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Math Expert V
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In a survey,it was found that 10% of the students who are susceptible  [#permalink]

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Question Stats: 33% (03:11) correct 67% (03:15) wrong based on 150 sessions

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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%

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GMAT 1: 720 Q51 V36 In a survey,it was found that 10% of the students who are susceptible  [#permalink]

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Bunuel 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%

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.
Attachments percent-table.pdf [93.46 KiB]

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GMAT 1: 560 Q42 V25 GMAT 2: 570 Q43 V27 GMAT 3: 710 Q49 V39 Re: In a survey,it was found that 10% of the students who are susceptible  [#permalink]

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Bunuel 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%

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.

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.
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Re: In a survey,it was found that 10% of the students who are susceptible  [#permalink]

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Bunuel 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%

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Posts: 15
Re: In a survey,it was found that 10% of the students who are susceptible  [#permalink]

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2
Bunuel 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%
Imo, option E.
Below is the solution, imo.
Attachment: IMG_20180528_143654_1.jpg [ 62.56 KiB | Viewed 3694 times ]

Thanks and regards,
Sharan Salem
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Thanks and regards,
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Re: In a survey,it was found that 10% of the students who are susceptible  [#permalink]

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Bunuel 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%

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Re: In a survey,it was found that 10% of the students who are susceptible  [#permalink]

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1
Bunuel 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%

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: 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: 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: 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: 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%.

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Re: In a survey,it was found that 10% of the students who are susceptible  [#permalink]

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Bunuel 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%

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 Re: In a survey,it was found that 10% of the students who are susceptible   [#permalink] 14 Jul 2019, 08:56
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