|
Author |
Message |
|
TAGS:
|
|
|
Manager
Joined: 18 Oct 2009
Posts: 53
Schools: Kellogg
Followers: 33
Kudos [?]:
257
[0], given: 3
|
Of a group of people, 10 play piano, 11 play guitar, 14 play [#permalink]
 30 Oct 2009, 21:32
Question Stats:
31% (02:07) correct
68% (01:09) wrong based on 1 sessions
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
_________________
GMAT Strategies: slingfox-s-gmat-strategies-condensed-96483.html
|
|
|
|
|
|
|
Senior Manager
Joined: 20 Mar 2008
Posts: 461
Followers: 1
Kudos [?]:
49
[0], given: 5
|
Re: Overlapping Sets Problem [#permalink]
30 Oct 2009, 21:48
slingfox wrote: Can someone tell explain how they go about solving this one?
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 Let single piano players = p Let single guitar players = g Let single violin players = v Given, p + g + v + 3 + 20 = 10 + 11 + 14. Hence, p + g + v = 35 - 23 = 12D.
|
|
|
|
|
|
Senior Manager
Joined: 18 Aug 2009
Posts: 313
Followers: 2
Kudos [?]:
50
[0], given: 9
|
Re: Overlapping Sets Problem [#permalink]
30 Oct 2009, 21:52
35 with overlaps. 35-20=15 two or more. 15-3=12 two instruments. (D)
Venn diagrams helps in these cases. 3 circles, each for Piano, Guitar and Violin. Shade the intersecting areas (the place where all three circles meet is 3, rest of the overlap shaded area would be 10+14+11-3-20... edit here as I forgot subtracting 20)
|
|
|
|
|
|
Senior Manager
Joined: 18 Aug 2009
Posts: 313
Followers: 2
Kudos [?]:
50
[0], given: 9
|
Re: Overlapping Sets Problem [#permalink]
30 Oct 2009, 23:24
gmattokyo wrote: slingfox wrote: The OA from Veritas is B. I keep getting A whereas two people have gotten D  Did Veritas give any explanation? Unless there is a hidden trap (q looks straightforward enough) which makes the venn diagram wrong, I still don't see how it could be 6. Here is one approach to get B... shoot!! 3 people play all three instruments. So they got counted in 10 of Piano, 11 of Guitar and 14 of Violin. So people who play 1 or 2 instruments is 35-3x3=26 Given 20 people play 1 instrument only... people who play 2 instruments= 26-20=6 
|
|
|
|
|
|
Manager
Joined: 18 Oct 2009
Posts: 53
Schools: Kellogg
Followers: 33
Kudos [?]:
257
[0], given: 3
|
Re: Overlapping Sets Problem [#permalink]
30 Oct 2009, 23:40
This problem was included in an in-class handout, so there is no explanation, only an answer. Here is how I did the problem: P = 10 G = 11 V = 14 PGV = 3 Let PG + PV + GV = X Number of People in Exactly One Set = 20 = P + G + V -2(X) + 3*PGV Solving for this you get: 2X = (10 + 11 +14) + 3*3 - 20 = 24 So X = 12 Formula for people in exactly two sets = X - 3*PGV = 12 - 3*3 = 3 My Answer: 3 FYI: formulae-for-3-overlapping-sets-69014.html
_________________
GMAT Strategies: slingfox-s-gmat-strategies-condensed-96483.html
|
|
|
|
|
|
Senior Manager
Joined: 18 Aug 2009
Posts: 313
Followers: 2
Kudos [?]:
50
[0], given: 9
|
Re: Overlapping Sets Problem [#permalink]
30 Oct 2009, 23:56
slingfox, I'm trying to understand how you derived, meanwhile here is the venns I used
Attachments
vennSaviour.GIF [ 11.33 KiB | Viewed 6189 times ]
|
|
|
|
|
|
Senior Manager
Joined: 18 Aug 2009
Posts: 313
Followers: 2
Kudos [?]:
50
[0], given: 9
|
Re: Overlapping Sets Problem [#permalink]
31 Oct 2009, 01:12
slingfox wrote: GmatTokyo, take a look at iCandy's post in this thread (it is really helped me understand the formulas for 3 set venn diagrams): formulae-for-3-overlapping-sets-69014.htmlslingfox, yes I had a look at that thread... great formulas. But yet to figure out what is wrong where... something's gotta give  will go for a run and break, and return with fresh perspective!
