Question

GRAND CITY CENSUS REPORTS (1950-1980)

Which of the following, if true, most helps to reconcile the increase in housing units with the decline in population shown in the table above?

• A. The percentage of families that included adult children living at home increased during the 1970's.
• B. The number of people moving to Grand City from other cities gradually decreased during the three decades.
• C. The number of housing units that were vacant in Grand City fell steadily between 1950 and 1980.
• D. The number of adults who lived alone in Grand City housing units increased dramatically between 1950 and 1980.
• E. Many housing units that were occupied by only one family in 1950 were occupied by two or more families in 1980.

Hint:

When faced with a paradox involving two changing totals (like population and housing), always investigate the ratio or average that connects them. The explanation for the paradox often lies in how this underlying ratio has changed.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
This is a "reconcile the paradox" question. We are presented with two seemingly contradictory trends: from 1950 to 1980, the population of Grand City declined, while the number of housing units increased. We need to find an explanation that resolves this discrepancy.
Step 2: Key Formula or Approach:
The link between population and housing units is the average number of people per housing unit (household size). \[ \text{Average Household Size} = \frac{\text{Total Population}}{\text{Number of Housing Units}} \] If the population is decreasing while housing units are increasing, it must mean that the average number of people living in each unit is decreasing. We are looking for a reason for this decrease.
Step 3: Detailed Explanation:
Let's check the data to confirm the trend in household size: - 1950: \( \frac{500,000}{214,000} \approx 2.34 \) people per unit. - 1980: \( \frac{425,000}{237,000} \approx 1.79 \) people per unit. The average household size did indeed decrease significantly. Now let's evaluate the options to see which one explains this decrease.

(A) An increase in adult children living at home would \textit{increase} the average household size, which deepens the paradox.
(B) A decrease in people moving to the city helps explain the population decline but does not explain why more housing units were needed.
(C) A decrease in vacant units would mean more of the existing units were being filled, but it doesn't explain why the number of units needed to be increased while the population was falling.
(D) A dramatic increase in the number of adults living alone directly explains the decrease in average household size. If more people live by themselves, more housing units are needed to house the same number of people. This trend would require an increase in housing units even as the total population declines. This resolves the paradox.
(E) An increase in multiple families occupying single units would \textit{increase} the average household size, which is the opposite of what the data shows.
Step 4: Final Answer:
The paradox is resolved by a decrease in the average number of people per household. An increase in the number of people living alone is a direct cause of this trend.