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# In a certain math class, one-tenth of the students cheated on a test

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Math Expert
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In a certain math class, one-tenth of the students cheated on a test  [#permalink]

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01 Nov 2019, 04:17
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Difficulty:

85% (hard)

Question Stats:

51% (02:28) correct 49% (02:32) wrong based on 137 sessions

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In a certain math class, one-tenth of the students cheated on a test and were caught but one-fifth of the students who cheated did not get caught. What fraction of the class cheated on the test?

(A) 21/100
(B) 1/10
(C) 1/8
(D) 1/12
(E) 3/25

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Re: In a certain math class, one-tenth of the students cheated on a test  [#permalink]

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01 Nov 2019, 05:25
1
This question is slightly tricky if one reads it at one go. Conversion from words to maths is key to this question.
The question asks for the ratio of students cheated to a total no of students. Say, total= 100 students.
As per the question, one-tenth of the students cheated on a test and were caught. So 1/10th of total = 10 students.
Now comes the tricky part. The question states that 1/5th of the students who cheated (not the students) didn't get caught. Let S be students who cheated. So 1/5th of S didn't get caught that means 4/5th got caught. We already have 10 students who cheated and got caught.
4/5th of S=10. S=50/4. [S cannot be a fraction, but 100 was an arbitrary number, so ignore whatever value S has here].
Finally, Students cheated to total students = S/100 = (50/4)/100 = 1/8.
Hence, C is the correct answer.
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Re: In a certain math class, one-tenth of the students cheated on a test  [#permalink]

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01 Nov 2019, 05:35
Bunuel wrote:
In a certain math class, one-tenth of the students cheated on a test and were caught but one-fifth of the students who cheated did not get caught. What fraction of the class cheated on the test?

(A) 21/100
(B) 1/10
(C) 1/8
(D) 1/12
(E) 3/25

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let total students = 100
who cheated and got caught= 1/10 * 100 = 10
1/5th of students who cheated did not get caught so 4/5 of students cheated and got caught ; i.e 4x/5 =10 ; x= 50/4 students got caught
fraction ; 50/4* 1/100 = 1/8
IMO C
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Re: In a certain math class, one-tenth of the students cheated on a test  [#permalink]

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01 Nov 2019, 06:44
let the total number students = 40

lets number of students who cheated = x

1/10*40 = cheated+caught= 4 students

4/5(x)= 4

therefore total number of students who cheated= 5

ratio= 5/40= 1/8

option C is the correct option!
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Re: In a certain math class, one-tenth of the students cheated on a test  [#permalink]

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02 Nov 2019, 02:17
lets say total no of students is 100
total nos of studetns who cheated is x
cheated and caught=1/10=10
cheated and not caught=x/5

therefore, 10+x/5=x, solving for x=12.5=1/8.Ans C
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Re: In a certain math class, one-tenth of the students cheated on a test  [#permalink]

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02 Nov 2019, 06:31
2
Bunuel wrote:
In a certain math class, one-tenth of the students cheated on a test and were caught but one-fifth of the students who cheated did not get caught. What fraction of the class cheated on the test?

(A) 21/100
(B) 1/10
(C) 1/8
(D) 1/12
(E) 3/25

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Let the total number of students = 100
As per the below table structure,

10 + X/5 = X
--> 10 = 4X/5
--> X = 10*5/4 = 25/2

Number of students cheated = 25/2
--> Fraction of class cheated = 25/2/100 = 1/8

IMO Option C
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Re: In a certain math class, one-tenth of the students cheated on a test  [#permalink]

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19 Nov 2019, 01:33
Bunuel wrote:
In a certain math class, one-tenth of the students cheated on a test and were caught but one-fifth of the students who cheated did not get caught. What fraction of the class cheated on the test?

(A) 21/100
(B) 1/10
(C) 1/8
(D) 1/12
(E) 3/25

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Let's assume there are 100x students.
Now, 10x cheated and were caught.
Now 10x = $$\frac{4}{5}*cheated$$.
so cheated = 12.5x
and the proportion of cheated in class = $$\frac{12.5x}{100x}$$ = $$\frac{1}{8}$$
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Re: In a certain math class, one-tenth of the students cheated on a test  [#permalink]

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23 Dec 2019, 05:37
1
Let number of students = s
Let number of cheaters = c

Given: No. of cheaters who got caught = $$\frac{s}{10}$$
And, No. of cheaters who did not get caught = $$\frac{c}{5}$$

Therefore,
$$\frac{s}{10} + \frac{c}{5} = c,$$
$$\frac{s}{10} = \frac{4c}{5},$$
$$\frac{c}{s} = \frac{5}{40} = \frac{1}{8}$$

Hope this helps.
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Re: In a certain math class, one-tenth of the students cheated on a test  [#permalink]

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26 Dec 2019, 03:28
2 x 2 grid method would be best for this problem.
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In a certain math class, one-tenth of the students cheated on a test  [#permalink]

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28 Dec 2019, 07:51
Bunuel wrote:
In a certain math class, one-tenth of the students cheated on a test and were caught but one-fifth of the students who cheated did not get caught. What fraction of the class cheated on the test?

(A) 21/100
(B) 1/10
(C) 1/8
(D) 1/12
(E) 3/25

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Assume 100 students
one tenth cheated and caught 10 no
one fifth of those cheated did not get caught so 4/5 th get caught
so four fifth caught equals to 10 no
so all of those cheated equals to 12.5 no ( fraction is ok as i have assumed 100 )

percentage of cheated = 12.5/100 =1/8
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In a certain math class, one-tenth of the students cheated on a test   [#permalink] 28 Dec 2019, 07:51
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