BSEP - Basic Skills Education Program Ratios and Proportions Questions and Answers

Question 1

A military map has a scale of 1:50,000. If the distance between two points on the map is 4.5 centimeters, what is the actual ground distance between the two points in kilometers?

Accepted Answer

2.25 km

Answer

The scale 1:50,000 means 1 unit on the map equals 50,000 of the same units on the ground. Therefore, 4.5 cm on the map represents 4.5 * 50,000 = 225,000 cm on the ground. To convert centimeters to kilometers, you divide by 100,000 (since there are 100 cm in a meter and 1,000 meters in a kilometer). So, 225,000 cm / 100,000 = 2.25 km.

Question 2

A piece of equipment requires a fuel-oil mixture with a ratio of 40:1 (40 parts gasoline to 1 part oil). If a container is filled with 5 gallons of gasoline, how many fluid ounces of oil must be added? (Note: 1 gallon = 128 fluid ounces)

Accepted Answer

16 oz

Answer

First, convert the 5 gallons of gasoline to fluid ounces: 5 gallons * 128 fl oz/gallon = 640 fl oz. The ratio is 40 parts gasoline to 1 part oil. Set up the proportion: 40/1 = 640/x. Cross-multiply to solve for x: 40x = 640. Divide both sides by 40: x = 16 fluid ounces.

Question 3

In a simple gear system, a drive gear with 60 teeth is meshed with a driven gear with 20 teeth. Which of the following correctly expresses the gear ratio of the drive gear to the driven gear?

Accepted Answer

3:1

Answer

The gear ratio is the ratio of the number of teeth on the drive gear to the number of teeth on the driven gear. This is expressed as 60:20. To simplify, divide both numbers by their greatest common divisor, which is 20. 60 ÷ 20 = 3 and 20 ÷ 20 = 1. The simplified ratio is 3:1.

Question 4

A vertical flagpole casts a shadow 12 feet long. At the same time, a soldier who is 6 feet tall casts a shadow 4 feet long. What is the height of the flagpole?

Accepted Answer

18 feet

Answer

This is a problem of similar triangles. The ratio of an object's height to its shadow's length is the same for both the soldier and the flagpole. Set up the proportion: (soldier's height) / (soldier's shadow) = (flagpole's height) / (flagpole's shadow). This gives 6/4 = H/12. Cross-multiply to get 4 * H = 6 * 12, or 4H = 72. Divide by 4 to find H = 18 feet.

Question 5

A maintenance check finds that 5% of the vehicles in a motor pool are not mission-capable. Which of the following represents the ratio of mission-capable vehicles to non-mission-capable vehicles?

Accepted Answer

19:1

Answer

If 5% of vehicles are non-mission-capable, then 100% - 5% = 95% are mission-capable. The ratio of mission-capable to non-mission-capable is 95 to 5, or 95:5. To simplify this ratio, divide both numbers by their greatest common divisor, which is 5. 95 ÷ 5 = 19, and 5 ÷ 5 = 1. The simplified ratio is 19:1.

BSEP - Basic Skills Education Program Practice Test

BSEP - Basic Skills Education Program Practice Test

BSEP - Basic Skills Education Program Ratios and Proportions Questions and Answers