Three stoplights on different streets each operate on their own independent schedules, as follows: the first stoplight is red 1 minute out of every 2 minutes (1 minute red, then 1 minute green), the second is red 2 minutes out of every 3 minutes (2 minutes red, then 1 minute green) and the third is red 3 minutes out of every 5 minutes (3 minutes red, then 2 minutes green.) At 9:00 am each stoplight turns red. The lights are either red or green (don’t worry about yellow). What time is it when the next 1-minute segment of time in which all three stoplights are red begins? 

A cylinder and a rectangular prism have the same volume. If the length, width and height of the rectangular prism are doubled and the radius of the cylinder is doubled, what is the ratio of the volume of the new cylinder to the volume of the new rectangular prism? Express your answer as a common fraction.

Five wooden disks are numbered -3, -2, 1, 4 and 7. If two disks are chosen at random, without replacement, what is the probability that their product is negative? Express your answer as a common fraction.

The sum of three different two-digit prime numbers is 79. The largest of the numbers is 43. The difference of the other two is 10. What is the product of the three numbers?

  What is the minimum number of 3-inch by 5-inch index cards needed to completely cover a 3-foot by 4-foot rectangular desktop without cutting the index cards?

Mary leaves New York City at 9:00 am, traveling to Charlotte, NC, at an average rate of 55 miles per hour. Simba leaves one hour later than Mary and follows Mary’s route at an average rate of 65 miles per hour. At what time will Simba catch up to Mary?

  AutoMakers, Inc. is a car manufacturer and currently has three operational plants cleverly named Plant A, Plant B and Plant C. Plant A can produce 100 cars a day. Plant B can produce 80 cars a day. Plant C can produce only 70 cars a day. If all three plants are running at full production capacity, how many full days are needed to produce 1600 cars?

Suppose there are 50 policies that generate the following five claims in 2009:

$7500

$5000

$3000

$11,500

$8000 

1) What is the frequency? Express your answer as a decimal to the nearest hundredth. 

2) What is the severity of the five claims?

3) How much premium should be charged if 15% of the charged premium is to be used for expenses and 5% of the charged premium is for profit?

A certain disease is expected to infect 1 out of every 10,000 individuals in a country. A test for the disease is 99.5% accurate. It never gives a false indication when it is negative, so 0.5% of the people who take the test will get inaccurate readings, all of which will be false positives (meaning that the people test positive but do not have the disease). Let us suppose you test positive; what is the probability that you actually have the disease? Express your answer as a percent to the nearest whole number.

  Sneaky Joe has a loaded die with the numbers 1, 2 and 3 each having a probability of 1/4 of being rolled and the numbers 4, 5 and 6 each having a probability of 1/12 of being rolled. No one but Joe knows about the loaded die. Sneaky Joe offers to take the following bet with you: You roll the die. If the result is an even number, you win $x; if it’s an odd number, you lose and pay Joe $5. How much should Sneaky Joe pay you for a win to make this a fair bet? 

  An insurance company has sold 10,000 policies. The policyholders are classified using gender (Male or Female) and age (Young or Old). Of these policyholders, 3000 are Old, 4000 are Young Males and 4000 are Female. How many of the company’s policyholders are Old Females?

  The probability that a particular state will have neither a hailstorm nor a tornado in a given month is 55%. In the same period, the probability of a hailstorm is 35% and the probability of a tornado is 25%. If the probability of a hailstorm and the probablity of a tornado are independent but not mutually exclusive, what is the probability of both a hailstorm and a tornado occurring in a given month? Express your answer as a decimal to the nearest hundredth.

Torque is a measure of “rotational force,” and it is equal to force times distance. A motor at the end of an 8-inch robot arm is lifting a 3-pound weight. How much torque is the motor generating? Note: Torque is measured in foot-pounds.

A robot has a battery life of 3 hours while carrying 0 pounds. The robot’s maximum velocity is 20 feet per minute. For every pound that the robot needs to carry, the total amount of battery time the robot will operate while traveling at maximum velocity decreases by 8 minutes. Starting with a fully charged battery, how many feet can the robot travel at maximum velocity while carrying 10 pounds?

In 2003, NASA launched the rover Spirit onto the surface of Mars to explore our planetary neighbor. Near the end of January 2010, Mars was 99.33 million km away from Earth. Assume the speed of communication is at the speed of light, which is 300,000,000 m/s. If a researcher on Earth requested information from Spirit about its temperature, how long did the researcher have to wait for a reply after sending the request? Express your answer in the form x minutes y seconds, where x and y are whole numbers.

Obstacles such as fallen trees, fences and ditches can be difficult for wheeled robotic vehicles to overcome. Imagine that a specially equipped robot could jump over such things. At the peak of the jump, the robot’s vertical velocity is 0 m/s. Standard gravity on Earth, g, is 9.8 m/s2. If the time it takes to fall from the peak is 1.7 s, how high did the robot jump? Height is equal to ½(g)(t)2, where g = gravity and t = time to fall to the ground, in seconds. Express your answer as a decimal to the nearest hundredth.

We can increase the frame rate if we decrease the size of the picture. If we wanted to send back square frames at a rate of 30 frames/second, how many pixels wide would a square frame (same size high as wide) be? Express your answer as a decimal to the nearest tenth. 

A communication network can carry 128,000,000 bits per second. A digital video camera on the network makes pictures that are 640 pixels wide by 480 pixels high. Each pixel is composed of 3 bytes. A byte is 8 bits. A picture is called a “frame.” How many frames per second from the camera can this network carry? Express your answer to the nearest whole number.

How far away can location X be if we want the UAV to arrive back home with a fuel reserve of 0.5 hour?

An unmanned aerial vehicle (UAV) carries 45 gallons of fuel. It burns fuel at a rate of 3 gph (gallons/hour) and flies at a speed of 160 mph (miles/hour). We want to fly it to a location X, fly it in the area for 1 hour, and then fly it back to its launching point. What is the greatest number of miles away from the UAV’s launching point can location X be?