Over 95 percent of people who have asthma, a bronchial condition...

Question

Which of the following most logically completes the passage?

Over 95 percent of people who have asthma, a bronchial condition, suffer from hay fever, a susceptibility to allergic inflammation of the nasal passages. The percentage of hay-fever sufferers who also have asthma has to be lower than 95 percent, however, since _____.

(A) hay fever can make the development of asthma more likely
(B) asthma is a much less common ailment than hay fever
(C) medically, asthma is a much more serious condition than hay fever
(D) only a small percentage of people suffer from hay fever
(E) the number of people who have both of these ailments is greater than the number of people who have only one of them

Source: EA (Tagging as GMAT Prep, as no option for EA, although most EA questions tend to share the same pool as GMAT Prep)

TargetMBA007 · Answer

https://gmatclub.com/forum/fact-asthma- ... 18649.html - related question

Yugank_Aggarwal · Answer

Why is it B and not E?
B doesn't really make sense as we are not told about how frequent or how severe asthma is or how frequently asthma happens.

On the other hand, E does offer us an explanation of why the number might be lower.

Can someone please shed some light on this?

Thank you

TargetMBA007 · Answer

The stem states that over 95% of people with asthma also have hay fever. This implies that nearly all asthma sufferers are part of the larger group of hay fever sufferers. If asthma were as common or more common than hay fever, the percentage of hay fever sufferers who also have asthma would be close to or above 95%. However, because asthma is much less common than hay fever, the set of hay fever sufferers is much larger, and therefore, the percentage of hay fever sufferers who also have asthma is much lower. Hence, answer (B) correctly explains the observed percentages.

Let's test some numbers

Asthma: 100
Asthma patients who also have HF: 96 (over 95% of all Asthama patients)

B says, the total no. of people who have HF is "MUCH higher" than the total no. of people who have asthma. Let's use extreme values to test this
Total Hay Fever patients: 1000
Total Asthama patients: 100
% = 10% (which is lower than 95%)

Now, technically we can say use these numbers, even though a 10% diff is not necessarily much higher, but note that as 95% of 900 people would need to have HF as per the statement in the stem, as the no. of Asthama patients go up, so will the no. of hay fever patients, but the opposite is not necessarily the case.
Total Hay Fever patients: 1000
Total Asthama patients: 900
% = 90% (which is lower than 95%)

Adarsh_24 · Answer

Let’s think in extreme,

Fever and AIDS.

The percentage of people with AIDS having fever is greater than people with fever having AIDS.
Why? Because the fever is very common illness than AIDS. so chances of AIDS patient getting fever is higher than fever patient getting AIDS( for explanation’s sake let’s forget that AIDS can cause fever etc. complexities)

Option E says that intersection of 2 sets are larger than non-intersection parts. Intersection is larger doesn’t say why one set has a preference over the other set in the intersecting part.

siddhantvarma · Answer

Let number of poeple who have Asthama = 100
People with Asthama + Hay fever = 95
Now we’re saying that hay-fever sufferers who also have asthma has to be lower than 95%
Let x : number of people who have hay fever ONLY
Total number of people who have Hay fever = 95 + x
Number of people who have both Asthama + Hay fever = 95

Percentage of hay-fever sufferers who also have Asthama: (95/95+x)*100 < 95 => 9500 < 95*95 + 95x
Divide the above inequality by 95;
100 < 95 + x => x > 5

Number of people who have hay fever ONLY is at least 5
Total number of people who have hay fever = 95 + x => at least 100
We started with number of people who have Asthama to be 100
From the above, we know that number of people with hay fever will be > number of people with Asthama

(B) tells us exactly that

Advait01 · Answer

Let number of poeple who have Asthama = 100
People with Asthama + Hay fever = 95
Now we’re saying that hay-fever sufferers who also have asthma has to be lower than 95%
Let x : number of people who have hay fever ONLY
Total number of people who have Hay fever = 95 + x
Number of people who have both Asthama + Hay fever = 95

Percentage of hay-fever sufferers who also have Asthama: (95/95+x)*100 < 95 => 9500 < 95*95 + 95x
Divide the above inequality by 95;
100 < 95 + x => x > 5

Number of people who have hay fever ONLY is at least 5
Total number of people who have hay fever = 95 + x => at least 100
We started with number of people who have Asthama to be 100
From the above, we know that number of people with hay fever will be > number of people with Asthama

(B) tells us exactly that

Over 95 percent of people who have asthma, a bronchial condition...

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Over 95 percent of people who have asthma, a bronchial condition...

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