okdongdong wrote:
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.
The correct answer would be E.
It is easy to eliminate A and B. Also, we can say nothing about C since, we have no information about the number of people having neither.
This leaves us with D and E: Now suppose the number of people who have asthma is 100, 95 of these have hay fever. And since the number of people with asthma is less than the number of people with hay fever, let us assume that the number of people with hay fever is 110. Total number of people = (5+95+15 = 115)
Now, 95% of people with asthma also have hay fever, and we also know that the number of people with hay fever is higher.
So, the same number of people which is common between the two will make a smaller percentage over a larger base, i.e,
95/100 > 95/115. This will hold true taking any numbers. So, E should be the correct one here!
D states that the number who have both is greater than those who have only one.
If Asthma= 100, both= 95, hay fever = 200,
Now here, again 95/100 > 95/205 . So, E holds true, but D would not hold true: number of people having both (95)< number having only 1 (5+105=110).Thus, E is the correct answer choice.
Hi
mikemcgarry, Can you please review my reasoning and explanations and let me know if there is any flaw in the same. Thanks