A particular botanist classifies a species of plant as tall if its typical height when fully grown is more than...
GMAT Algebra : (Alg) Questions
A particular botanist classifies a species of plant as tall if its typical height when fully grown is more than 100 centimeters. Each of the following inequalities represents the possible heights \(\mathrm{h}\), in centimeters, for a specific plant species when fully grown. Which inequality represents the possible heights \(\mathrm{h}\), in centimeters, for a tall plant species?
\(106\lt \mathrm{h}\lt 158\)
\(80\lt \mathrm{h}\lt 100\)
\(42\lt \mathrm{h}\lt 87\)
\(17\lt \mathrm{h}\lt 85\)
1. TRANSLATE the classification rule
- Given information:
- A plant species is "tall" if its height is more than 100 cm
- We need \(\mathrm{h \gt 100}\) for the plant to be classified as tall
- What this tells us: We need to find which inequality represents heights that are ALL above 100 cm
2. INFER the key requirement
- For a plant species to be classified as "tall," every possible height in its range must be greater than 100 cm
- This means we need an inequality where the smallest possible value is still greater than 100
3. APPLY CONSTRAINTS to each choice
- Check each inequality to see if ALL values are greater than 100:
Choice A: \(\mathrm{106 \lt h \lt 158}\)
- Smallest possible height: just above 106 cm
- Since \(\mathrm{106 \gt 100}\), every height in this range exceeds 100 cm ✓
Choice B: \(\mathrm{80 \lt h \lt 100}\)
- Heights range from just above 80 to just below 100
- Since all heights are less than 100, none qualify as "tall" ✗
Choice C: \(\mathrm{42 \lt h \lt 87}\)
- Heights range from just above 42 to just below 87
- Since \(\mathrm{87 \lt 100}\), none qualify as "tall" ✗
Choice D: \(\mathrm{17 \lt h \lt 85}\)
- Heights range from just above 17 to just below 85
- Since \(\mathrm{85 \lt 100}\), none qualify as "tall" ✗
Answer: A
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak INFER skill: Students misunderstand the classification requirement and think that if ANY heights in the range exceed 100 cm, the species qualifies as "tall."
For example, they might incorrectly reason: "Choice B goes up to 100, so some plants could be tall." They fail to recognize that for a species classification, ALL typical heights must meet the criteria, not just some possible heights.
This leads to confusion and guessing among the incorrect choices.
The Bottom Line:
The key insight is understanding that species classification applies to the entire range of typical heights, not individual plants. Every possible height for a "tall" species must exceed the 100 cm threshold.
\(106\lt \mathrm{h}\lt 158\)
\(80\lt \mathrm{h}\lt 100\)
\(42\lt \mathrm{h}\lt 87\)
\(17\lt \mathrm{h}\lt 85\)