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Between 1975 and 1985, nursing-home occupancy rates averaged 87 percent of capacity, while admission rates remained constant, at an average...

GMAT Critical Reasoning : (CR) Questions

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Between 1975 and 1985, nursing-home occupancy rates averaged 87 percent of capacity, while admission rates remained constant, at an average of 95 admissions per 1,000 beds per year. Between 1985 and 1988, however, occupancy rates rose to an average of 92 percent of capacity, while admission rates declined to 81 per 1,000 beds per year.

If the statements above are true, which of the following conclusions can be most properly drawn?

A
The average length of time nursing-home residents stayed in nursing homes increased between 1985 and 1988.
B
The proportion of older people living in nursing homes was greater in 1988 than in 1975.
C
Nursing home admission rates tend to decline whenever occupancy rates rise.
D
Nursing homes built prior to 1985 generally had fewer beds than did nursing homes built between 1985 and 1988.
E
The more beds a nursing home has, the higher its occupancy rate is likely to be.
Solution

Passage Visualization

Passage Statement Visualization and Linkage
Between 1975 and 1985, nursing-home occupancy rates averaged 87 percent of capacity, while admission rates remained constant, at an average of 95 admissions per 1,000 beds per year. Period 1 Baseline (1975-1985):
  • Occupancy Rate: 87% of capacity
  • Admission Rate: 95 per 1,000 beds/year

Concrete Example: In a 1,000-bed facility:
  • 870 beds occupied on average
  • 95 new admissions per year
  • Pattern: Moderate occupancy with steady new admissions
Between 1985 and 1988, however, occupancy rates rose to an average of 92 percent of capacity, while admission rates declined to 81 per 1,000 beds per year. Period 2 Changes (1985-1988):
  • Occupancy Rate: 92% of capacity (+5% increase)
  • Admission Rate: 81 per 1,000 beds/year (-14 admissions decrease)

Concrete Example: Same 1,000-bed facility:
  • 920 beds occupied on average (+50 more beds filled)
  • 81 new admissions per year (-14 fewer admissions)
  • Paradox: Higher occupancy despite fewer new admissions
Overall Implication:
The data reveals a counterintuitive pattern: nursing homes became MORE occupied while admitting FEWER new residents. This suggests that existing residents are staying longer in nursing homes. In practical terms: if fewer people are entering but more beds are filled, then people already there must be remaining for extended periods.

Valid Inferences

Inference: The average length of stay for nursing home residents increased between 1985 and 1988 compared to the 1975-1985 period.

Supporting Logic: Since occupancy rates rose from 87% to 92% while admission rates simultaneously declined from 95 to 81 per 1,000 beds per year, the only way to maintain higher occupancy with fewer new admissions is if existing residents remained in the facilities for longer periods. The mathematics requires that if fewer people are entering but more beds are occupied, then the people already there must be staying longer.

Clarification Note: This inference is supported by the mathematical relationship between the variables, but the passage does not provide information about the underlying reasons for longer stays, such as changes in health conditions, discharge policies, or family circumstances.

Answer Choices Explained
A
The average length of time nursing-home residents stayed in nursing homes increased between 1985 and 1988.
CORRECT - This directly follows from the mathematical relationship in the data. If occupancy rates increased from \(87\%\) to \(92\%\) while admission rates simultaneously decreased from \(95\) to \(81\) per \(1,000\) beds, the only way to explain higher occupancy with fewer new admissions is that existing residents are staying longer. This is a logical inference we can properly draw from the given statistics.
B
The proportion of older people living in nursing homes was greater in 1988 than in 1975.
INCORRECT - The passage doesn't provide information about the total population of older people or what proportion lived in nursing homes. We only have data about occupancy rates within existing nursing homes, not about the broader demographic trends or whether more nursing homes were built.
C
Nursing home admission rates tend to decline whenever occupancy rates rise.
INCORRECT - This suggests a general trend or causal relationship, but we only have data from two specific time periods. We can't establish that admission rates 'tend to decline whenever' occupancy rates rise based on just these two data points. This overgeneralizes from limited information.
D
Nursing homes built prior to 1985 generally had fewer beds than did nursing homes built between 1985 and 1988.
INCORRECT - The passage provides no information about when nursing homes were built or how many beds they had. The data focuses on occupancy and admission rates, not construction timelines or facility sizes. This choice introduces information not supported by the passage.
E
The more beds a nursing home has, the higher its occupancy rate is likely to be.
INCORRECT - Similar to choice D, the passage doesn't discuss the relationship between facility size (number of beds) and occupancy rates. We have no data comparing different-sized nursing homes, so we can't draw this conclusion about larger facilities having higher occupancy rates.
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