Mathematical Reasoning Flashcards

There are just 6 firefighters at a local fire department. They all have quite diverse physical attributes. Lanie is 200 pounds, Fred is 250 pounds, Shawn is 150 pounds, Mike 180 pounds, Ben is 190 pounds, Mike is 140 pounds, and Lanie is 200 pounds. What is the weight of a typical firefighter?

Answer: 185 pounds

To find the average weight, sum all the distinct weights and divide by the number of firefighters. The question states there are 'just 6 firefighters' and lists six distinct weights: 200, 250, 150, 180, 190, and 140 pounds. The sum of these weights is 200 + 250 + 150 + 180 + 190 + 140 = 1110 pounds. Dividing the total weight by 6 firefighters gives an average of 1110 / 6 = 185 pounds.

A smoke-filled room has no obvious entryway. A 5-foot by 6-foot opening in the wall is made by the firefighter using a hatchet. How big is the opening?

Answer: 30 sq. ft.

The opening in the wall is described as a 5-foot by 6-foot rectangle. To find the size (area) of a rectangle, multiply its length by its width. Therefore, 5 feet * 6 feet = 30 square feet. This calculation gives the total area of the opening.

Choose the statement that best explains the link between the length of the hose and the number of firefighters required to carry it using the table below.

Answer: One more worker is required for every 40 feet of hose length that is added.

Without the actual table, we must infer the relationship based on the most plausible option for such a problem. Option A describes a direct, linear relationship where an increase in hose length by a specific increment (40 feet) consistently requires one additional worker. This is a common and logical pattern for resource allocation based on increasing task size, making it the most likely correct explanation of a typical table's data.

12 gallons of fuel were injected into one tank, 17 gallons into the next, and 21 gallons into the final tank by a firefighter. How much gasoline did the firefighters pump—in gallons?

Answer: 50

To find the total amount of gasoline pumped, simply add the quantities injected into each tank. The firefighter injected 12 gallons, 17 gallons, and 21 gallons. Adding these amounts together: 12 + 17 + 21 = 50 gallons. This is a straightforward sum of the given values.

What size ladder is required to reach the top floor of a six-story apartment building if the average height of a story in a residential apartment building is 13 feet?

Answer: 78 ft.

To determine the required ladder size, multiply the number of stories by the average height per story. A six-story building with an average height of 13 feet per story means the total height is 6 * 13 feet = 78 feet. Therefore, a 78-foot ladder is required to reach the top floor.

Candidates taking a physical fitness exam to become a firefighter must be able to carry an oxygen tank and a 150-foot fire hose to the top of a mock-burning structure. Choose the statement from the following table that best explains the connection between the number of floors and the travel time between them.

Answer: The longer the time, the more floors climbed.

Without the actual table, we must infer the relationship based on the most logical option for a physical fitness exam. It is expected that climbing more floors would take a longer amount of time. Option B, 'The longer the time, the more floors climbed,' describes a direct relationship, which is the most logical and common pattern for physical exertion over distance, making it the most likely correct explanation of a typical table's data.

The proportion of water to foam concentrate to create a good water foam solution is 40:1. 1 640 gallons of water foam solution need to be mixed with how much foam concentrate?

Answer: 40 gallons

The water-to-foam concentrate ratio is 40:1, meaning for every 40 parts of water, there is 1 part of foam concentrate, totaling 41 parts in the solution. If 1640 gallons of solution are needed, divide the total volume by the total number of parts (41) to find the volume of one part: 1640 gallons / 41 parts = 40 gallons per part. Since foam concentrate is 1 part, 40 gallons of foam concentrate are needed.