Lin fills a water tank at a constant rate. The function \(\mathrm{W(t) = 18t + 120}\) models the volume, in...
GMAT Algebra : (Alg) Questions
Lin fills a water tank at a constant rate. The function \(\mathrm{W(t) = 18t + 120}\) models the volume, in gallons, of water in the tank t minutes after she begins filling it. Which statement is the best interpretation of the y-intercept of the graph of \(\mathrm{y = W(t)}\) in the xy-plane in this context?
- Lin adds approximately 18 gallons of water each minute.
- The tank held approximately 18 gallons when she began filling it.
- The tank held approximately 120 gallons when she began filling it.
- The tank will be full after approximately 120 minutes.
Lin adds approximately \(18\) gallons of water each minute.
The tank held approximately \(18\) gallons when she began filling it.
The tank held approximately \(120\) gallons when she began filling it.
The tank will be full after approximately \(120\) minutes.
1. TRANSLATE the question requirements
- We need to interpret the y-intercept of \(\mathrm{W(t) = 18t + 120}\)
- The y-intercept occurs when \(\mathrm{t = 0}\)
- We need to find what this means in the context of filling a water tank
2. TRANSLATE to find the y-intercept value
- Evaluate \(\mathrm{W(0)}\):
\(\mathrm{W(0) = 18(0) + 120}\)
\(\mathrm{W(0) = 120}\) - The y-intercept is 120
3. INFER the contextual meaning
- Since \(\mathrm{W(t)}\) gives the volume t minutes after filling begins
- When \(\mathrm{t = 0}\), this represents the moment Lin starts filling
- Therefore \(\mathrm{W(0) = 120}\) means the tank already contained 120 gallons when she began
4. INFER why other choices are incorrect
- Choice (A): 18 is the slope (rate of filling), not the y-intercept
- Choice (B): Confuses the slope value (18) with the initial amount
- Choice (D): Treats 120 as time rather than volume
Answer: C
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE reasoning: Students confuse slope with y-intercept, focusing on the coefficient 18 instead of the constant term 120.
They see "18 gallons per minute" and think this must be what the question is asking about, leading them to select Choice (A) or (B).
Second Most Common Error:
Poor contextual INFER skills: Students find the correct y-intercept value (120) but misinterpret what it represents in the problem context.
They might think 120 refers to time instead of volume, leading them to select Choice (D) or become confused and guess.
The Bottom Line:
This problem tests whether students can distinguish between the slope and y-intercept of a linear function, then correctly interpret the y-intercept's meaning within the given context. Success requires both mathematical translation skills and contextual reasoning.
Lin adds approximately \(18\) gallons of water each minute.
The tank held approximately \(18\) gallons when she began filling it.
The tank held approximately \(120\) gallons when she began filling it.
The tank will be full after approximately \(120\) minutes.