According to a report on housing in a certain province, 9/10 of housing units (single-family dwellings) are occupied and the...
GMAT Two Part Analysis : (TPA) Questions
According to a report on housing in a certain province, \(\frac{9}{10}\) of housing units (single-family dwellings) are occupied and the rest are vacant. Of the occupied housing units, the report indicates that \(\frac{2}{3}\) are owner occupied (occupied by one or more of their owners) and the rest are rentals. The report also indicates that \(\frac{2}{5}\) of owner-occupied housing units and \(\frac{3}{5}\) of rentals are each occupied by fewer than three people.
Statement: Of all housing units in the province, X percent are owner occupied and occupied by fewer than three people, and Y percent are rentals and occupied by fewer than three people. Select for X and for Y the options that complete the statement so that it is most accurate based on the information provided. Make only two selections, one in each column.
Phase 1: Owning the Dataset
Starting with Concrete Numbers
Let's use 100 total housing units to make our calculations straightforward.
Visual Organization
Since we're dealing with nested categories (housing units → occupied/vacant → owner/rental → people count), a hierarchical tree diagram works best:
Total Housing Units: 100 ├── Occupied: 90 (\(\frac{9}{10}\)) │ ├── Owner-occupied: 60 (\(\frac{2}{3}\) of occupied) │ │ ├── <3 people: 24 (\(\frac{2}{5}\) of owner-occupied) │ │ └── ≥3 people: 36 (\(\frac{3}{5}\) of owner-occupied) │ └── Rentals: 30 (\(\frac{1}{3}\) of occupied) │ ├── <3 people: 18 (\(\frac{3}{5}\) of rentals) │ └── ≥3 people: 12 (\(\frac{2}{5}\) of rentals) └── Vacant: 10 (\(\frac{1}{10}\))Phase 2: Understanding the Question
We need to find:
- X: Percentage of ALL housing units that are owner-occupied AND have <3 people
- Y: Percentage of ALL housing units that are rentals AND have <3 people
? Key insight: The percentages are of ALL housing units (100), not just occupied units.
Phase 3: Finding the Answer
Systematic Calculations
From our visualization:
- Owner-occupied with <3 people = 24 units
- Rentals with <3 people = 18 units
Calculating percentages:
- X = \(\frac{24}{100}\) = 24%
- Y = \(\frac{18}{100}\) = 18%
Looking at our answer choices: [12, 18, 20, 24, 36, 40]
- X = 24 ✓ (available)
- Y = 18 ✓ (available)
Phase 4: Solution
Final Answer:
- X = 24
- Y = 18
Our visual clearly shows that 24% of all housing units are owner-occupied with fewer than three people, and 18% are rentals with fewer than three people.