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# Highmont private school polled the graduating class of 125 for the mus

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Math Expert
Joined: 02 Sep 2009
Posts: 55274
Highmont private school polled the graduating class of 125 for the mus  [#permalink]

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20 Jul 2017, 21:42
00:00

Difficulty:

75% (hard)

Question Stats:

39% (02:39) correct 61% (03:37) wrong based on 38 sessions

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Highmont private school polled the graduating class of 125 for the musical genres they listen to. 88% indicated at least one of the following genres: indie rock, classical, country, and electronica. Of these students, 40% responded they listen to only one of the four genres. The average number of students within each distinct group of those who listen to exactly two genres is greater than the total number of those who listen to exactly three genres. If the only lack of overlap in musical tastes was in country and electronica, what is the greatest number of students who could listen to classical, country, and indie rock?

(A) 5
(B) 6
(C) 9
(D) 10
(E) 13

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Joined: 24 Apr 2016
Posts: 331
Re: Highmont private school polled the graduating class of 125 for the mus  [#permalink]

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21 Jul 2017, 10:28
1
1
Given:

88% indicated at least one of the following genres: indie rock, classical, country, and electronica = 0.88 * 125 = 110

Of the 110, 40% responded they listen to only one of the four genres = 0.4 * 110 = 44 = A + B + C + D

Remaining = 110 - 44 = 66 = (E + F + G + H + I) + (K + L) ==> (E + F + G + H + I) = 66 - (K + L)

The average number of students within each distinct group of those who listen to exactly two genres is greater than the total number of those who listen to exactly three genres

==> (E + F + G + H + I)/5 > (K + L)

==> [66 - (K + L)]/5 > (K + L)

==> 66 - K - L > 5K + 5L

==> 66 - 6L > 6K

==> 11 - L > K

==> K < 11 - L

what is the greatest number of students who could listen to classical, country, and indie rock?

So K will be greatest when L is the least, i.e. L = 1

==> K < 11 - 1

==> K < 10, therefore K = 9

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Re: Highmont private school polled the graduating class of 125 for the mus   [#permalink] 21 Jul 2017, 10:28
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