An ecologist is tracking the growth of two different species of bamboo, Species A and Species B. The height of...
GMAT Algebra : (Alg) Questions
An ecologist is tracking the growth of two different species of bamboo, Species A and Species B. The height of a plant of Species A, \(\mathrm{h_A}\), in centimeters, is modeled by the equation \(\mathrm{h_A = 10 + 4t}\). The height of a plant of Species B, \(\mathrm{h_B}\), in centimeters, is modeled by the equation \(\mathrm{h_B = 16 + 7t}\). In both models, \(\mathrm{t}\) is the number of days after the initial measurement. According to the models, what is the difference in the daily growth rates, in centimeters per day, between Species A and Species B?
1. TRANSLATE the problem information
- Given information:
- Species A height equation: \(\mathrm{h_A = 10 + 4t}\)
- Species B height equation: \(\mathrm{h_B = 16 + 7t}\)
- t represents days after initial measurement
- Need to find: difference in daily growth rates
2. INFER what the coefficients mean
- In any linear equation of the form \(\mathrm{y = mx + b}\):
- The coefficient m tells us the rate of change
- Here, the coefficient of t tells us how many centimeters each species grows per day
- From the equations:
- Species A grows 4 centimeters per day (coefficient of t is 4)
- Species B grows 7 centimeters per day (coefficient of t is 7)
3. SIMPLIFY the calculation
- The difference in daily growth rates:
- Species B rate - Species A rate = \(\mathrm{7 - 4 = 3}\) cm per day
Answer: A) 3
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE skill: Students may focus on the constant terms (10 and 16) instead of the coefficients of t, thinking these represent growth rates or that the answer involves these numbers.
Students might calculate \(\mathrm{16 - 10 = 6}\) and select Choice C (6), confusing initial heights with growth rates.
Second Most Common Error:
Poor INFER reasoning: Students may correctly identify the coefficients but get confused about which rate to subtract from which, or add them instead of finding the difference.
This confusion might lead them to calculate \(\mathrm{7 + 4 = 11}\) and select Choice E (11), or subtract in the wrong order getting \(\mathrm{4 - 7 = -3}\), then taking the absolute value to get 3 but second-guessing themselves.
The Bottom Line:
This problem tests whether students understand that in linear models representing growth over time, the coefficient of the time variable represents the rate of change, not the constant term which represents the initial value.