GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Aug 2018, 06:27

### 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

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

Author Message
TAGS:

### Hide Tags

Manager
Status: mba here i come!
Joined: 07 Aug 2011
Posts: 230

### Show Tags

27 Aug 2011, 12:22
1
1
those who play single instrument = 20
those who don't play a single instrument (play 2 or 3) = 35-20 = 15

those who play 2 instruments = 15-3 = 12 (3 play all three instruments)
_________________

press +1 Kudos to appreciate posts

Intern
Joined: 29 Aug 2011
Posts: 20

### Show Tags

06 Sep 2011, 12:43
I worked on this using Venn Diagram. Got the answer 6 in one shot. The answer is how many play 2 instruments so we need to count the people who also play 3 instruments ( given already 3).
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8195
Location: Pune, India

### Show Tags

06 Sep 2011, 21:57
MBAhereIcome wrote:
those who play single instrument = 20
those who don't play a single instrument (play 2 or 3) = 35-20 = 15

those who play 2 instruments = 15-3 = 12 (3 play all three instruments)

The 35 that you counted: 10 + 11 + 14 double counts the number of people who play only 2 instruments and triple counts the number of people who play all 3 instruments. The circle of 10 of piano includes the red and the green region. The circle of 11 of Guitar includes the red and green region too. Similarly, the circle of 14 of violin includes the red and the green region too. So each red region is counted twice and the green region is counted 3 times.

Attachment:

Ques2.jpg [ 14.89 KiB | Viewed 5487 times ]

So 35 - 20 = 15
15 - 3 = 12 (Subtract once the triple counted green region. Now everything is double counted)
12/2 = 6 = Total number of people who play 2 or 3 instruments.
_________________

Karishma
Veritas Prep GMAT Instructor

Save up to \$1,000 on GMAT prep through 8/20! Learn more here >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Intern
Joined: 29 Aug 2011
Posts: 20
Re: Of a group of people, 10 play piano, 11 play guitar, 14 play  [#permalink]

### Show Tags

05 Feb 2012, 02:18
slingfox 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

Total folks = 10 + 11 + 14 = 35
20 Play only one instrument. So no of people playing two or more instruments = 35 - 20 = 15.
From the venn diagrams we know that 15 represents the intersection part between Piano, Guitar and Violin. In the venn diagram, people having all the three capabilities are counted thrice. Hence people playing exactly two instruments = 15 - 3 (3) = 6

Hence B.
Direct formulas may not be applicable all the time. Focus on which area is being counted and how many times.
Manager
Joined: 31 Jan 2012
Posts: 73
Re: Of a group of people, 10 play piano, 11 play guitar, 14 play  [#permalink]

### Show Tags

05 Feb 2012, 02:47
The way I did it was add up all the instruments together, so 10 + 11 +14 = 35. I knew 3 people played all 3, so I subtract 3 from each of the instruments, so 7+8+11 = 26. I know this is the amount of instruments played by a person who plays 1 or 2 instruments. Since the amount of people that play 1 instrument is 20, you subtract all the single instrument from the total. 26-20=6, so 6 instrument. We know that people in this group play 2 instruments, so there is 3 people playing 6 instruments. 3 people who plays exactly 2 instruments + 3 people who plays exactly 3 = 6 people who play 2 or more instruments.
Manager
Status: MBA Aspirant
Joined: 12 Jun 2010
Posts: 144
Location: India
WE: Information Technology (Investment Banking)

### Show Tags

05 Feb 2012, 03:19
VeritasPrepKarishma wrote:
MBAhereIcome wrote:
those who play single instrument = 20
those who don't play a single instrument (play 2 or 3) = 35-20 = 15

those who play 2 instruments = 15-3 = 12 (3 play all three instruments)

The 35 that you counted: 10 + 11 + 14 double counts the number of people who play only 2 instruments and triple counts the number of people who play all 3 instruments. The circle of 10 of piano includes the red and the green region. The circle of 11 of Guitar includes the red and green region too. Similarly, the circle of 14 of violin includes the red and the green region too. So each red region is counted twice and the green region is counted 3 times.

