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

Question

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.

CrackverbalGMAT · Accepted Answer

Occupancy rate at a given time = No. of beds occupied / total number of beds.

We know that the occupancy rate has increased, from 87% to 92%.

three possibilities emerge - 
1. The number of patients who are admitted has increased and hence the number of beds occupied also increases
2. The number of patients has remained the same, but the number of beds has reduced.
3. Patients spend more time being admitted. This leads to an increase in occupancy rates even though the other factors may not have changed.

Now, we are told that admission rates have decreased, from 95 per 1000 beds to 81 per 1000 beds.

Admission rates = No. of patients admitted / total number of beds.

We can rule out possibility 1 because if this quantity increases then the total number of beds has to increase much more (because the admission rates drop).
If the number of beds increases much more than the number of patients, then the occupancy rate will drop, not increase.

We can rule out possibility 2 because if the number of beds has reduced then the average number of patients admitted should decrease much more (because the admission rates drop).
If that is the case, then occupancy rates will not increase, as the numerator decreases by a higher proportion than the denominator

We are left with possibility 3. Which answer option states this? Option A.

B - Incorrect.
We are concerned with the entire population, not just with older people. Also, we are referring to periods, not one particular year.

C - Incorrect.
We cannot draw this conclusion from just two data points about two periods.

D - Incorrect.
We cannot conclude about individual nursing homes. Also, from the discussion above we cannot infer anything about the number of beds.

E - Incorrect.
We cannot conclude this based on just 2 data points.

KarishmaB · Answer

Assume there are 1000 beds.

Period 1
Occupancy Rate = 87% (870 beds out of 1000 occupied at any given time on avg)
Admission rates = 95 new admissions per year

Period 2
Occupancy Rate = 92% (920 beds out of 1000 occupied at any given time on avg)
Admission Rates = 81 new admissions per year

So in period 2, more beds are occupied but fewer new admissions take place. Why? Because people are not leaving. We have fewer new admissions but more beds are occupied. Who is occupying these beds? The people who took admission before. So people are staying longer. If they were leaving, you would need more new admissions to fill up more beds. Hence (A) is correct.

(B) The proportion of older people living in nursing homes was greater in 1988 than in 1975.

Not the data we are discussing.

(C) Nursing home admission rates tend to decline whenever occupancy rates rise.

"Whenever" creates a rule that must be followed every time. This is not necessary. Though it may sound logical that since occupancy rates are higher, fewer beds are available so admission rates will decline but what if people stay for a very short time so new admissions keep happening. And since occupancy rates are higher, the new admission rates will become high too. We cannot deduce what happens in "every" case. It depends on how long people stay.
 aritrar4

(D) Nursing homes built prior to 1985 generally had fewer beds than did nursing homes built between 1985 and 1988.

Actual number of beds is irrelevant.

(E) The more beds a nursing home has, the higher its occupancy rate is likely to be.

Irrelevant.

Answer (A)

ChiranjeevSingh · Answer

Understanding the Passage

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.

Option Evaluation

(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.

abhijit_sen · Answer

(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.

siddharthmuzumdar · Answer

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.

aritrar4 · Answer

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 !

AndrewN · Answer

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

thesip2323 · Answer

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?

MartyTargetTestPrep · Answer

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.

egmat · Answer

This is a tricky Critical Reasoning question that tests your ability to spot the logical relationship between occupancy rates and admission rates. Let's break down what's happening here.

Understanding the Data:

Let me walk you through what we're given:
-  1975-1985:  87% occupancy, 95 admissions per 1,000 beds/year
-  1985-1988:  92% occupancy, 81 admissions per 1,000 beds/year

Notice the paradox here? Occupancy went  up  (more beds filled), but admissions went  down  (fewer new people entering). How can nursing homes be more full with fewer people coming in?

The Key Insight:

Think about it like a hotel - if a hotel has higher occupancy but fewer new guests checking in, what must be happening? The existing guests must be staying longer! The same logic applies here.

Let's make this concrete with numbers. In a 1,000-bed facility:
- Period 1: 870 beds occupied, 95 new admissions yearly
- Period 2: 920 beds occupied, only 81 new admissions yearly

So we have 50 more beds filled but 14 fewer people entering each year. The only mathematical way this works is if residents are staying longer.

Why (A) is Correct:

Choice (A) states: "The average length of time nursing-home residents stayed in nursing homes increased between 1985 and 1988."

This directly follows from our analysis. With higher occupancy and lower admissions, residents  must  be staying longer - it's the only logical conclusion that fits the data.

Quick elimination of other choices: 
- (B): We don't know about the total elderly population
- (C): Can't generalize a trend from just two data points
- (D) & (E): No information about facility sizes or construction dates

You can check out the  step-by-step solution on Neuron by e-GMAT  to master the systematic framework for solving all paradox-based CR questions. You can also explore other GMAT official questions with detailed solutions on Neuron for structured practice  here .

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

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GMAT Critical Reasoning (CR) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

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From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards