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# At Typico High School, 60% of the students like dancing

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At Typico High School, 60% of the students like dancing  [#permalink]

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Updated on: 08 Mar 2019, 03:53
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Difficulty:

95% (hard)

Question Stats:

32% (02:08) correct 68% (02:25) wrong based on 37 sessions

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At Typico High School, 60% of the students like dancing, and the rest dislike it. Of those who like dancing, 80% say that they like it, and the rest say that they dislike it. Of those who dislike dancing, 90% say that they dislike it, and the rest say that they like it. What fraction of students who say they dislike dancing actually like it?

(A) 10% (B) 12 % C) 20% (D) 25% (E) 100/3 %

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Originally posted by Noshad on 08 Mar 2019, 03:35.
Last edited by Noshad on 08 Mar 2019, 03:53, edited 1 time in total.
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Re: At Typico High School, 60% of the students like dancing  [#permalink]

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08 Mar 2019, 03:49
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At Typico High School, 60% of the students like dancing, and the rest dislike it. Of those who like dancing, 80% say that they like it, and the rest say that they dislike it. Of those who dislike dancing, 90% say that they dislike it, and the rest say that they like it. What fraction of students who say they dislike dancing actually like it?

(A) 10% (B) 12 % C) 20% (D) 25% (E) 100/3 %

Say there are 100 students.

Students who like dancing = 60% of 100 = 60
Of these, 80% of 60 SAY they like it = 48 SAY they like it
Rest SAY they don't like it = 12 SAY they don't like it

Students who dislike dancing = 40% of 100 = 40
Of these, 90% of 40 SAY they dislike it = 36 SAY they dislike it
Rest SAY they like it = 4 SAY they like it

So 12 + 36 = 48 SAY they dislike dancing. Of these 12 actually like it so 12/48 = 25%

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At Typico High School, 60% of the students like dancing  [#permalink]

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08 Mar 2019, 04:10
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Assuming that there is 100 students, we can distribute the given percentages into a table.
Total number who say dislike = 48, from which 12 actually like,
so the fraction $$= \frac{12}{48} = 0.25 = 25$$%
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Re: At Typico High School, 60% of the students like dancing  [#permalink]

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08 Mar 2019, 04:17

I did not understand the methodology.

Can you please explain with a brief solution.
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Re: At Typico High School, 60% of the students like dancing  [#permalink]

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08 Mar 2019, 10:00
At Typico High School, 60% of the students like dancing, and the rest dislike it. Of those who like dancing, 80% say that they like it, and the rest say that they dislike it. Of those who dislike dancing, 90% say that they dislike it, and the rest say that they like it. What fraction of students who say they dislike dancing actually like it?

(A) 10% (B) 12 % C) 20% (D) 25% (E) 100/3 %

solved using 2x2 matrix

------- like dancing --------- dislike dancing--------total
like-----48------------------4--------------------52
dislike--12-----------------36--------------------48
total----60-----------------40--------------------100

fraction of students who say they dislike dancing actually like it : 12/48
= 25%
IMO D
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Re: At Typico High School, 60% of the students like dancing   [#permalink] 08 Mar 2019, 10:00
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