Attachment:
Ques2.jpg

So 35 - 20 = 15
15 - 3 = 12 (Subtract once the triple counted green region. Now everything is double counted)
12/2 = 6 = Total number of people who play 2 or 3 instruments.

Hi, Dont you think the answer should be A i.e. 3 since the question asks for how many people who play 2 instruments and not atleast 2 instruments.
Math Expert
Joined: 02 Sep 2009
Posts: 47983
Of a group of people, 10 play piano, 11 play guitar, 14 play  [#permalink]

### Show Tags

05 Feb 2012, 03:47
2
slingfox 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

To elaborate more.

Look at the diagram below:

To solve this question one should fundamentally understand two things:
1. What does the question ask: "How many play 2 instruments?" So, we should find the sum of the sectors 1, 2, 3, and 4. Notice that those who play two instruments include also those who play all three instruments, (sector 4);

2. What happens when we sum all three groups, 10 piano players, 11 guitar players and 14 violin players? When we add these three groups, we'll get 10+11+14=35 but some sections are counting more than once in this number: sections 1, 2, and 3 are counted twice and section 4 thrice. Now, if we subtract those who play only one instrument (inner white sections on the diagram), we'll get 35-20=15, so twice sections 1, 2, and 3 plus thrice section 4 equals to 15.

Since, 15 counts section 4, those who play all the instruments, thrice then of 15-3=12 counts these section twice. So, now 12 counts all sections 1, 2, 3 and 4 twice. We need to count them once thus divide this number by 2 --> 12/2=6 play 2 instruments.

Detailed analysis of this concept is here: http://gmatclub.com/forum/formulae-for- ... ml#p729340

subhajeet wrote:
Hi, Dont you think the answer should be A i.e. 3 since the question asks for how many people who play 2 instruments and not atleast 2 instruments.

No, if it were the case question would ask: "how many play EXACTLY 2 instruments?" How many play 2 instruments, means how many play at least 2 instruments, hence this group includes also those who play all 3 instruments.

Refer to the link above for more on this issue.

Hope it helps.

Attachment:

Union_3sets.gif [ 11.63 KiB | Viewed 5396 times ]

_________________
Senior Manager
Joined: 24 Aug 2009
Posts: 477
Schools: Harvard, Columbia, Stern, Booth, LSB,
Of a group of people, 10 play piano, 11 play guitar  [#permalink]

### Show Tags

22 Aug 2012, 09:49
1
Question wordings are very poor or at least very ambiguous.
"How many play 2 instruments?" can be inferred in 2 ways (both of which are right) which creates unnecessary confusion
1) Play Exactly 2 instruments
2) Play at least 2 instruments
_________________

If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS.
Kudos always maximizes GMATCLUB worth
-Game Theory

If you have any question regarding my post, kindly pm me or else I won't be able to reply

Senior Manager
Joined: 10 Jul 2013
Posts: 316
Re: Of a group of people, 10 play piano, 11 play guitar, 14 play  [#permalink]

### Show Tags

15 Aug 2013, 15:18
1
slingfox 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

guitar = 11
piano = 10
violin = 14

1 or 2 instruments player = 10-3 +11-3 +14-3 = 35-9 = 26
1 instruments player = 20
so 2 instruments player = 26-20 = 6 =B
_________________

Asif vai.....

Manager
Joined: 21 Aug 2012
Posts: 124

### Show Tags

15 Aug 2013, 20:05
VeritasPrepKarishma wrote:
MBAhereIcome wrote:
those who play single instrument = 20
those who don't play a single instrument (play 2 or 3) = 35-20 = 15

those who play 2 instruments = 15-3 = 12 (3 play all three instruments)

The 35 that you counted: 10 + 11 + 14 double counts the number of people who play only 2 instruments and triple counts the number of people who play all 3 instruments. The circle of 10 of piano includes the red and the green region. The circle of 11 of Guitar includes the red and green region too. Similarly, the circle of 14 of violin includes the red and the green region too. So each red region is counted twice and the green region is counted 3 times.

Attachment:
Ques2.jpg

So 35 - 20 = 15
15 - 3 = 12 (Subtract once the triple counted green region. Now everything is double counted)
12/2 = 6 = Total number of people who play 2 or 3 instruments.

