NEW HERE? LEARN MORE
closeclose
It is currently 19 Apr 2024, 09:57
Register
GMAT Focus Tests
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

Kevin must select 3 friends from different social groups to invite to

8 posts Go to First Unread Post
Print view
NEW TOPIC
POST REPLY
Question banks

GMAT Question Banks

Downloads
My Bookmarks
Reviews
SORT BY:
Date
Kudos
User avatar
P
MonkeyDDes
Manager
Manager
Joined: 06 Jul 2021
Posts: 81
Location: Peru
Concentration: Operations, General Management
GPA: 3.3
WE:Engineering (Other)
Kevin must select 3 friends from different social groups to invite to [#permalink] New post  21 Aug 2021, 07:00
1
Kudos
4
Bookmarks
00:00
A
B
C
D
E

Difficulty:

35% (medium)

Question Stats:

70% (01:56) correct 30% (02:00) wrong based on 102 sessions
Hide Show timer Statistics
Kevin must select 3 friends from different social groups to invite to his party. He has 5 friends in a music club, and 4 friends in a reading club. At least one of the invited friends must be from the music club. How many different combinations of friends can Kevin invite to his party?

A.30
B.40
C.60
D.70
E.80
ShowHide Answer
Official Answer
Official Answer and Stats are available only to registered users. Register/Login.
User avatar
L
mSKR
VP
VP
Joined: 14 Aug 2019
Posts: 1380
Location: Hong Kong
Concentration: Strategy, Marketing
Schools: IE (A) IIML-IPMX '22 (A) HKUST '22
GMAT 1: 650 Q49 V29
GPA: 3.81
Re: Kevin must select 3 friends from different social groups to invite to [#permalink] New post  21 Aug 2021, 08:36
5 F in music club--atleast one
4F in reading club

MMM-》 5C3--》= 10--> this combination can not be selected as they would be from all same club ( against informaiton given ina rgument)
MMR-》 5C2 + 4= 14
MRR-> 5+ 4*3/2= 11


I get answer 25

how the correct answer is 80?
User avatar
P
MonkeyDDes
Manager
Manager
Joined: 06 Jul 2021
Posts: 81
Location: Peru
Concentration: Operations, General Management
GPA: 3.3
WE:Engineering (Other)
Re: Kevin must select 3 friends from different social groups to invite to [#permalink] New post  21 Aug 2021, 08:48
1
Kudos
mSKR wrote:
5 F in music club--atleast one
4F in reading club

MMM-》 5C3--》= 10--> this combination can not be selected as they would be from all same club ( against informaiton given ina rgument)
MMR-》 5C2 + 4= 14
MRR-> 5+ 4*3/2= 11


I get answer 25

how the correct answer is 80?


We divide the solution into cases, knowing that the answer is based on the calculation of combinations

Case 1: Invite 3 friends from the music club.
Combinations: 5C3 = 10

Case 2: Invite 2 music friends and 1 reading friend.
Combinations: 5C2 * 4C1 = 10 * 4 = 40

Case 3: Invite 1 musician friend and 2 reading friends
Combinations: 5C1 * 4C2 = 5 * 6 = 30

Total: 10 + 40 + 30 = 80
User avatar
L
mSKR
VP
VP
Joined: 14 Aug 2019
Posts: 1380
Location: Hong Kong
Concentration: Strategy, Marketing
Schools: IE (A) IIML-IPMX '22 (A) HKUST '22
GMAT 1: 650 Q49 V29
GPA: 3.81
Re: Kevin must select 3 friends from different social groups to invite to [#permalink] New post  21 Aug 2021, 08:56
1
Kudos
MonkeyDDes wrote:
mSKR wrote:
5 F in music club--atleast one
4F in reading club

MMM-》 5C3--》= 10--> this combination can not be selected as they would be from all same club ( against informaiton given ina rgument)
MMR-》 5C2 + 4= 14
MRR-> 5+ 4*3/2= 11


I get answer 25

how the correct answer is 80?


