The Quasi JX is a new car model. Under ideal driving conditions, the Quasi Jx's fuel economy is E kilometers...
GMAT Two Part Analysis : (TPA) Questions
The Quasi JX is a new car model. Under ideal driving conditions, the Quasi Jx's fuel economy is \(\mathrm{E}\) kilometers per liter (\(\mathrm{E \, km/L}\)) when its driving speed is constant at \(\mathrm{S}\) kilometers per hour (\(\mathrm{S \, km/h}\)).
In terms of the variables \(\mathrm{S}\) and \(\mathrm{E}\), select the expression that represents the number of liters of fuel used in 1 hour of driving under ideal driving conditions at a constant speed \(\mathrm{S}\), and select the expression that represents the number of liters of fuel used in a 60 km drive under ideal driving conditions at a constant speed \(\mathrm{S}\).
Phase 1: Owning the Dataset
Start with Concrete Numbers
Let's pick specific values to understand the relationships:
- Speed \(\mathrm{S = 100\,km/h}\)
- Fuel economy \(\mathrm{E = 20\,km/L}\)
Visualization
Since we're dealing with rates and relationships, let's create a simple rate diagram:
Fuel Economy: E km/L → Car travels E kilometers using 1 liter Speed: S km/h → Car travels S kilometers in 1 hour Key Relationship: Distance = Fuel Economy × Fuel Used Fuel Used = Distance ÷ Fuel Economy
Phase 2: Understanding the Question
Breaking Down the Requirements
Statement 1: Liters of fuel in 1 hour
- In 1 hour, the car travels S kilometers (since speed = S km/h)
- To find fuel used: \(\mathrm{Distance ÷ Fuel\,Economy = S ÷ E}\)
Statement 2: Liters of fuel in 60 km
- The car travels 60 kilometers
- To find fuel used: \(\mathrm{Distance ÷ Fuel\,Economy = 60 ÷ E}\)
Key Insight
The fundamental formula is: Fuel Used = Distance Traveled ÷ Fuel Economy
Phase 3: Finding the Answer
Systematic Analysis
For Statement 1 (Liters in 1 hour):
- Distance in 1 hour = S km
- Fuel used = \(\mathrm{S ÷ E = S/E}\) liters
Verifying with our example: \(\mathrm{100\,km ÷ 20\,km/L = 5\,liters}\) ✓
For Statement 2 (Liters in 60 km):
- Distance = 60 km
- Fuel used = \(\mathrm{60 ÷ E = 60/E}\) liters
Verifying with our example: \(\mathrm{60\,km ÷ 20\,km/L = 3\,liters}\) ✓
Phase 4: Solution
Final Answer
- Statement 1 (Liters of fuel in 1 hour): \(\mathrm{S/E}\)
- Statement 2 (Liters of fuel in 60 km): \(\mathrm{60/E}\)
Both answers follow directly from the relationship: when fuel economy is E km/L, the fuel needed equals distance divided by E.