Between 1975 and 1985, nursing-home occupancy rates averaged 87 percen

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. - Occupancy rate = 87% = 87 beds occupied for every 100 beds = 870 beds occupied for every 1000 beds

Admission rate = 95 admissions per 1000 beds

Thus, for every 1000 beds, 870 are occupied while there are 95 admissions.

How can so many beds be occupied while there are only 95 admissions?
There’s only way: on average, individuals in nursing homes are staying for many years.

How many years, on average?

870/95 i.e. about 9 years.

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.
- Occupancy rate = 92% = 92 beds occupied for every 100 beds = 920 beds occupied for every 1000 beds

Admission rate = 81 admissions per 1000 beds

How many years, on average, an individual stays in nursing homes?

920/81 i.e. about 11 years.



(A)The average length of time nursing-home residents stayed in nursing homes increased between 1985 and 1988.
Correct- As we understood from the passage, the average length of stay must be longer to account for the changes in occupancy and admission rates.

(B)The proportion of older people living in nursing homes was greater in 1988 than in 1975.
Incorrect- The proportion talked about in this option can be thought of in two ways:

1. Number of older people in nursing homes/Number of older people in the population

This proportion tells us how big a segment of the older people in the population is of those living in nursing homes

2. Number of older people in nursing homes/Number of people in nursing homes
This proportion tells us how big a segment of the people in nursing homes is of older people
None of these proportions are can be inferred from the passage.

The first proportion cannot be inferred since we have no information about the number of older people in the population.

The second proportion cannot be inferred since we don’t know whether older people stay longer in nursing homes than younger people. Besides, even if, for our discussion sake, we assume that older people stay longer in nursing homes than younger people, we still cannot infer this proportion because it’s possible that the average length of stay increased because of older people staying for even longer in 1988 than in 1975 and not because there were proportionately more older people in nursing homes.

(C)Nursing home admission rates tend to decline whenever occupancy rates rise.
Incorrect- Just on the basis of a certain movement between data points, we cannot infer a trend. This option says that nursing home admission rates TEND to decline whenever occupancy rates rise. We cannot infer this TENDENCY from movements in just two time periods. Doing so would be the same as concluding that CJ tends to get sick by eating a banana from the facts that CJ did not have a banana yesterday and was not sick and that CJ had a banana today and is sick today.

(D)Nursing homes built prior to 1985 generally had fewer beds than did nursing homes built between 1985 and 1988.
Incorrect- Since both the data points are per 1000 beds, we cannot say anything about the total number of beds for any time period. Besides, this option is talking about number of beds per nursing home. We have ZERO information about the number of nursing homes and the number of beds in them.

(E)The more beds a nursing home has, the higher its occupancy rate is likely to be.
Incorrect- The passage nowhere talks about the number of beds or occupancy rates of individual nursing homes.

(A) The average length of time nursing-home residents stayed in nursing homes increased between 1985 and 1988.
I think this explains the discrepancy properly. Although admission rates declined, the average length of stay increased and this phenomenon leads to increased occupancy rates.

(B) The proportion of older people living in nursing homes was greater in 1988 than in 1975.
First of all older people are not discussed in passage, and secondly they constitute just a part of entire patients and not the complete part. Moreover this is not discussed in passage above so no conclusion of this sort can be drawn.

(C) Nursing home admission rates tend to decline whenever occupancy rates rise.
Although this can be a plausible conclusion but there is no relationship shown between increased admission rates and declining occupancy rates.

(D) Nursing homes built prior to 1985 generally had fewer beds than did nursing homes built between 1985 and 1988.
Hospital capacity is not discussed in passage above so no conclusion of this sort can be drawn.

(E) The more beds a nursing home has, the higher its occupancy rate is likely to be.
Hospital capacity is not discussed in passage above so no conclusion of this sort can be drawn.

So Answer is A.

The argument is basically stating that over two different time periods, occupancy rates in nursing homes increased. However, during those same time periods, the admission rates at the nursing homes decreased. The question asks us to find an answer that Resolves the Paradox (the question stem says "Find the Conclusion" but the conclusion is actually resolving the paradox)

(A) The average length of time nursing-home residents stayed in nursing homes increased between 1985 and 1988. - This helps explain why the occupancy increased (people stayed in nursing homes for a longer duration). This also explains why admission rates decreased (Less people stayed for a longer time occupying more number of beds). CORRECT ANSWER.

(B) The proportion of older people living in nursing homes was greater in 1988 than in 1975 - Older people not mentioned in the stimulus. So, a definite conclusion about them cannot be drawn.

(C) Nursing home admission rates tend to decline whenever occupancy rates rise. - As already pointed out above, just two time periods are taken into consideration in the stimulus. Those two time periods need not be representative of the entire truth in general. Thus, this statement, drawn as a generalization, may not necessarily be true. This option, IMO, is more of a real-world-true scenario and that is why a trap.

(D) Nursing homes built prior to 1985 generally had fewer beds than did nursing homes built between 1985 and 1988. - Not necessarily true. Does not resolve the paradox.

(E) The more beds a nursing home has, the higher its occupancy rate is likely to be. - Maybe real-world-true but not necessitated by the premises. A definite conclusion cannot be drawn.

I'm not sure I follow the logic behind A being the right answer in this case.

between 1975 and 1985, average occupancy = 87%
between 1985 and 1988, average occupancy = 92%

While it is a possibility that the occupancy rates rose between '85 and '88, there is also a possibility that the rate from '85 to '88 remained constant (or even declined). Maybe '85 had a surprisingly high amount of occupancy rates which again declined in 86, 87 and 88, but was enough to keep average of the period between 85 to 88, higher than that of 75 to 85.

Option C on the other hand states that the "Nursing home admission rates tend to decline whenever occupancy rates rise." which is concurring with the data given in the argument. While I agree that this conclusion is unstable based on just the two data points that the argument has provided, I feel the same uncertainty for option A as well.

VeritasKarishma AndrewN could you please help me out with this confusion? Thanks !

Hello, aritrar4. The whenever of choice (C) is the nail in its coffin. Most answers that incorporate such absolute or definitive language—e.g., all, always, never, must, cannot—will end up being incorrect, and this one is no exception. We cannot predict an ironclad trend based on a single correlation. Regarding (A), I think CrackVerbalGMAT has outlined it best above. Consider those three possibilities carefully, and it will lead you straight to the correct reasoning. Please let me know if it still does not make sense to you.

Thank you for thinking to ask me about this question.

- Andrew

Can you argue that the number of nursing facilities perhaps closed down which decreased the number of beds but left the same number of people requiring a bed therefore increasing occupancy rates? This would then make sense why admission rates decrease, no?

Notice that the passage makes clear that admission rates were "95 admissions per 1,000 beds per year" and that "admission rates declined to 81 per 1,000 beds per year."

So, the information we have is not on total numbers of admissions. It's on the admissions per 1000 beds.

Thus, a change in the number of nursing homes would make no difference. After all, regardless of how many nursing homes there are, the admissions per 1000 beds represents the same thing.

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