A homeowner has installed two systems of gutters and 100-liter barrels to collect water that runs off of her roof,...
GMAT Two Part Analysis : (TPA) Questions
A homeowner has installed two systems of gutters and 100-liter barrels to collect water that runs off of her roof, one system on the north side and the other on the south side. Sixty percent of the water that falls on her roof runs into the gutters of the north side system and the remaining 40 percent runs into the south side gutters. All water then drains into the barrels. No barrel is attached to both of the gutter systems, and all barrels contain only water that has drained from the gutters. Suppose that all of the barrels take in water at the same rate and over the same period of time.
Select for North side and South side numbers of barrels that are jointly consistent with this supposition and the given information. Make only two selections, one in each column.
Phase 1: Owning the Dataset
Visualization
Let's create a simple diagram showing the water distribution:
Roof Water (100%) | _____|_____ | | 60% 40% | |North Side South Side | |[Barrels] [Barrels]
Key Information
- North side system: receives \(60\%\) of roof water
- South side system: receives \(40\%\) of roof water
- All barrels:
- Hold 100 liters each
- Fill at the same rate
- Fill over the same time period
- No barrel serves both systems
Phase 2: Understanding the Question
We need to find the number of barrels on each side that maintains the \(60:40\) water distribution ratio.
Key Insight
Since all barrels fill at the same rate over the same time period, each barrel collects the same amount of water. Let's call this amount B liters per barrel.
If North side has N barrels and South side has S barrels:
- North side collects: \(\mathrm{N} \times \mathrm{B}\) liters total
- South side collects: \(\mathrm{S} \times \mathrm{B}\) liters total
The ratio of water collected must match the distribution ratio:
\(\mathrm{N} \times \mathrm{B} : \mathrm{S} \times \mathrm{B} = 60\% : 40\%\)
Simplifying:
\(\mathrm{N} : \mathrm{S} = 60 : 40 = 3 : 2\)
Therefore, the number of North barrels must be 1.5 times the number of South barrels.
Phase 3: Finding the Answer
Let's check which values from our choices [3, 4, 5, 6, 7] satisfy the \(3:2\) ratio:
If South = 4 → North should be \(4 \times 1.5 = 6\)
Is 6 in our choices? Yes! ✓
? Stop here - we found our answer.
Let's verify: \(6:4 = 3:2\) ✓
Phase 4: Solution
North side: 6 barrels
South side: 4 barrels
This maintains the required \(3:2\) ratio, ensuring that with equal filling rates, the North side collects \(60\%\) of the water while the South side collects \(40\%\).