Critical Reasoning

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.
B.Asthma is a prerequisite for the development of hay fever.
C.Those who have neither hay fever nor asthma comprise less than 5 percent of the total population.
D.The number of people who have both of these ailments is greater than the number of people who have only one of them.
E.The percentage of people suffering from hay fever who also have asthma is lower than 95 percent

This is a pretty "mathy" CR question. These are often pretty tricky.

PREMISES:
- 95% of asthma sufferers have hay fever.
- Hay fever is MORE COMMON than asthma

Let's say that we have a population of 1000 people and 100 people have asthma. The first premise tells us that 95 people suffer from BOTH asthma AND hay fever.
Since hay fever is more common, the number of hay fever sufferers must be GREATER than 100.
So, there must be 6 or more people who have hay fever but not asthma.


A.Hay fever is a prerequisite for the development of asthma.
Since there are people who have asthma but not hay fever, this statement is not supported. ELIMINATE A

B.Asthma is a prerequisite for the development of hay fever.
Since there are people who have hay fever but not asthma, this statement is not supported. ELIMINATE B.

C.Those who have neither hay fever nor asthma comprise less than 5 percent of the total population.
In our example above, it could be the case that the MAJORITY of the population has neither hay fever nor asthma. ELIMINATE C.

D.The number of people who have both of these ailments is greater than the number of people who have only one of them.
In our example above, we already showed that there are more people with asthma only than with both. ELIMINATE D.

NOTE: By the process of elimination, we could just choose E, and move onto the next question. Let's examine it for "fun"

E.The percentage of people suffering from hay fever who also have asthma is lower than 95 percent
In other words, (# of people with BOTH hay fever AND asthma)/(# of people with people with hay fever) < 0.95
This is true.
Check our example, we have (# of people with BOTH hay fever AND asthma)/(# of people with people with hay fever) = 95/(some number GREATER than 100)
= less than 0.95

Answer: E

Cheers,
Brent