Question:\(\mathrm{W(m) = 180 - 2m}\). The water level of a reservoir, in feet above sea level, can be modeled by...
GMAT Algebra : (Alg) Questions
\(\mathrm{W(m) = 180 - 2m}\). The water level of a reservoir, in feet above sea level, can be modeled by the function W defined above, where \(\mathrm{W(m)}\) is the water level m months after January 2020. Of the following, which is the best interpretation of the equation \(\mathrm{W(15) = 150}\)?
- The water level in this reservoir is predicted to be 15 feet above sea level in April 2021.
- The water level in this reservoir is predicted to be 150 feet above sea level in January 2021.
- The water level in this reservoir is predicted to be 150 feet above sea level in April 2021.
- The water level in this reservoir is predicted to be 150 feet above sea level in March 2022.
The water level in this reservoir is predicted to be 15 feet above sea level in April 2021.
The water level in this reservoir is predicted to be 150 feet above sea level in January 2021.
The water level in this reservoir is predicted to be 150 feet above sea level in April 2021.
The water level in this reservoir is predicted to be 150 feet above sea level in March 2022.
1. TRANSLATE the equation \(\mathrm{W(15) = 150}\)
- Given information:
- \(\mathrm{W(m) = 180 - 2m}\) (function for water level)
- \(\mathrm{m}\) represents months after January 2020
- \(\mathrm{W(m)}\) represents water level in feet above sea level
- We need to interpret \(\mathrm{W(15) = 150}\)
- What this tells us: When \(\mathrm{m = 15}\), the water level \(\mathrm{W = 150}\) feet above sea level
2. INFER what \(\mathrm{m = 15}\) means in calendar terms
- Since \(\mathrm{m}\) represents months after January 2020, \(\mathrm{m = 15}\) means 15 months after January 2020
- Strategy: Add 15 months to January 2020
3. SIMPLIFY the calendar calculation
- January 2020 + 15 months:
- January 2020 + 12 months = January 2021
- January 2021 + 3 more months = April 2021
4. Combine the information
- \(\mathrm{W(15) = 150}\) means: The water level is predicted to be 150 feet above sea level in April 2021
Answer: C
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE skill: Students confuse which number represents what in \(\mathrm{W(15) = 150}\)
They might think the 15 represents the water level and 150 represents the time, leading to interpretations like '15 feet above sea level.' This confusion about function notation causes them to select Choice A (15 feet above sea level in April 2021).
Second Most Common Error:
Poor SIMPLIFY execution: Students make calendar arithmetic errors when calculating 15 months after January 2020
Common mistakes include:
- Thinking 15 months = 1 year 3 months, but adding incorrectly to get January 2021 instead of April 2021
- Or calculating 15 months as March 2022 (adding 15 months to the wrong starting point)
These calendar calculation errors lead them to select Choice B (January 2021) or Choice D (March 2022).
The Bottom Line:
This problem tests whether students can correctly interpret function notation and perform accurate calendar arithmetic - two skills that seem simple but require careful attention to avoid mixing up the input/output relationship and month-counting errors.
The water level in this reservoir is predicted to be 15 feet above sea level in April 2021.
The water level in this reservoir is predicted to be 150 feet above sea level in January 2021.
The water level in this reservoir is predicted to be 150 feet above sea level in April 2021.
The water level in this reservoir is predicted to be 150 feet above sea level in March 2022.