An agricultural scientist studying the growth of corn plants recorded the height of a corn plant at the beginning of...
GMAT Algebra : (Alg) Questions
An agricultural scientist studying the growth of corn plants recorded the height of a corn plant at the beginning of a study and the height of the plant each day for the next \(\mathrm{12}\) days. The scientist found that the height of the plant increased by an average of \(\mathrm{1.20}\) centimeters per day for the \(\mathrm{12}\) days. If the height of the plant on the last day of the study was \(\mathrm{36.8}\) centimeters, what was the height, in centimeters, of the corn plant at the beginning of the study?
1. TRANSLATE the problem information
- Given information:
- Plant height increased by 1.20 cm per day on average
- This continued for 12 days
- Height on the last day (day 12) was 36.8 cm
- Need to find: height at the beginning of the study
2. INFER the mathematical relationship
- Key insight: If we know the final height and how much the plant grew total, we can work backwards to find the starting height
- Total growth = daily growth rate × number of days
- Initial height + Total growth = Final height
3. SIMPLIFY to calculate total growth
- Total growth over 12 days = \(\mathrm{1.20\ cm/day \times 12\ days = 14.4\ cm}\)
4. SIMPLIFY to find initial height
- Since Initial height + Total growth = Final height
- \(\mathrm{Initial\ height = Final\ height - Total\ growth}\)
- \(\mathrm{Initial\ height = 36.8\ cm - 14.4\ cm = 22.4\ cm}\)
Answer: 22.4 cm (can also be expressed as \(\mathrm{112/5\ cm}\))
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE skill: Students misinterpret what the problem is asking and try to find the final height instead of the initial height, or they confuse which values to add versus subtract.
Some students might incorrectly think: "The plant grew 1.20 cm per day for 12 days, and ended at 36.8 cm, so it must have started at \(\mathrm{36.8 + (1.20 \times 12)}\)." This leads them to calculate \(\mathrm{36.8 + 14.4 = 51.2\ cm}\), which would be incorrect.
Second Most Common Error:
Poor SIMPLIFY execution: Students correctly set up the problem but make arithmetic errors, especially in the multiplication \(\mathrm{1.20 \times 12}\), calculating it as 12.4 or 14.0 instead of 14.4.
This leads to incorrect final answers like 24.4 cm or 22.8 cm, causing confusion about which approach is correct.
The Bottom Line:
This problem requires students to think backwards from the final result, which challenges their ability to clearly translate word problems and understand the inverse relationship between addition and subtraction in growth scenarios.