GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 22 Jan 2020, 01:24

### 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

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

# M70-28

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 60561

### Show Tags

03 Sep 2018, 06:10
00:00

Difficulty:

55% (hard)

Question Stats:

55% (01:42) correct 45% (02:30) wrong based on 22 sessions

### HideShow timer Statistics

Of the 27 participants in a talent show, 13 are singers, 14 are musicians, and 9 are dancers. If 4 people are both singers and dancers, 3 are both singers and musicians and 1 person is all three, how many people are both dancers and musicians?

A. 0
B. 1
C. 2
D. 3
E. 4

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 60561

### Show Tags

03 Sep 2018, 06:10
1
Official Solution:

Of the 27 participants in a talent show, 13 are singers, 14 are musicians, and 9 are dancers. If 4 people are both singers and dancers, 3 are both singers and musicians and 1 person is all three, how many people are both dancers and musicians?

A. 0
B. 1
C. 2
D. 3
E. 4

We’ll go for ALTERNATIVE because the numbers in the answers are easy to use.

Since we have three overlapping sets, we’ll draw a Venn diagram, and instead of going into redundant calculations, we’ll try the median answer (C) 2 and see whether it works out:

The third layer, consisting of all three groups, is made up of 1 person. This makes the number of people who are singers and musicians (but not dancers) 3 – 1 = 2, and the number of singer-dancers (but not musicians) 4 – 1 = 3. The number of people who only sing is 13 – 1 – 2 – 3 = 7. Now, if answer (C) is correct, the number of those who only dance is 9 – 3 – 1 – 1 = 4, and the number of those who are only musicians is 14 – 2 – 1 – 1 = 10. So the overall number of participants is: 7 + 3 + 1 + 2 + 10 + 1 + 4 = 28, instead of 27. (C) is eliminated.

We can just check a random answer, but note that the answer we need to check is actually a larger one in order to make both ‘just musicians’ and ‘just dancers’ groups smaller (and thus making the total number of participants smaller). Let’s see answer choice (D) 3:

As we’ve seen before, we have 1 person in all three groups; 2 who are singers and musicians (but not dancers); 3 singer-dancers (but not musicians); and 7 only sing. Now, if answer (D) is correct, the number of those who only dance is 9 – 3 – 1 – 2 = 3, and the number of those who are only musicians is 14 – 2 – 1 – 2 = 9. So the total number of participants is: 7 + 3 + 1 + 2 + 9 + 2 + 3 = 27. That’s our answer!

_________________
Intern
Joined: 11 Mar 2018
Posts: 6

### Show Tags

07 Sep 2018, 08:02
1
shouldn't it be 4?
Intern
Joined: 24 Jul 2014
Posts: 2
Location: India
Schools: Babson '22 (A\$)
GMAT 1: 590 Q46 V26
GPA: 2.78

### Show Tags

09 Oct 2018, 07:10
can you please explain with the help of Venn diagram
Intern
Joined: 11 Sep 2018
Posts: 2
Location: Myanmar
Concentration: Healthcare, General Management
WE: Other (Health Care)

### Show Tags

02 Nov 2018, 02:04
1
since one person is all three, it makes 3 people (both singers and dancers but not musician) and 2 people (both singers and musician but not dancer). So, the number of people who can only sing is 7. If the number of people who is both musician and dancer but not singer is 2 (plus one person who does all three), musician alone is 9 and dancer alone is 3. Singer (7+2+1+3=13), Musician (2+1+2+9=14), Dancer (1+3+2+3=9).

Total = 7+2+1+9+2+3+3=27
Intern
Joined: 10 Oct 2018
Posts: 3
Location: India
WE: General Management (Non-Profit and Government)

### Show Tags

03 Dec 2018, 04:52
I'm getting a 4 too. (13-3-2-1 +14-2-1 +9-3-1) = 7+11+5= 23, (27-23)=4 . Where am I going wrong ?
Intern
Joined: 22 Jan 2019
Posts: 5
Location: United States
Schools: Haas EWMBA '22

### Show Tags

18 Feb 2019, 01:21
1
Bunuel wrote:
Of the 27 participants in a talent show, 13 are singers, 14 are musicians, and 9 are dancers. If 4 people are both singers and dancers, 3 are both singers and musicians and 1 person is all three, how many people are both dancers and musicians?

