is the value of l in the list above?

1. $l>7.2$
2. The median of the numbers in the list is 14.7.

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 $m-1$ 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.

What is the value of $m_1+n_2$?

1. $n_1{n}_2+n_1{m}_1+n_2{m}_2+m_1{m}_2=4$
2. $n_1+m_2=1$

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. $m=5$