It is currently 11 Dec 2017, 21:56

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Of a group of people, 10 play piano, 11 play guitar, 14 play

Author Message
Senior Manager
Joined: 08 Aug 2005
Posts: 251

Kudos [?]: 67 [0], given: 0

Of a group of people, 10 play piano, 11 play guitar, 14 play [#permalink]

### Show Tags

21 Apr 2006, 03:44
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Of a group of people, 10 play piano, 11 play guitar, 14 play violin, 3 play all the instruments, 20 play only one instrument. How many play 2 instruments?

A. 3
B. 6
C. 9
D. 12
E. 15

Kudos [?]: 67 [0], given: 0

Director
Joined: 06 Feb 2006
Posts: 893

Kudos [?]: 131 [0], given: 0

### Show Tags

21 Apr 2006, 04:24
I would also need a clear instructions on this puzzle

Kudos [?]: 131 [0], given: 0

Director
Joined: 24 Oct 2005
Posts: 658

Kudos [?]: 16 [0], given: 0

Location: London

### Show Tags

21 Apr 2006, 06:06
I get the ans as 12.

10 play piano,
11 play guitar,
14 play violin.

Out of this 3 people play all 3. Remaining = 32
20 play only 1.
So, those playing 2 out of 3 games is 32-20=12

Kudos [?]: 16 [0], given: 0

Manager
Joined: 23 Jan 2006
Posts: 191

Kudos [?]: 41 [0], given: 0

### Show Tags

21 Apr 2006, 06:44
is it 2?
Added & subtracted many eqs. will explain if right...

Kudos [?]: 41 [0], given: 0

Senior Manager
Joined: 24 Jan 2006
Posts: 251

Kudos [?]: 5 [0], given: 0

### Show Tags

21 Apr 2006, 06:54
If those 3 guys who play all instruments and those 20 who play only one instrument are not from group of people stated earlier on (viz. 10 piano players, 11 guitar players and 14 violin players) and if these are the only players i.e. total no of players is 58 then answer is 12.

Kudos [?]: 5 [0], given: 0

Manager
Joined: 23 Jan 2006
Posts: 191

Kudos [?]: 41 [0], given: 0

### Show Tags

21 Apr 2006, 06:56
gmatacer wrote:
If those 3 guys who play all instruments and those 20 who play only one instrument are not from group of people stated earlier on (viz. 10 piano players, 11 guitar players and 14 violin players) and if these are the only players i.e. total no of players is 58 then answer is 12.

yeah. tricky wording. I thoght that they wera all inclusive, for a total of 35 people...

PS - I meant "3" in my original answer. Faulty arithmetic :-/

Kudos [?]: 41 [0], given: 0

Director
Joined: 13 Nov 2003
Posts: 788

Kudos [?]: 64 [0], given: 0

Location: BULGARIA

### Show Tags

21 Apr 2006, 08:00
Hallo,
think it is C
20=35-people with 2 instruments-6

Kudos [?]: 64 [0], given: 0

Senior Manager
Joined: 05 Jan 2006
Posts: 381

Kudos [?]: 94 [0], given: 0

### Show Tags

21 Apr 2006, 08:30
couldn's solve but one thing is sure number of people is not 35! i will solve it tonight at home.

Kudos [?]: 94 [0], given: 0

Senior Manager
Joined: 05 Jan 2006
Posts: 381

Kudos [?]: 94 [0], given: 0

### Show Tags

21 Apr 2006, 09:05
I am getting answer of 3 if it's correct I will explain...

Kudos [?]: 94 [0], given: 0

Senior Manager
Joined: 09 Mar 2006
Posts: 444

Kudos [?]: 8 [2], given: 0

### Show Tags

21 Apr 2006, 10:23
2
KUDOS
I think the answer is 3.

Total counted: 35 ( 10 + 11 + 14 )
however those who play all the instr. are counted 3 times , and those
who play 2 intstr. are counted 2 times hence the equation :

35 = 3 *3 + 2 *x + 20

x=3

Last edited by deowl on 21 Apr 2006, 15:27, edited 1 time in total.

Kudos [?]: 8 [2], given: 0

VP
Joined: 21 Sep 2003
Posts: 1057

Kudos [?]: 82 [0], given: 0

Location: USA

### Show Tags

21 Apr 2006, 10:27
It the Q is interpreted as "exactly 2": then it is 3
If the Q is interpreted as "atleast 2": then it is 6
_________________

"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed."

- Bernard Edmonds

Kudos [?]: 82 [0], given: 0

Director
Joined: 13 Nov 2003
Posts: 788

Kudos [?]: 64 [0], given: 0

Location: BULGARIA

### Show Tags

21 Apr 2006, 10:35
ON a second thought agree with 3

Kudos [?]: 64 [0], given: 0

Senior Manager
Joined: 08 Jun 2004
Posts: 494

Kudos [?]: 95 [0], given: 0

Location: Europe

### Show Tags

21 Apr 2006, 12:07
Vote for 6 people, so the answer is 'B'.

10 play piano, 11 play guitar, 14 play violin,
3 play all the instruments,
20 play only one instrument.

