Last visit was: 20 Nov 2025, 03:30 It is currently 20 Nov 2025, 03:30
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 20 Nov 2025
Posts: 105,408
Own Kudos:
Given Kudos: 99,987
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,408
Kudos: 778,462
 [30]
2
Kudos
Add Kudos
28
Bookmarks
Bookmark this Post
Most Helpful Reply
User avatar
quantumliner
Joined: 24 Apr 2016
Last visit: 26 Sep 2018
Posts: 242
Own Kudos:
779
 [10]
Given Kudos: 48
Posts: 242
Kudos: 779
 [10]
6
Kudos
Add Kudos
4
Bookmarks
Bookmark this Post
General Discussion
User avatar
garcmillan
Joined: 24 Sep 2015
Last visit: 15 Sep 2020
Posts: 71
Own Kudos:
Given Kudos: 79
Location: Spain
Concentration: Strategy, Entrepreneurship
GPA: 3.9
WE:Management Consulting (Consulting)
Posts: 71
Kudos: 136
Kudos
Add Kudos
Bookmarks
Bookmark this Post
avatar
chacinluis
Joined: 17 Jan 2020
Last visit: 29 Nov 2020
Posts: 28
Own Kudos:
Given Kudos: 7
Posts: 28
Kudos: 12
Kudos
Add Kudos
Bookmarks
Bookmark this Post
"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
[(# of in Indie rock that listen to exactly two genres)+(# of in Classical that listen to exactly two genres)+(# of in Electronica that listen to exactly two genres)+(# of in Country that listen to exactly two genres)] /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?
User avatar
EgmatQuantExpert
User avatar
e-GMAT Representative
Joined: 04 Jan 2015
Last visit: 02 Apr 2024
Posts: 3,663
Own Kudos:
Given Kudos: 165
Expert
Expert reply
Posts: 3,663
Kudos: 20,169
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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
Attachments

image20.png
image20.png [ 14.4 KiB | Viewed 4629 times ]

User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 20 Nov 2025
Posts: 21,719
Own Kudos:
Given Kudos: 300
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 21,719
Kudos: 27,002
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
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
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
User avatar
parth111
Joined: 13 Apr 2023
Last visit: 13 Apr 2024
Posts: 11
Own Kudos:
Given Kudos: 16
Posts: 11
Kudos: 9
Kudos
Add Kudos
Bookmarks
Bookmark this Post
garcmillan
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


Hello,
Here, in your solution, why can't J be 0?
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,597
Own Kudos:
Posts: 38,597
Kudos: 1,079
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Moderators:
Math Expert
105408 posts
Tuck School Moderator
805 posts