A. 0
B. 1
C. 2
D. 3
E. 4

If S=singers, M=musicians and D=dancers, we have:
D∩S=4, S∩M=3 and S∩M∩D=1
We are looking for D∩M=1+x (because S∩M∩D=1)
Dx is the part of circle D without the intersections with the other circles
Mx is the part of circle M without the intersections with the other circles
Thus, we have 3 equations with 3 unknowns:
Mx+Dx+13+x=27
Mx+3+x=14 (Because m=14)
Dx+4+x=9 (Because d=9)

Which gives x=2 and D∩M=1+x=3

PS: I couldn't upload a file because I have less than 5 posts, but if you make a Venn diagram, you'll see what I am talking about.
Manager
Joined: 07 Jan 2019
Posts: 63
WE: Engineering (Manufacturing)

### Show Tags

01 Jun 2019, 03:11
I think this is a high-quality question and I don't agree with the explanation. If we are considering D) to be correct while substituting options why are we plugging in 2 instead of 3?
Intern
Joined: 05 May 2019
Posts: 4

### Show Tags

27 Jun 2019, 21:25
Kindly explain with venn diagram, I am also getting 4
_________________
Chetna Kohli
Preparing for GMAT 2020-2021
India, Mumbai.
Not an engineer, but attempt each day to master the calculations
Intern
Joined: 11 Apr 2019
Posts: 3

### Show Tags

18 Jul 2019, 05:57
27 = 13(s) + 14(m) + 9(d) - (4(ds) + 3(ms) + 1(smd) + X(md))
27 = 36 - (8 + X)
27 = 28 - X
X = 1
I got 1! What's wrong here?
Manager
Joined: 10 Mar 2018
Posts: 74
Location: India
Concentration: Entrepreneurship, Marketing
Schools: IIML IPMX "21
GMAT 1: 680 Q44 V38
WE: Design (Retail)

### Show Tags

29 Jul 2019, 11:50
_________________
~ETERNAL~
Intern
Joined: 03 Apr 2017
Posts: 1

### Show Tags

08 Aug 2019, 10:20
I think this is a high-quality question and I don't agree with the explanation. Answer has to be 2
Intern
Joined: 07 Oct 2019
Posts: 1
Location: United States
Concentration: General Management, Social Entrepreneurship
GMAT 1: 700 Q48 V37
GMAT 2: 710 Q50 V36
GPA: 3.67
WE: Engineering (Telecommunications)

### Show Tags

14 Oct 2019, 00:03

By Venn diagram constraint:
Let's denote #Singers by S, #dancers by D and #Musicians by M

Total = S + M+ D - (People who are exactly 2 out of 3) - 2(People who are all 3) + People who are None

27 = 13 + 14 + 9 - (People who do exactly 2 out of 3) - 2(1) + 0

Or (People who do exactly 2 out of 3) = 7. (i)

This leaves us with:
(Exactly both S and D) = (Both S and D) - (People who are all 3) = 4 - 1 = 3 (ii)
(Exactly both S and M) = (Both S and M) - (People who are all 3) = 3 - 1 = 2 (iii)

Leaving us with (Exactly both D and M) = (i) - [(ii) + (iii)] = 7 - (3+2) = 2

Giving us #(Both D and M) = (Exactly both D and M) + (People who are all 3) = 2 + 1 = 3
Intern
Joined: 03 Sep 2019
Posts: 1

### Show Tags

18 Oct 2019, 05:45
2
answer to this question is 0
Re M70-28   [#permalink] 18 Oct 2019, 05:45
Display posts from previous: Sort by

# M70-28

Moderators: chetan2u, Bunuel