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.
12
18
20
24
36
40
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.