A conservationist is managing a fish population in a lake. The population is estimated using the model below.P = 1500...
GMAT Algebra : (Alg) Questions
A conservationist is managing a fish population in a lake. The population is estimated using the model below.
\(\mathrm{P = 1500 + 4.5n - 7.2s}\)
In the model, P is the estimated fish population at the end of the year, n is the number of thousands of native aquatic plants added to the lake, and s is the number of non-native sunfish in the lake. Which of the following is the best interpretation of the number 7.2 in this context?
For every additional non-native sunfish, the fish population is estimated to increase by \(\mathrm{7.2}\).
For every additional non-native sunfish, the fish population is estimated to decrease by \(\mathrm{7.2}\).
For every \(\mathrm{7.2}\) thousand native aquatic plants added, the fish population is estimated to decrease by \(\mathrm{1}\).
The total decrease in the fish population from non-native sunfish is estimated to be \(\mathrm{7.2}\).
1. TRANSLATE the equation components
- Given equation: \(\mathrm{P = 1500 + 4.5n - 7.2s}\)
- Where:
- P = fish population at year end
- n = thousands of native plants added
- s = number of non-native sunfish
2. INFER what the coefficient 7.2 represents
- The number 7.2 appears in the term '\(\mathrm{-7.2s}\)'
- This term shows how non-native sunfish (variable s) affect the population
- The coefficient \(\mathrm{-7.2}\) tells us the rate of change per sunfish
3. APPLY CONSTRAINTS to interpret the negative coefficient
- Since the coefficient is \(\mathrm{-7.2}\) (negative), each additional sunfish causes a decrease
- For every 1 additional sunfish, population decreases by 7.2
- This rules out any interpretation suggesting an increase
Answer: B
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE reasoning: Students focus on the number 7.2 but miss the crucial negative sign in front of it.
They see '7.2' and immediately think this represents how much the population increases, completely overlooking that it's actually '\(\mathrm{-7.2}\)' in the equation. This fundamental misreading of the mathematical notation leads them to select Choice A (increase by 7.2).
Second Most Common Error:
Poor INFER skill: Students confuse which variable the coefficient 7.2 is attached to in the equation.
They see 7.2 in the problem and incorrectly associate it with the native plants (n) rather than recognizing it's the coefficient of the sunfish variable (s). This confusion about variable relationships causes them to select Choice C, thinking 7.2 relates to plants rather than sunfish.
The Bottom Line:
This problem requires careful attention to mathematical notation (the negative sign) and precise identification of which variable each coefficient modifies. Students who rush through without systematic analysis of each term often make critical errors.
For every additional non-native sunfish, the fish population is estimated to increase by \(\mathrm{7.2}\).
For every additional non-native sunfish, the fish population is estimated to decrease by \(\mathrm{7.2}\).
For every \(\mathrm{7.2}\) thousand native aquatic plants added, the fish population is estimated to decrease by \(\mathrm{1}\).
The total decrease in the fish population from non-native sunfish is estimated to be \(\mathrm{7.2}\).