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

Question

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

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

quantumliner · Accepted Answer

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

Answer is C

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garcmillan · Answer

Hi all,

This is a good question to practice overlapping sets. It's a long one so it would only appear in high scores (+700)

Solution is provided in the image below

ANSWER C

chacinluis · Answer

"The average number of students within each distinct group of those who listen to exactly two genres"
this phrase is a bit confusing. My interpretation would be let's find the average of how many students in each distinct group listen to exactly two genres.

So we would get 
  /4

But one of the answers above gets the average of students that listen to exactly two genres per genre.
(total # of students that listen to exactly two genres)/(# of genres)

Which is the right interpretation?

EgmatQuantExpert · Answer

To Find

• The greatest number of students who could listen to classical, country, and indie rock.

Approach and Working Out

• We can consider the image below and only assume the variables with respect to a and b.
 o The minimum for electronica, Indie rock, and classical can be 1.
o Hence, the combination of classical, country, indie rock is taken as b – 1.

• We can do the following steps to get to the numbers.
 o 88% of 125 = 110
o 40% of 110 = 44
o Remaining = 66.
o 5a + b = 66

• Here, a > b.
 o If a = b then,
o 6b = 66
o b = 11

• But we know that a > b hence the maximum value b can take is 10.
 o b – 1 = 9

Correct Answer: Option C

ScottTargetTestPrep · Answer

Solution:
 
We have 0.88(125) = 110 students who listen to at least one of the four genres. We also have 0.4(110) = 44 students who listen to exactly one of the four genres. This leaves us 110 - 44 = 66 students who listen to more than one genre. However, since there is no overlap in country and electronica, we don't have any students who listen to all four genres. In other words, the 66 students either listen to exactly two genres or exactly three genres.

The two-genre groups are: indie rock & classical, indie rock & country, indie rock & electronica, classical & country, and classical & electronica.

The three-genre groups are: indie rock & classical & country and indie rock & classical & electronica.

Let's say the average number of students in the two-genre groups is n and the average number of students in the three-genre groups is m, we have:

4n + 2m = 66

2n + m = 33

We are also given that n > 2m. Therefore, 2n > 4m. So 2n + m > 4m + m = 5m. That is, we have:

33 > 5m

6.6 > m

However, since 2n + m = 33 and n must be an integer, we see that m must be odd. In that case, the largest value of m is 5. Since m is the average number of students in the 2 three-genre groups, the total number of students of the 2 three-genre groups is 2 x 5 = 10. Since each of these 2 groups has at least 1 student, we can assume that the "indie rock & classical & electronica" group has exactly 1 student, so that the number of students in the "indie rock & classical & country" group will be 9, which is the maximum number of students it can have.

Answer: C

parth111 · Answer

Hello, 
Here, in your solution, why can't J be 0?

bumpbot · Answer

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

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