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Re: In a survey,it was found that 10% of the students who a

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Re: In a survey,it was found that 10% of the students who a [#permalink] New post 26 Mar 2017, 22:41
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harigrestudent97 wrote:
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%
[Reveal] Spoiler: OA
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Re: In a survey,it was found that 10% of the students who a [#permalink] New post 27 Mar 2017, 12:33
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Please share the source of the question. The question seems to be strangely worded.
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Re: In a survey,it was found that 10% of the students who a [#permalink] New post 14 Apr 2017, 10:33
Answer :

Try to assume a certain number of students i.e 100. The question states 10 % are susceptible and are less than 20 years of age. Hence the student count becomes 90. The question then states that 40 % are not susceptible and are more then 20 years of age. Hence we get 36 students from this statement.Finally the question states 9 % of total students are susceptible and more than 20 years of age, which yields 9. Hence the percentage of students not susceptible and are more than 20 years of age is 36/45 x 100 = 80 %. Answer is E
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Re: In a survey,it was found that 10% of the students who a [#permalink] New post 26 Sep 2017, 06:14
This question seems to be very popular on other GRE forums, unless there is no source specified anywhere.

However, here is my try:

We know 9% of the total are >20 and susceptible (so 9 out of our hypothetical 100 people). We know these 9 are 90% of the susceptible (b/c we're told that 10% of the susceptible are <20). That means there must be 10 total susceptible.

How many of the remaining 90 are not susceptible? 40% according to the question, so 36.

Then, we can take this 36 and divide by the total number of people >20:

36/[9 + 36] = 0.8, or 80%.

Answer E!
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Re: In a survey,it was found that 10% of the students who a [#permalink] New post 28 May 2018, 18:22
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harigrestudent97 wrote:
harigrestudent97 wrote:
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%


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
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