A town parks director has specified that for every 3 aspen trees in the downtown park, there should be exactly...
GMAT Two Part Analysis : (TPA) Questions
A town parks director has specified that for every 3 aspen trees in the downtown park, there should be exactly 2 birch trees and 4 fir trees, while for every 1 larch tree in the park, there should be exactly 3 spruce trees and 2 aspen trees. Currently, the park includes exactly 12 aspens, 8 birches, 15 firs, 8 larches, and 18 spruces.
The parks director's specifications will be met by reducing the number of trees of exactly one of these types and increasing the number of trees of exactly one other of these types. Select for Reduced the type of tree that needs to be reduced in number, and for Increased the type of tree that needs to be increased, to meet the parks director's specifications in the manner described in the given information. Make only two selections, one in each column.
Let's visualize this problem to make it crystal clear...
Phase 1: Understanding the Dataset
Let's organize the current tree counts and required ratios:
Current Trees:
| Tree Type | Current Count |
| Aspen | 12 |
| Birch | 8 |
| Fir | 15 |
| Larch | 8 |
| Spruce | 18 |
Director's Specifications:
- Ratio 1: For every 3 aspens → exactly 2 birches AND 4 firs
- Ratio 2: For every 1 larch → exactly 3 spruces AND 2 aspens
Phase 2: Analyzing the Requirements
Let's check if current counts meet the specifications:
For Ratio 1 (Aspen:Birch:Fir = \(3:2:4\)):
- With 12 aspens, we need:
- Birches: \(12 \div 3 \times 2 = 8\) ✓ (matches current)
- Firs: \(12 \div 3 \times 4 = 16\) (need 16, have 15)
For Ratio 2 (Larch:Spruce:Aspen = \(1:3:2\)):
- With 8 larches, we need:
- Spruces: \(8 \times 3 = 24\) (need 24, have 18)
- Aspens: \(8 \times 2 = 16\) (need 16, have 12)
Phase 3: Finding the Solution
Key insight: Aspens appear in BOTH ratios, creating a constraint we must satisfy.
From Ratio 2: Number of aspens = 2 × number of larches
Since we currently have 12 aspens, the number of larches should be: \(12 \div 2 = 6\)
Let's verify what happens if we adjust to 6 larches:
- With 6 larches, we need:
- Spruces: \(6 \times 3 = 18\) ✓ (matches current)
- Aspens: \(6 \times 2 = 12\) ✓ (matches current)
And with 12 aspens maintained:
- Birches: 8 ✓ (already correct)
- Firs: 16 (need to increase from 15)
Phase 4: Solution
To meet the director's specifications:
- Reduced: Larch (from 8 to 6)
- Increased: Fir (from 15 to 16)
This creates a perfectly balanced park where:
- 12 aspens : 8 birches : 16 firs (ratio \(3:2:4\)) ✓
- 6 larches : 18 spruces : 12 aspens (ratio \(1:3:2\)) ✓