We divide the solution into cases, knowing that the answer is based on the calculation of combinations

Case 1: Invite 3 friends from the music club.
Combinations: 5C3 = 10

Case 2: Invite 2 music friends and 1 reading friend.
Combinations: 5C2 * 4C1 = 10 * 4 = 40

Case 3: Invite 1 musician friend and 2 reading friends
Combinations: 5C1 * 4C2 = 5 * 6 = 30

Total: 10 + 40 + 30 = 80


Kevin must select 3 friends from different social groups to invite to his party
i think MMM should not be applicable

btw, i got my mistake. it should be * not +

thanks1
User avatar
L
EgmatQuantExpert
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3726
Kevin must select 3 friends from different social groups to invite to [#permalink] New post  30 Aug 2021, 05:35
Expert Reply

Solution



Given
    • Kevin has 5 friends in a music club and 4 friends in a reading club.

To find
    • Ways of selecting 3 friends such that at least one must be from the music club.

Approach and Working out

Since at least one of the invited friends must be from the music club, thus, we can have the following cases.
Case 1:
    • Exactly one friend belongs to the music club. In this case, the rest two must be from the reading club.
    • Thus, combinations = \((5C_1)(4C_2) = 5×6 = 30\)
Case 2:
    • Exactly two friends belong to the music club. In this case, the remaining one must be from the reading club.
    • Thus, combinations = \((5C_2)(4C_1) = 10×4 = 40\)
Case 3:
    • All three friends belong the music club.
    • Thus, combinations = \(5C_3 = 10\)

Total number of combinations = 30 + 40 + 10 = 80.

Correct Answer: Option E
_________________
Free Trial: Get 25 AI powered videos | 400 practice questions | 8 free webinars

Case studies: How a personalized study plan can save you 60+ hours

MBA admits: M7 admits | INSEAD admits | ISB admits [40+ case studies]


Learn why e-GMAT has 10X more 700+ verified scores than other GMATClub partners – Read our 2000+ reviews
Signature Read More
User avatar
P
Showmeyaa
Senior Manager
Senior Manager
Joined: 24 Jun 2019
Posts: 432
Location: India
Concentration: Marketing, Strategy
Reviews Badge
Re: Kevin must select 3 friends from different social groups to invite to [#permalink] New post  04 Sep 2021, 01:36
1
Kudos
1
Bookmarks
MonkeyDDes wrote:
Kevin must select 3 friends from different social groups to invite to his party. He has 5 friends in a music club, and 4 friends in a reading club. At least one of the invited friends must be from the music club. How many different combinations of friends can Kevin invite to his party?

A.30
B.40
C.60
D.70
E.80


At least one of the friends invited from music club = Total friends invited - no friends invited from music club
So, total = \(9C_3\) = 84
No friends invited from music club = \(4C_3\) = 4
So, at least one = 84 - 4 = 80

IMO, (E)!
_________________
Learning by posting. Feel free to correct me!
Signature Read More
User avatar
D
rvgmat12
Senior Manager
Senior Manager
Joined: 19 Oct 2014
Posts: 394
Location: United Arab Emirates
Schools: Wharton '23 Booth '23 INSEAD Jan'21 Intake
GMAT ToolKit User Reviews Badge
Re: Kevin must select 3 friends from different social groups to invite to [#permalink] New post  04 Sep 2021, 02:55
1 from music + 2 from music + all from music=

5C1*4C2+5C2*4C1+5C3 = 30+40+10 = 80
avatar
G
Foreheadson
Manager
Manager
Joined: 22 Jun 2020
Posts: 156
Location: Georgia
Concentration: Finance, General Management
Schools: Booth '25 (WL) Darden '25
GMAT 1: 720 Q51 V38
GPA: 3.71
Kevin must select 3 friends from different social groups to invite to [#permalink] New post  18 Sep 2021, 15:02
Can anyone explain why can we not calculate strait 5*8C2? reason behind is that 5C1=5 since 1 must be invited from music. and no other condition. so 8 people left in total and we need to choose 2 of them. so 8C2=28. 5*28=140. I understand this is flawed but can't figure out what am I missing here?

Maybe Bunuel could help?



update:

I think I got it now. the question is not really about friends. so friends are not different, they are labaled as music guy or reading guy. The question asks about combinations of clubs, not people. Question could be clearer regarding this matter.


Posted from my mobile device
GMAT Club Bot
gmatclubot
Kevin must select 3 friends from different social groups to invite to [#permalink]
18 Sep 2021, 15:02
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
Moderators:
Bunuel
Math Expert
92758 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

cron

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions