Question

On turning 65 years old, everyone living in the town of Malton becomes eligible to receive a card that guarantees discounts. Census records for 1990 show that 2,450 inhabitants of Malton turned 64 in that year. Yet, in 1991 over 3,000 people applied for and properly received discount cards. So clearly some of Malton's population growth between 1990 and 1992 must be attributable to migration into the city by people in their mid-60's.
Which of the following is an assumption on which the argument depends?

• A. The town of Malton has no complete census records for 1991.
• B. The overall size of the population of Malton grew by over 500 during 1990.
• C. Fewer people applied for and received discount cards in 1991 than did so in 1992.
• D. Among the people 65 years old or older who moved into Malton in 1991, there was no one who did not apply for a discount card.
• E. In general, people who applied for and received discount cards in 1991 first became eligible to do so in that year.

Hint:

The Negation Test is a powerful tool for assumption questions. Identify the conclusion and the evidence, then find the logical gap between them. The assumption is the bridge across that gap. To test an option, negate it. If the negated statement makes the conclusion fall apart, you've found the necessary assumption.

Answer 1

Answer: (E)

Step 1: Understanding the Concept:
This question asks for a necessary assumption of the argument. An assumption is an unstated premise that must be true for the argument's conclusion to be valid. The argument's conclusion is that migration of older people must account for the surprisingly high number of new discount card recipients.
Step 2: Detailed Explanation:
Let's break down the argument: - Premise 1: Everyone becomes eligible for a discount card upon turning 65. - Premise 2 (Data): In 1990, 2,450 residents turned 64. One would expect these 2,450 people to turn 65 and become eligible in 1991.
- Premise 3 (Data): In 1991, over 3,000 people received new discount cards. - Conclusion: The difference (\(3000 - 2450 = 550+\)) must be due to people in their mid-60s moving into the town.
The argument assumes that the only source of new 65-year-olds in 1991, other than the group that turned 64 in 1990, is migration. It overlooks another possibility: people who were already over 65 but had not previously applied for a card could have applied in 1991. For the argument's logic to hold, it must assume that this other possibility is not a significant factor.
Let's evaluate the options using the "Negation Test". If we negate a necessary assumption, the argument should fall apart.
- (A) This is irrelevant. The argument uses census data; it doesn't depend on the absence of other data.
- (B) Overall population growth is not directly relevant to the specific age group being discussed.
- (C) A comparison to 1992 is irrelevant to the argument about 1991.
- (D) This is not necessary. The argument can still work even if some new migrants didn't apply; it just means the number of migrants was even higher.
- (E) Let's negate this statement: "In general, people who applied for and received discount cards in 1991 did NOT first become eligible to do so in that year." This negated statement means that many of the 3,000+ applicants were people who turned 65 in previous years (1990, 1989, etc.) but only decided to apply for the card in 1991. This would provide a large pool of applicants that are not new residents, completely destroying the conclusion that migration must be the cause of the discrepancy. Since negating this statement ruins the argument, it must be a necessary assumption.
Step 3: Final Answer:
The argument assumes that the people who applied for cards in 1991 were newly eligible in 1991, ruling out the possibility of a backlog of older, eligible residents who simply hadn't applied before.