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Out of 50 people surveyed, 20 said they liked Rock, 23 said they liked

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Joined: 07 Jun 2018
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Out of 50 people surveyed, 20 said they liked Rock, 23 said they liked  [#permalink]

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New post 27 Dec 2018, 02:05
3
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A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

64% (03:07) correct 36% (03:13) wrong based on 58 sessions

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Out of 50 people surveyed, 20 said they liked Rock, 23 said they liked Hip Hop and 27 said they liked Alternative. In addition, 7 people said they liked both Rock and Hip Hop, and of those 7, 3 said they liked Alternative as well. If 10 only liked Hip Hop, 14 liked only Alternative and all of the 50 surveyed people liked at least one of the three types of music, how many liked Rock?

a. 8
b. 9
c. 12
d.13
e. 17
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Re: Out of 50 people surveyed, 20 said they liked Rock, 23 said they liked  [#permalink]

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New post 27 Dec 2018, 04:36
Top Contributor
Please refer the attached image for the initial picture of the problem:

Given that 7 people like Rock and Hip hop and of those 7, 3 also like Alternative => 3 likes all three and (7-3=4) like only Rock and Hip Hop.

Now adding everything to get total for Hip Hop
4 + 3 + (like only Hip Hop and Alternative) + 10 = 23
Like only Hip Hop and alternative = 23 - 10 - 4 - 3 = 6

Now adding everything to get total for Alternative
3 + 6 + (like only Rock and Alternative) + 14 = 27
Like only Rock and Alternative = 27 - 14 - 6 - 3 = 4

Now adding everything to get total for Rock
3 + 4 + (like only Rock) + 4 = 20
Like only Rock = 20 - 4 - 4 - 3 = 9

So, Answer will be B

Hope it helps!
Jazzmin wrote:
Out of 50 people surveyed, 20 said they liked Rock, 23 said they liked Hip Hop and 27 said they liked Alternative. In addition, 7 people said they liked both Rock and Hip Hop, and of those 7, 3 said they liked Alternative as well. If 10 only liked Hip Hop, 14 liked only Alternative and all of the 50 surveyed people liked at least one of the three types of music, how many liked Rock?

a. 8
b. 9
c. 12
d.13
e. 17

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Re: Out of 50 people surveyed, 20 said they liked Rock, 23 said they liked   [#permalink] 27 Dec 2018, 04:36
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Out of 50 people surveyed, 20 said they liked Rock, 23 said they liked

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