Fact: Asthma, a bronchial condition, is much less common

First thing to note is that the answer MUST be true given the facts.

A) We are told that over 95 percent of people who have asthma suffer from hay fever, so it could be 96 percent which shows that hay fever is not a prerequisite for development of asthma, as for this to even be considered the case it should be 100 percent.

B) This is similar to B, but also knowing that asthma is less common than hay fever rules this out.

C)We have no way of proving this from the data given.

D)The number of people with asthma is less common than the number of people with hay fever and 95% of these have hay fever so there is no way of proving whether this is true. As we do not know the percent of people with the more common hay fever who have asthma.

E) This is true as hay fever is much more common (read as there being a LOT more hay fever sufferers) so even if 100 percent of people who had asthma had hay fever, this would not be 95% of hay fever sufferers. Because then the statement would read that they are almost as common.

Simplified (using numbers):
Hay FeverMUCH more common than Asthma (1000 hay fever vs 100 asthma)
95% of Asthma sufferers have hay fever (95 have both)
So less than 95% who have the more common hay fever have asthma (1000 hay fever, 95 both)

Hope this helps
So less than

It is possible to mentally solve this question.
PASSAGE

Asthma, a bronchial condition, is much less common ailment than hay fever, an allergic inflammation of the nasal passages.

From this, we can assume some representative numbers. Say, 100 people have asthma while 500 people have hay fever, out of a population of 1000.

Fact: Over 95 percent of people who have asthma also suffer from hay fever.

96 of those who have asthma have hay fever as well.
So 4 have only asthma
96 have both
404 have only hay fever.
496 are healthy.

Now let us look at the options.
Answer Choice Analysis

A- Talks about prerequisites. We are given no information that states one is a prerequisite for the other. In fact, there are people with only one and not the other for both diseases. So, this can't be true.

B- Same explanation applies here as well!

C-Those who have neither are almost 50% of our considered population. So, definitely not true.

D-People who have both-96. People who have only one- 4+404=408. Not less than 96. Hence option D is clearly wrong!

That leaves E- Number of people suffering from hay fever-500
Those who have asthma among them- 96
The percentage- 96x100/500 is definitely smaller than 95.
Clearly, option E is correct!

The support for the OA of this question is actually bizarrely simple.

As people have discussed, one can eliminate A, B, C, and D.

So, we are left with E.

All of the choices other than E can be proven wrong through math. E is different, but people are still seeking to prove it correct by using math.

The truth is that there is no way to prove E by using math. Rather, there is one simple statement that supports E.

"Asthma, a bronchial condition, is much less common ailment than hay fever"

95% is not "much less common". "much less common" is not 95% or even 90%. "much less common" has to be something much less, perhaps 70%.

So, the words "much less common" are the only support we have for E. That support is not great, but fortunately, all of the other choices can be eliminated, and so this question is gettable, even though it's not that great of a question.

(E) I've found it by elimination all the other option choices.

So, if (E) is correct, please, explain why

I agree with E, but i certainly was tempted by D too.

The overlapped part of two population should be fewer than each of them.

This problem can be done by using a Venn Diagram as well

Consider given statement: Hay fever is much more common than Asthma and over 95% of people suffering from Asthma also suffer from Hay fever

St A: I don't think so. We have people with Asthma but not hayfever (Area in yellow)
St B: We have people with Hay fever but no Asthma. (Area in red)
St C: Those who have neither...the entire white area need not be less than 5% of the total population
St D: The no. of people who have both (In Black) is not greater than the ones who have one of the dieseases
St E: % of People suffering from Hay Fever +Asthma (Black) is less than 95% percent. Yes.

People who have Asthma and Hay Fever constitute 95% of people with Asthma ie. Black Area/ Yellow+ black Area = 95%

So Black Area (both)/ Red Area (Hay Fever) has to be less than 95 as Red is greater than Yellow ie. Hayfever is more common than Asthma.

Ans E

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?

