Problem Solving

If m and p are positive integers and m 2 + p 2 < 100 , what is the greatest possible value of mp ?

How many of the integers that satisfy the inequality (x + 2) (x + 3) (x − 2) ≥ 0 are less than 5?

The light in a restroom operates with a 15-minute timer that is reset every time the door opens as a person goes in or out of the room. Thus, after someone enters or exits the room, the light remains on for only 15 minutes unless the door opens again and reset the timer for another 15 minutes. If the times listed above are the times at which the door opened from 8:00 to 10:00, approximately how many minutes during this two-hour period was the light off ?

The interior of a rectangular carton is designed by a certain manufacturer to have a volume of x cubic feet and a ratio of length to width to height of 3:2:2. In terms of x, which of the following equals the height of the carton, in feet?

What number is 108 more than two-thirds of itself?

The price of gasoline at a service station increased from $1.65pergallonlastweekto$1.82 per gallon this week. Sally paid $26.40 for gasoline last week at the station. How much more will Sally pay this week at the station for the same amount of gasoline?

The average distance between the Sun and a certain planet is approximately 2.3 x 10^14 inches. Which of the following is closest to the average distance between the Sun and the planet, in kilometers?

In quadrilateral ABCD above, what is the length of AB ?

Tanks A and B are each in the shape of a right circular cylinder. The interior of Tank A has a height of 10 meters and a circumference of 8 meters, and the interior of tank B has a height of 8 meters and a circumference of 10 meters. The capacity of tank A is what percent of the capacity of tank B?

If 1 x − 1 x + 1 = 1 x + 4 , then x could be

If a sphere with radius r is inscribed in a cube with edges of length e, which of the following expresses the relationship between r and e ?

The figure above shows a path around a triangular piece of land. Mary walked the distance of 8 miles from P to Q and then walked the distance of 6 miles from Q to R. If Ted walked directly from P to R, by what percent did the distance that Mary walked exceed the distance that Ted walked?

Which of the following is closest to √ 4.2 (1 , 590) 15.7 − − − − √ ?

In a certain high school, 80 percent of the seniors are taking calculus, and 60 percent of the seniors who are taking calculus are also taking physics. If 10 percent of the seniors are taking neither calculus nor physics, what percent of the seniors are taking physics?

Mark and Ann together were allocated n boxes of cookies to sell for a club project. Mark sold 10 boxes less than n and Ann sold 2 boxes less than n. If Mark and Ann have each sold at least one box of cookies, but together they have sold less than n boxes, what is the value of n?

During a recent storm, 9 neighborhoods experienced power failures of durations 34, 29, 27, 46, 18, 25, 12, 35, and 16 minutes, respectively. For these 9 neighborhoods, what was the median duration, in minutes, of the power failures?

A service provider charges c dollars for the first 50 hours of service used per month and 40 cents for each 30 minutes in excess of 50 hours used during the month. If x is an integer greater than 50, which of the following expressions gives this service provider's charge, in dollars, for a month in which x hours of service were used?

Based on the rates above, how much would Company X charge a customer with a low-use contract for using 95 message units in a month?

A ladder of a fire truck is elevated to an angle of 60° and extended to a length of 70 feet. If the base of the ladder is 7 feet above the ground, how many feet above the ground does the ladder reach?

The graph above shows the height of the tide, in feet, above or below a baseline. Which of the following is closest to the difference, in feet, between the heights of the highest and lowest tides on July 13 at Bay Cove?