Not a difficult problem but a little bit tricky

Considering that the numbers are in percentages and weird, especially the 9%. Difficult to pik a number to have a net number. However, the answer choices are far apart so we can also work by estimation

TS= total students

These can be divided into two categories : T with tubercolosis and those without NO tubercolosis

Those with T can be divided further into those \(\geq 20\) and those < 20 years

Now, in those kind of question usually is best to look at the phrase we do have in the end, to have the overall total of people involved. In this case

If 9% of the total students are more than or equal to 20 years of age and are susceptible to tuberculosis

So we do have T and \(\geq 20\) are 9%

This means that the other three categories involved T and <20, NT and \(\geq 20\), NT and <20 are 91%

Then we have that the category T and <20 is 10%

Therefore the two categories NT and \(\geq 20\) , NT and <20 are 81%

Of this last categories NT and \(\geq 20\) is 40% = 38.4 and NT and <20 is 48.6

The question is

what percentage of the students, that are 20 years old or more, are not susceptible to tuberculosis?

means \(\frac{38.4}{48.6}=66.6\)

The other answer choices are inferior to this value. So the answer must be E

Can someone please explain this with matrix solution approach is that possible??

** srry for the dashes and slashes, the text editor does not format white spaces properly.

Let x equal total number of susceptible, y be the total of non susceptible, and the total number of students be 100. You can also represent the total number of students with a variable but choosing 100 is always a good strategy for these types of questions because 100 works well with percentages.


||||||||||||||||||||||||younger than 20||||||||older or equal than 20|||||||||||||Total

Susceptible ---------------0.10x------------------------0.9x -------------------------------x

Not Susceptible------------0.6y------------------------0.4y--------------------------------y

Total-------------------------------------------------------z---------------------------------100


If 10% of the total people who are susceptible are younger than 20, then the remaining 90% of the total people who are susceptible must equal or older than 20.
Susceptible AND younger than 20 = 0.10x, and susceptible and equal to or older than 20 = 0.9x

If 40% of the total who are not susceptible are older than or equal to 20 years old, then the remaining 60% of those who are not susceptible must be younger than 20
Not susceptible and younger than 20 = 0.6y, and not susceptible and older than or equal to 20 = 0.4y

9% of the the total amount of people are equal to or older than 20 and susceptible
0.9(100) = 9 <--- 9 people are older than or equal to 20 and susceptible, therefore 9 = 0.9x --> x = 10

Now look down on the total column, since x = 10, then y must equal 90. x = 10, y = 90

let z equal the number of total people who are equal to or older than 20. To find the percentage of people who are equal to or older than 20 who are not susceptible, you need to divide 0.4y by z

z = 0.9x + 0.4y = 0.9(10) + 0.4(90) = 45
0.4y = 0.4(90) = 36

36 / 45 = 0.8

Therefore, the answer is 80%.

awwwwwwwwwww

what amazing solution

Assume there are 100 students.

Since 90% of the susceptible students are at least 20 years old, and this group represents 9 students, the total number of susceptible students is 10. Therefore, 90 students are not susceptible.

Of those 90, 40% are at least 20 years old:

0.40×90=36

So the total number of students aged 20 or older is:

9+36=45

Therefore:

36/45×100=80%

Answer: E. 80%