A. Hay fever is a prerequisite for the development of asthma
Not possible, then 100% of people with Asthma would be having hay fever.
B. Asthma is a prerequisite for the development of hay fever
Might be possible, but 5 % people did not get the hay fever.
C. Those who have neither hay fever nor asthma comprise less than 5 percent of the total population
Out of scope.
D. The number of people who have both of these ailments is greater than the number of people who have only one of them
Can't say. # might be greater.
E. The percentage of people suffering from hay fever who also have asthma is lower than 95 percent.
This must be true. If it is not lower then fact 1 will become untrue.
Fact 1:Asthma, a bronchial condition, is much less common ailment than hay fever, an allergic inflammation of the nasal passages.

|------------BOTH-------------|---------------------
....At-most 94.9%...................at-least 5.1%.. } Hay fever
----|-------------BOTH------------|
5%...............95%.......... } Asthama

Pre-thinking - Asthma is much less common ailment than hay fever. ---- this says more people have HF then A.you can figure out "much less".
Although who ever has asthma 95% of them has hay fever.

let say A = 100 out of this 95 has HF. total of HF = 200
figures are for argument sake.

If the information given as facts above is true, which of the following must also be true?

A. Hay fever is a prerequisite for the development of asthma -- nothing as such mentioned. we don't know.

B. Asthma is a prerequisite for the development of hay fever --- nope else all/only 100 would have HF.

C. Those who have neither hay fever nor asthma comprise less than 5 percent of the total population --- Do we even know total population. This one is true but for that you have to use outside information.

D. The number of people who have both of these ailments is greater than the number of people who have only one of them --- 95 > 105 ?

E. The percentage of people suffering from hay fever who also have asthma is lower than 95 percent. --- True

Pure math (overlapping sets). Since Asthma < Hay Fever. Let's say 100<200, then if Asthma + Hay Fever from Asthma is 95/100 , and the same number 95 will be smaller than 95% from Hay fever, (95/200). See attachement below.

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.


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.


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).


We have absolutely no information about the total population, so we can't accept this statement. Eliminate choice (C).


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).


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!

GMATNinja karishma In E, the answer choice shouldn't have said 95 percent of the total population?

The passage tells us that:

• Asthma is "much less common" than hay fever -- so, many MORE people have hay fever than asthma
• "Over 95 percent of people who have asthma also suffer from hay fever" -- so, the vast majority of people with asthma also have hay fever

(E) discusses the "percentage of people suffering from hay fever who also have asthma." On a venn diagram, this would be overlap between the two populations.

We know that this overlap comprises over 95% of people who suffer from asthma. But how does the number of people in the overlap compare to the overall number of people who have hay fever?

Because the total number of people with hay fever is much GREATER than the number of people who have asthma, the number of people in the overlap must make up a SMALLER percentage of people with hay fever.

Think about it this way:

• [number of people with both asthma and hay fever/number of people with asthma] > 95%

The number of people with hay fever is much GREATER than the number of people with asthma, so:

• [number of people with both asthma and hay fever/number of people with hay fever] MUST be less than 95%.

Because of this, (E) is the correct answer. It isn't necessary to change (E) to compare people with asthma/hay fever to the total population.

I hope that helps!

Option Elimination - This is an inference question, so please be cautious of the outside information. The argument provides percentages, and the standard trap will talk about numbers. Moreover, we have two independent conditions, and the argument has no causal connection; a common trap would be establishing a casualty between the two.

A. Hay fever is a prerequisite for the development of asthma - Trying to establish causality when there is none in the argument. Distortion.

B. Asthma is a prerequisite for the development of hay fever - Trying to establish causality when there is none in the argument. Moreover, it contradicts the argument. Hay fever is more common than asthma, so how come asthma can be a prerequisite for hay fever? Distortion.

C. Those who have neither hay fever nor asthma comprise less than 5 percent of the total population - We have no idea about the "total population. Moreover, we don't even have absolute hay fever and asthma numbers to calculate the percentage. Out of scope.

D. The number of people who have both of these ailments is greater than the number of people who have only one of them - The argument doesn't even talk about number. Distortion.

E. The percentage of people suffering from hay fever who also have asthma is lower than 95 percent. - This is the only odd one out, but it's good to understand the meaning. Let's say, for the sake of discussion and clarity, we take numbers. The number of people with asthma is X, and those with hay fever is Y. Argument says Y is much higher than X. So Y>X. More than 95% of X is >0.95X; say it's 0.96X, so 0.96X/Y <95%? Yes. Remember, Y is much higher than X. Say X is 100 and Y is 200. 96/200 is certainly less than 95%. Why did we not consider the total population? Remember, this is an inference question. Have we been told about the total population in the argument anywhere? No. Also, it'll be a very sorry situation if the entire population has hay fever, asthma, or both. I get it: COVID, a pandemic, is an exception.