The function V defined by \(\mathrm{V(t) = 55 - 0.75t}\) can be used to model the volume of gasoline, in...
GMAT Algebra : (Alg) Questions
The function V defined by \(\mathrm{V(t) = 55 - 0.75t}\) can be used to model the volume of gasoline, in liters, in a car's tank \(\mathrm{t}\) minutes after it has started to leak. Which of the following is the best interpretation of the number 55 in this context?
The car's tank will be empty of gasoline after 55 minutes.
The initial volume of gasoline in the tank was 55 liters.
The volume of gasoline in the tank decreases by 55 liters each minute.
The maximum capacity of the tank is 55 liters.
1. TRANSLATE the function components
- Given function: \(\mathrm{V(t) = 55 - 0.75t}\)
- \(\mathrm{V(t)}\) = volume of gasoline in liters
- \(\mathrm{t}\) = time in minutes after the leak started
- This is a linear function in the form \(\mathrm{V(t) = b + mt}\)
2. INFER what the number 55 represents
- In a linear function \(\mathrm{V(t) = b + mt}\), the value \(\mathrm{b}\) is the y-intercept
- The y-intercept occurs when the independent variable equals zero
- So we need to evaluate: What is \(\mathrm{V(0)}\)?
3. SIMPLIFY to find the initial condition
- \(\mathrm{V(0) = 55 - 0.75(0)}\)
- \(\mathrm{V(0) = 55}\)
4. INFER the real-world meaning
- Since \(\mathrm{t = 0}\) represents "the moment the leak started"
- \(\mathrm{V(0) = 55}\) means there were 55 liters in the tank when the leak began
- Therefore, 55 represents the initial volume of gasoline
Answer: B
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak INFER skill: Students confuse the y-intercept (55) with the slope \(\mathrm{-0.75}\) and think 55 represents the rate of change.
They see "55" and "decreases" in the context and incorrectly conclude that the volume decreases by 55 liters each minute, not recognizing that \(\mathrm{-0.75}\) is actually the rate of decrease.
This may lead them to select Choice C (The volume decreases by 55 liters each minute)
Second Most Common Error:
Poor TRANSLATE reasoning: Students mix up units and think 55 (which has units of liters) represents time instead of volume.
They see the number 55 and incorrectly assume it must relate to the "minutes" mentioned in the problem, not recognizing that 55 has volume units.
This may lead them to select Choice A (The tank will be empty after 55 minutes)
The Bottom Line:
Success requires recognizing that in linear functions, the constant term (y-intercept) represents the initial value when the independent variable equals zero, and carefully tracking what each number represents in the real-world context.
The car's tank will be empty of gasoline after 55 minutes.
The initial volume of gasoline in the tank was 55 liters.
The volume of gasoline in the tank decreases by 55 liters each minute.
The maximum capacity of the tank is 55 liters.