Andy is considering enlarging his existing garden, which is rectangular. He has two options. If he increases the length of...
GMAT Two Part Analysis : (TPA) Questions
Andy is considering enlarging his existing garden, which is rectangular. He has two options. If he increases the length of the existing garden by \(5\text{ m}\) and does not change the width, then the area of the enlarged rectangular garden will be twice the area of the existing garden. On the other hand, if he increases the width of the existing garden by \(2\text{ m}\) and does not change the length, then the area of the enlarged rectangular garden will be 1.5 times the area of the existing garden.
From the Dimensions column in the following table, identify a length and a width, in meters, for Andy's existing garden that are consistent with Andy's two options. Make only two selections, one in for each column.
Phase 1: Owning the Dataset
Visual Representation
Let's draw Andy's garden transformation options:
Original Garden:
+--------+
| | W
| LW |
+--------+
L
Option 1 (Length +5m):
+-------------+
| | W Area = 2LW
| |
+-------------+
L + 5
Option 2 (Width +2m):
+--------+
| |
| | W+2 Area = 1.5LW
| |
+--------+
L
Phase 2: Understanding the Question
Setting Up Equations
Let \(\mathrm{L}\) = original length and \(\mathrm{W}\) = original width
From Option 1:
- New area = \(\mathrm{(L + 5) \times W = 2LW}\)
- Expanding: \(\mathrm{LW + 5W = 2LW}\)
- Simplifying: \(\mathrm{5W = LW}\)
- Therefore: \(\mathrm{L = 5}\)
From Option 2:
- New area = \(\mathrm{L \times (W + 2) = 1.5LW}\)
- Expanding: \(\mathrm{LW + 2L = 1.5LW}\)
- Simplifying: \(\mathrm{2L = 0.5LW}\)
- Therefore: \(\mathrm{W = 4}\)
Key Insight
We've determined that the existing garden must have:
- Length = 5 meters
- Width = 4 meters
Phase 3: Finding the Answer
Verification
Let's verify our answer works for both scenarios:
Original area: \(\mathrm{5 \times 4 = 20 \, m^2}\)
Option 1 check: \(\mathrm{(5 + 5) \times 4 = 10 \times 4 = 40 \, m^2 = 2 \times 20}\) ✓
Option 2 check: \(\mathrm{5 \times (4 + 2) = 5 \times 6 = 30 \, m^2 = 1.5 \times 20}\) ✓
Both conditions are satisfied!
Phase 4: Solution
Final Answer
- Statement 1 (Length): 5
- Statement 2 (Width): 4
Our answer perfectly satisfies both area expansion requirements. The existing garden has dimensions of \(\mathrm{5m \times 4m}\).