GED Mathematical Reasoning TestQuantitative Problem Solving with Rational NumbersHard
A map has a scale of 1:25,000. If two cities are 8.5 centimeters apart on the map, what is the actual distance between them in kilometers?
- A2.125 km
- B21.25 km
- C212.5 km
- D0.2125 km
Show answer & explanationAnswer & explanation
Correct answer: A. 2.125 km
The scale 1:25,000 means 1 cm on the map equals 25,000 cm in reality. First, find the actual distance in cm: 8.5 cm * 25,000 = 212,500 cm. Then, convert cm to km: 100 cm = 1 m, 1000 m = 1 km, so 1 km = 100,000 cm. Therefore, 212,500 cm / 100,000 cm/km = 2.125 km.
Why the other options are wrong
- B. This is 21250 meters, or 212,500 cm / 100.
- C. This is 212,500 meters, or 212,500 cm * 100.
- D. This is 2125 meters, or 212,500 cm / 1000, not 100,000.
Map Scales and Unit Conversion
A map scale represents the ratio of a distance on the map to the corresponding distance on the ground. Converting between units (e.g., cm to km) requires knowing the standard conversion factors.
- Scale factor applies to linear distances.
- 1 meter = 100 centimeters.
- 1 kilometer = 1000 meters.
- Therefore, 1 kilometer = 100,000 centimeters.
Memory trick: Scale up first, then slide the decimal, from little map to real-world colossal.