The question only states that how many play 2 instruments.
Nowhere it is mentioned that it asks for only 2 instruments or atleast 2 instruments???
_________________

MODULUS Concept ---> http://gmatclub.com/forum/inequalities-158054.html#p1257636
HEXAGON Theory ---> http://gmatclub.com/forum/hexagon-theory-tips-to-solve-any-heaxgon-question-158189.html#p1258308

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8195
Location: Pune, India

### Show Tags

15 Aug 2013, 22:26
jaituteja wrote:
VeritasPrepKarishma wrote:
MBAhereIcome wrote:
those who play single instrument = 20
those who don't play a single instrument (play 2 or 3) = 35-20 = 15

those who play 2 instruments = 15-3 = 12 (3 play all three instruments)

The 35 that you counted: 10 + 11 + 14 double counts the number of people who play only 2 instruments and triple counts the number of people who play all 3 instruments. The circle of 10 of piano includes the red and the green region. The circle of 11 of Guitar includes the red and green region too. Similarly, the circle of 14 of violin includes the red and the green region too. So each red region is counted twice and the green region is counted 3 times.

Attachment:
Ques2.jpg

So 35 - 20 = 15
15 - 3 = 12 (Subtract once the triple counted green region. Now everything is double counted)
12/2 = 6 = Total number of people who play 2 or 3 instruments.

The question only states that how many play 2 instruments.
Nowhere it is mentioned that it asks for only 2 instruments or atleast 2 instruments???

I understand the confusion. But the language of sets is very mathematical and literal. Say, if I ask you, whether you play an instrument and you have to answer in yes or no, you will say yes even if you play 2/3/4 instruments. Similarly, if I ask you whether you play two instruments, you will answer yes even if you play 3/4 instruments.

No of people who play two instruments includes number of people who play more than 2 too since these people certainly do play 2 instruments (and they play some more).

If 'at least' or 'only' is mentioned, we will consider it accordingly.
_________________

Karishma
Veritas Prep GMAT Instructor

Save up to \$1,000 on GMAT prep through 8/20! Learn more here >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Intern
Joined: 09 Jul 2013
Posts: 2
Re: Of a group of people, 10 play piano, 11 play guitar, 14 play  [#permalink]

### Show Tags

18 Aug 2013, 11:36
slingfox 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

play only piano 10-3=7
Play only guitar 11-3=8
Play only violin 14-3=11
so, 20=7+8+11-2overlapping set
2overlapping set=26-20=6
so, the best answer is (B)
Posted by Abdul Mannan Mian
Manager
Joined: 29 Aug 2013
Posts: 74
Location: United States
GMAT 1: 590 Q41 V29
GMAT 2: 540 Q44 V20
GPA: 3.5
WE: Programming (Computer Software)
Re: Of a group of people, 10 play piano, 11 play guitar, 14 play  [#permalink]

### Show Tags

14 Sep 2013, 03:09
saxenaashi wrote:
slingfox 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

Total folks = 10 + 11 + 14 = 35
20 Play only one instrument. So no of people playing two or more instruments = 35 - 20 = 15.
From the venn diagrams we know that 15 represents the intersection part between Piano, Guitar and Violin. In the venn diagram, people having all the three capabilities are counted thrice. Hence people playing exactly two instruments = 15 - 3 (3) = 6

Hence B.

Direct formulas may not be applicable all the time. Focus on which area is being counted and how many times.

Here "6" that you have got is counted twice i.e. 2(Exactly two) = 6 Therefore 3 will be exactly two..

Hence if question asks 2 instruments then it will be Exactly 2 + All = 3 + 3 = 6 people..
Intern
Joined: 15 Sep 2013
Posts: 5
Re: Tough Overlapping Set Problem- Veritas  [#permalink]

### Show Tags

20 Dec 2013, 09:15
35 TOTPeople - 20 individual instr - 3 ABC = 12 remain for 2 instr / 2 instr = ANS:6 people play 2
Intern
Joined: 10 Dec 2013
Posts: 20
Location: India
Concentration: Technology, Strategy
Schools: ISB '16 (S)
GMAT 1: 710 Q48 V38
GPA: 3.9
WE: Consulting (Consulting)
Re: Of a group of people, 10 play piano, 11 play guitar, 14 play  [#permalink]