Solved with Vienne diagram.

10-3+11-3+14-3 = 26,
26-20= 6 people.

Kudos [?]: 95 [0], given: 0

Manager
Joined: 23 Jan 2006
Posts: 191

Kudos [?]: 41 [0], given: 0

### Show Tags

21 Apr 2006, 13:34
getzgetzu wrote:
Of a group of people, 10 play piano, 11 play guitar, 14 play violin, 3 play all the instruments, 20 play only one instrument. How many play 2 instruments?

A. 3
B. 6
C. 9
D. 12
E. 15

Consider the following venn diagram:

build the following equations:
10 people play piano:
a+x+y+3=10
11 play guitar:
b+y+z+3=11
14 play violin:
c+x+z+3=14
20 play only 1 instrument:
a+b+c=20
How many play 2 instruments:
x+y+z = ?

add the first 3 eqs together:
a+b+c+2x+2y+2z+9=35
we know a+b+c=20
so
20+2x+2y+2z+9=35
2x+2y+2z=6
x+y+z=3

Kudos [?]: 41 [0], given: 0

Manager
Joined: 04 Apr 2006
Posts: 60

Kudos [?]: 2 [0], given: 0

Location: Land Of Opportunities

### Show Tags

22 Apr 2006, 03:34
kook44 wrote:
getzgetzu wrote:
Of a group of people, 10 play piano, 11 play guitar, 14 play violin, 3 play all the instruments, 20 play only one instrument. How many play 2 instruments?

A. 3
B. 6
C. 9
D. 12
E. 15

Consider the following venn diagram:

build the following equations:
10 people play piano:
a+x+y+3=10
11 play guitar:
b+y+z+3=11
14 play violin:
c+x+z+3=14
20 play only 1 instrument:
a+b+c=20
How many play 2 instruments:
x+y+z = ?

add the first 3 eqs together:
a+b+c+2x+2y+2z+9=35
we know a+b+c=20
so
20+2x+2y+2z+9=35
2x+2y+2z=6
x+y+z=3

Thanks for the detailed explaination. I somehow always make mistakes with the venn diagrams.

Kudos [?]: 2 [0], given: 0

Director
Joined: 06 Feb 2006
Posts: 893

Kudos [?]: 131 [0], given: 0

### Show Tags

22 Apr 2006, 04:04
kook44 wrote:
getzgetzu wrote:
Of a group of people, 10 play piano, 11 play guitar, 14 play violin, 3 play all the instruments, 20 play only one instrument. How many play 2 instruments?

A. 3
B. 6
C. 9
D. 12
E. 15

Consider the following venn diagram:

build the following equations:
10 people play piano:
a+x+y+3=10
11 play guitar:
b+y+z+3=11
14 play violin:
c+x+z+3=14
20 play only 1 instrument:
a+b+c=20
How many play 2 instruments:
x+y+z = ?

add the first 3 eqs together:
a+b+c+2x+2y+2z+9=35
we know a+b+c=20
so
20+2x+2y+2z+9=35
2x+2y+2z=6
x+y+z=3

Very nice explanation...

Kudos [?]: 131 [0], given: 0

Manager
Joined: 09 Apr 2006
Posts: 173

Kudos [?]: 3 [0], given: 0

Location: Somewhere in Wisconsin!

### Show Tags

23 Apr 2006, 21:13
It is the fastest method indeed!
_________________

Thanks,
Zooroopa

Kudos [?]: 3 [0], given: 0

Senior Manager
Joined: 12 Mar 2006
Posts: 363

Kudos [?]: 77 [0], given: 3

Schools: Kellogg School of Management

### Show Tags

23 Apr 2006, 21:59
the question says how many people play 2 instruments....does this mean atleast 2 instruments or only two instruments ?

depending on this the answer would be 3 or 6 ?

Kudos [?]: 77 [0], given: 3

Senior Manager
Joined: 08 Jun 2004
Posts: 494

Kudos [?]: 95 [0], given: 0

Location: Europe

### Show Tags

24 Apr 2006, 03:33
1. Need the Prof's explanation. Professor where are you?
2. Need the OA.

Kudos [?]: 95 [0], given: 0

GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5032

Kudos [?]: 456 [0], given: 0

Location: Singapore

### Show Tags

28 Apr 2006, 08:19
M8 wrote:
1. Need the Prof's explanation. Professor where are you?
2. Need the OA.

Kook's method is the way I did it. I'm surprised we even picked the same algerbraic expressions A,B,C, x,y,z!!

x = 3 should be the answer.

Kudos [?]: 456 [0], given: 0

28 Apr 2006, 08:19

Go to page    1   2    Next  [ 28 posts ]

Display posts from previous: Sort by

# Of a group of people, 10 play piano, 11 play guitar, 14 play

Moderator: chetan2u

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.