In a survey,it was found that 10% of the students who are susceptible

Question

In a survey,it was found that 10% of the students who are susceptible to tuberculosis are less than 20 years of age and 40% of the students who are not susceptible to tuberculosis are more than or equal to 20 years of age.If 9% of the total students are more than or equal to 20 years of age and are susceptible to tuberculosis,then what percentage of the students,that are 20 years old or more,are not susceptible to tuberculosis?

A) 20%
B) 36%
C) 45%
D) 54%
E) 80%

A) 20% 
B) 36% 
C) 45% 
D) 54% 
E) 80%

xalemsharan · Accepted Answer

Imo, option E. Below is the solution, imo. IMG_20180528_143654_1.jpg Thanks and regards, Sharan Salem

WizakoBaskar · Answer

Let T be the percent of students susceptible to TB and N be the percent of students who are not susceptible to TB. 
So, T + N = 100

Let L be the percent of students less than 20 years of age and G be the percent of students who are 20 years or older.
So, L + G =100

10% of the students who are susceptible to tuberculosis are less than 20 years of age
Therefore, 90% of the students who are susceptible to tuberculosis are 20 years or older. i.e,. 90% of T is 20 years or older. --- (1)
9% of the total students are more than or equal to 20 years of age and are susceptible to tuberculosis --- (2)

Equating (1) and (2), 90% of T = 9%
So, T = 10%. 
i.e., 10% of the students are susceptible to TB.

Therefore, 90% of the students are not susceptible to TB.
40% of the students who are not susceptible to tuberculosis are more than or equal to 20 years of age.
40% of 90% of students are 20 years old or more ,are not susceptible to tuberculosis = 36% of students.

Choice B.

The attached table makes it easier to run through the process.

US09 · Answer

Nice approach, but isn't the question asking : what percentage of students  that are 20 years old or more  are not susceptible to T? In my opinion, it should be (0.4N/ 0.4N + 0.9T)*100 = (3.6T/4.5T)*100 = 80%. Please correct me if my approach is wrong.

Naren7 · Answer

What is the correct answer?

Sent from my T1 7.0 using  GMAT Club Forum mobile app

ScottTargetTestPrep · Answer

We can divide the students into the following 4 groups (with the variables denoting the number in each):

1) ≥ 20 years of age and susceptible to tuberculosis = a

2) ≥ 20 years of age and not susceptible to tuberculosis = b

3) < 20 years of age and susceptible to tuberculosis = c

4) < 20 years of age and not susceptible to tuberculosis = d

We are given that 0.1(a + c) = c and 0.4(b + d) = b and 0.09(a + b + c + d) = a. We need to find b/(a + b).

Multiplying the first equation by 10, we have a + c = 10c → a = 9c → c = a/9.

Multiplying the second equation by 5, we have 2b + 2d = 5b → 2d = 3b → d = 3b/2.

Multiplying the third equation by 100, we have 9a + 9b + 9c + 9d = 100a. Substituting c = a/9 and d = 3b/2, we have:

9a + 9b + 9(a/9) + 9(3b/2) = 100a

9a + 9b + a + 27b/2 = 100a

18a + 18b + 2a + 27b = 200a

45b = 180a

b = 4a

So b/(a + b) = 4a/(a + 4a) = 4a/(5a) = 4/5 = 80%

Answer: E

GMATGuruNY · Answer

Every student is EITHER susceptible OR not.
Every student is EITHER more than or equal to 20 OR less than 20.
For an either/or problem, use a DOUBLE-MATRIX to organize the data.

Let S = susceptible, NS = not susceptible, M = more than or equal to 20 and L = less than 20.
Let the total number of paintings = 100.
The following matrix is yielded:
 https://thumb.ibb.co/dd0Kpo/matrix_susceptible_and_20_0.png

9% of the total students are more than or equal to 20 years of age and are susceptible to tuberculosis ..
The following matrix is yielded:
 https://thumb.ibb.co/drkfvT/matrix_susceptible_and_20_1.png

10% of the students who are susceptible to tuberculosis are less than 20 years of age .
Implication:
The 9 students who are susceptible and older constitute 90% of the total number of students who are susceptible:
 9 = \frac{9}{10}S 
 S = 10 .
The following matrix is yielded:
 https://thumb.ibb.co/bYqfvT/matrix_susceptible_and_20_2.png

40% of the students who are not susceptible to tuberculosis are more than or equal to 20 years of age. 
Since  \frac{2}{5}  of the 90 non-susceptible students =  \frac{2}{5} * 90 = 36 , the following matrix is yielded:
 https://thumb.ibb.co/mT3YFT/matrix_susceptible_and_20_final.png

Of the students who are 20 years old or more, what percentage are not susceptible to tuberculosis? 
In the resulting matrix:
 \frac{(NS-and-M)}{(total-M)} = \frac{36}{45} = \frac{4}{5}  = 80%.

E

Archit3110 · Answer

2x2 matrix
---<20---->=20---total
YTB--1-----9-------10
NTB--54---36-------90
total--55---45-------100

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

36/45= 80%
IMO E

Kinshook · Answer

Given: 1. In a survey,it was found that 10% of the students who are susceptible to tuberculosis are less than 20 years of age and 40% of the students who are not susceptible to tuberculosis are more than or equal to 20 years of age. 2. 9% of the total students are more than or equal to 20 years of age and are susceptible to tuberculosis. Asked: What percentage of the students,that are 20 years old or more,are not susceptible to tuberculosis? Screenshot 2020-04-29 at 11.27.14 PM.png The percentage of the students,that are 20 years old or more,are not susceptible to tuberculosis = 36%/45% = 80% IMO E MRkiso7ve_8

hkkat · Answer

xalemsharan , can you help me out to clarify this part?

total students: x+y

9% * (X+Y) = 90% of X

I don't understand it, a step before that it is 9%/x = 90%/X+Y ?

Thank you for your time

bumpbot · Answer

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In a survey,it was found that 10% of the students who are susceptible

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