### Show Tags

05 Feb 2014, 11:24
Hi,

I just used a very simple approach hope that might help some people who are trying to avoid cramming up the formula

People playing all three instruments = 3

Now subtract this from each group to remove the common part for all 3

Piano(Two or one) = 7
Guitar(Two or one) = 8
Violin(Two or one) = 11

Now if we sum all of the above we will get the number of people who play either two or one instrument
Sum(Two or one) = 26

Question tells us that there are 20 people who play exactly 1 instrument hence

26-20 = 6 = People playing two instruments

Hit Kudos if you found this helpful. Cheers and good luck
Intern
Joined: 14 Jan 2011
Posts: 26
Re: Of a group of people, 10 play piano, 11 play guitar, 14 play  [#permalink]

### Show Tags

24 Sep 2014, 08:36
Poorly written question,

if the question was how many people play at least 2 instruments than the answer would be 6

If the question was, as is implied by the majority of the answers, how many people played solely 2 instruments the answer would be 3.
Intern
Joined: 14 Jan 2011
Posts: 26
Of a group of people, 10 play piano, 11 play guitar, 14 play  [#permalink]

### Show Tags

24 Sep 2014, 08:37
Rohan_Kanungo wrote:
Hi,

I just used a very simple approach hope that might help some people who are trying to avoid cramming up the formula

People playing all three instruments = 3

Now subtract this from each group to remove the common part for all 3

Piano(Two or one) = 7
Guitar(Two or one) = 8
Violin(Two or one) = 11

Now if we sum all of the above we will get the number of people who play either two or one instrument
Sum(Two or one) = 26

Question tells us that there are 20 people who play exactly 1 instrument hence

26-20 = 6 = People playing two instruments

Hit Kudos if you found this helpful. Cheers and good luck

Your answer tells us how many slots for instrument players are left over, which is 6. However, you have to divide this number by 2 because the remaining players play 2 instruments. So the answer would be 3.
Manager
Joined: 08 Jun 2015
Posts: 114
Of a group of people, 10 play piano, 11 play guitar, 14 play  [#permalink]

### Show Tags

01 Aug 2015, 21:17
10 piano
11 guitar
14 violin
Total is 35
3 play all 3 instruments
20 play just one

That means that of the 35 counted, 20 of them are not duplicates.
15 are duplicates. Of the 15, 3 play all three instruments, so each person is counted 3 times so 9 total counts when they should be counted only 3 times. 35-20-9 = remaining number = 6, each of these include people who play two instruments, so they're repeated twice each. So, there are three people who play all two instruments. 3 people play all three + 3 people play two = 6 people that play at least 2 instruments (at least as opposed to only 2 instruments).
Manager
Joined: 14 Jul 2014
Posts: 187
Location: United States
Schools: Duke '20 (D)
GMAT 1: 600 Q48 V27
GMAT 2: 720 Q50 V37
GPA: 3.2
Re: Of a group of people, 10 play piano, 11 play guitar, 14 play  [#permalink]

### Show Tags

23 Aug 2015, 13:47
AHHH!! The key seems to be the 'play two instrument's' in the question. Was breaking my head over why not 3.
Intern
Joined: 25 May 2014
Posts: 41
Re: Of a group of people, 10 play piano, 11 play guitar, 14 play  [#permalink]

### Show Tags

19 Mar 2016, 04:27
slingfox 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

A: No of people only playing piano
B: No of people only playing Guitar
C: No of people only playing Violin
D: No of people playing only Piano and Guitar
E: No of people playing only piano and Violin
F: No of people laying only Violin and Guitar
G: No of people playing all three

35 = A+B+C+D+E+F+G
35=20+D+E+F+3
D+E+F=12
So No. of people playing ONLY 2 instruments is 12.
and No. of people playing 2 instrument = No of people playing ONLY 2 instrument + No. of people playing ONLY 3 instrument, which i equal to 12+3=15.
Re: Of a group of people, 10 play piano, 11 play guitar, 14 play &nbs [#permalink] 19 Mar 2016, 04:27

Go to page   Previous    1   2   3    Next  [ 43 posts ]

Display posts from previous: Sort by

# Events & Promotions

 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®.