shubham2312 wrote:
hi can you explain OE of this question in detail
Quote:
Fact: Asthma, a bronchial condition, is much less common ailment than hay fever, an allergic inflammation of the nasal passages.
Fact: Over 95 percent of people who have asthma also suffer from hay fever.
If the information given as facts above is true, which of the following must also be true?
The toughest part of this question is that it tells us about two populations, then challenges us by asking about percentages
of each group. So it's important to keep these groups clear.
Let's call the people with asthma "asthmatics." Over 95% of asthmatics also have hay fever.
Let's call the people with hay fever "hay fever folks." Some % of hay fever folks also have asthma.
As others have pointed out, process of elimination also helps us enormously with this question! So let's start vetting our choices, while being careful when thinking about which percentage of which group is being discussed.
Quote:
A. Hay fever is a prerequisite for the development of asthma
This choice can only be true if
every asthmatic also has hay fever. If a single asthmatic does not have hay fever, then hay fever
cannot be a prerequisite for asthma. We do know that 5% of asthmatics don't have hay fever. So choice (A) cannot be true, and we'll eliminate it.
Quote:
B. Asthma is a prerequisite for the development of hay fever
As with choice (A), this can only be true if
every hay fever folk also has asthma. The problem is, we're not told anything about how many hay fever folks there are in total.
So let's go back to what we do know: 95% of asthmatics also suffer from hay fever. This means the only way that (B) could be true is if every hay fever folk fits into that 95% of asthmatics. But if that were true, then there would be fewer hay fever folks than asthmatics. This can't possibly be the case, because we know from the prompt that that
hay fever is much more common than asthma. That's why eliminate (B).
Quote:
C. Those who have neither hay fever nor asthma comprise less than 5 percent of the total population
We have absolutely no information about the total population, so we can't accept this statement. Eliminate choice (C).
Quote:
D. The number of people who have both of these ailments is greater than the number of people who have only one of them
We have no idea how many people have these ailments. We only know that 95% of asthmatics also suffer from hay fever. Eliminate choice (D).
Quote:
E. The percentage of people suffering from hay fever who also have asthma is lower than 95 percent.
We've already ruled out every other choice, but let's be sure that choice (E)
must be true before moving on.
Analyzing this choice is a lot like analyzing choice (B):
- We know that 95% of asthmatics also suffer from hay fever.
- We know that hay fever is much more common than asthma. So the total number of hay fever folks must go beyond the portion that overlaps with asthmatics. How much bigger is the overall population of people with hay fever? There's no way of telling, but we know it must be much bigger, because hay fever is much more common.
- As the population of people with hay fever gets bigger than that overlapping portion, the percentage of hay fever folks who also have asthma goes down, starting from 100%.
- If the percentage of hay fever folks who also have asthma drops to 95%, then the total number of hay fever folks would have to be equal to the total number of asthmatics. This is the only way that overlap would be the same % of both populations. But we know this can't be true, because hay fever is much more common than asthma!
- That's why we know that the percentage of hay fever folks who also have asthma must be lower than 95 percent. If this percentage were 95 or higher, than the number of hay fever folks would match the number of asthmatics. This would contradict the prompt, so it cannot be the case.
We still don't know precisely, or even proportionally, how much bigger the population of hay fever folks is than the population of asthmatics. We don't need to. We've inferred that more than 5% of hay fever folks don't have asthma, so we'll keep (E) and move on.
I hope this helps!
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