|
|
|
|
|
|
Senior Manager
Joined: 20 Mar 2008
Posts: 461
Followers: 1
Kudos [?]:
49
[0], given: 5
|
Re: Overlapping Sets Problem [#permalink]
31 Oct 2009, 11:31
gmattokyo wrote: gmattokyo wrote: slingfox wrote: The OA from Veritas is B. I keep getting A whereas two people have gotten D Did Veritas give any explanation? Unless there is a hidden trap (q looks straightforward enough) which makes the venn diagram wrong, I still don't see how it could be 6. Here is one approach to get B... shoot!! 3 people play all three instruments. So they got counted in 10 of Piano, 11 of Guitar and 14 of Violin.So people who play 1 or 2 instruments is 35-3x3=26 Given 20 people play 1 instrument only... people who play 2 instruments= 26-20=6 That bold st. is the key. The 3 people who play all three instruments is included in each of these, "10 play piano, 11 play guitar, 14 play violin" so it has to be subtracted from each. It should have been: Let single piano players = p Let single guitar players = g Let single violin players = v Given, p + 3 + g + 3 + v + 3 + 20 = 10 + 11 + 14. Hence, p + g + v = 35 - 29 = 6
|
|
|
|
|
|
Intern
Joined: 15 Mar 2010
Posts: 5
Followers: 0
Kudos [?]:
1
[1] , given: 0
|
Re: Overlapping Sets Problem [#permalink]
16 Mar 2010, 00:48
1
This post received
KUDOS
Jivana wrote: gmattokyo wrote: gmattokyo wrote: The OA from Veritas is B. I keep getting A whereas two people have gotten D Did Veritas give any explanation? Unless there is a hidden trap (q looks straightforward enough) which makes the venn diagram wrong, I still don't see how it could be 6. Here is one approach to get B... shoot!! 3 people play all three instruments. So they got counted in 10 of Piano, 11 of Guitar and 14 of Violin.So people who play 1 or 2 instruments is 35-3x3=26 Given 20 people play 1 instrument only... people who play 2 instruments= 26-20=6 That bold st. is the key. The 3 people who play all three instruments is included in each of these, "10 play piano, 11 play guitar, 14 play violin" so it has to be subtracted from each. It should have been: Let single piano players = p Let single guitar players = g Let single violin players = v Given, p + 3 + g + 3 + v + 3 + 20 = 10 + 11 + 14. Hence, p + g + v = 35 - 29 = 6ie ppl playing only two instruments are counted twice if we add 10 , 11 , 14 ie 10 + 11 + 14 = 20 + 2B + 3 x 3 2B = 6 B = 3 , The Qn is how many ppl play two instruments = ppl playing only two instruments + ppl playing 3 instruments 3 + 3 = 6 -V
|
|
|
|
|
|
Senior Manager
Joined: 13 Dec 2009
Posts: 269
Followers: 8
Kudos [?]:
67
[1] , given: 13
|
Re: Overlapping Sets Problem [#permalink]
16 Mar 2010, 08:19
1
This post received
KUDOS
slingfox wrote: Can someone tell explain how they go about solving this one?
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 Lets' say PG+GV+VP = S where PG is intersection of piano and guitar, GV is intersection of guitar and violin and VP is intersection of violin and piano No. of players who play at least one instrument = 10+11+14 - S +3 or (P+G+V-(PG+GV+VP)+PGV) =38 - S No. of players who play at least one instrument also = 20+s-6 or (No.of people who play only one instrument + PG+GV+VP - 2 * PGV) 14+s = 38 - s =>2S = 24 => s = 12 No. of people who play only 2 instruments = PG+GV+VP - 2 * PGV = 12 - 2*3 = 6 So, answer is B
_________________
My debrief: done-and-dusted-730-q49-v40
|
|
|
|
|
|
Director
Joined: 25 Aug 2007
Posts: 959
WE 1: 3.5 yrs IT
WE 2: 2.5 yrs Retail chain
Followers: 38
Kudos [?]:
555
[0], given: 40
|
Re: Overlapping Sets Problem [#permalink]
13 May 2010, 07:59
IMO A. I am assuming that question is asking how many playing only 2 instruments. Let's say a = playing P only b = playing G only c = playing V only, and (a+b+c) = 20 d = playing P and G e = playing G and V f = playing V and P g = playing P, G and V = 3 Therefore, 10 = a+d+e+g 11 = b+d+f+g 14 = c+e+f+g ------------------------------ 35 = (a+b+c) + 2(d+e+f) + 3g ------------------------------ 35 = 20 + 2(d+e+f) + 3x3 = 20 + 2(d+e+f) + 9 = 29 + 2(d+e+f) Therefore, (d+e+f) = 3 Please tell me where I am wrong.
_________________
Want to improve your CR: cr-methods-an-approach-to-find-the-best-answers-93146.html
Tricky Quant problems: 50-tricky-questions-92834.html
Important Grammer Fundamentals: key-fundamentals-of-grammer-our-crucial-learnings-on-sc-93659.html
|
|
|
|
|
|
Director
Joined: 23 Apr 2010
Posts: 595
Followers: 2
Kudos [?]:
14
[0], given: 7
|
Re: Overlapping Sets Problem [#permalink]
10 Aug 2010, 01:10
If the question asks (which in fact it doesn't) how many people play only 2 instruments, then the answer is 3 (I used the same approach as ykaiim). If we want to find the number of people who play two instruments (i.e., 2 or more), then we have to add 3 (the number of people who play all three instruments) to the previous number. So we get 3+3 = 6.
|
|
|
|
|
|
Senior Manager
Status: ==GMAT Ninja==
Joined: 08 Jan 2011
Posts: 251
Schools: ISB, IIMA ,SP Jain , XLRI
WE 1: Aditya Birla Group (sales)
WE 2: Saint Gobain Group (sales)
Followers: 4
Kudos [?]:
38
[0], given: 46
|
Re: Overlapping Sets Problem [#permalink]
26 Aug 2011, 03:07
vin2010 wrote: ie 10 + 11 + 14 = 20 + 2B + 3 x 3
2B = 6
B = 3 ,
The Qn is how many ppl play two instruments
= ppl playing only two instruments + ppl playing 3 instruments
3 + 3 = 6
-V you got the exact point the question is not asking how many play ONLY TWO instrument but TWO instrument (which includes the no of people playing 3 instruments too)
_________________
WarLocK
_____________________________________________________________________________
The War is oNNNNNNNNNNNNN for 720+
see my Test exp here http://gmatclub.com/forum/my-test-experience-111610.html
do not hesitate me giving kudos if you like my post. 
|
|
|
|
|
|
Senior Manager
Status: mba here i come!
Joined: 07 Aug 2011
Posts: 271
Location: Pakistan
Concentration: Strategy, Marketing
GMAT 1: 680 Q46 V37
GMAT 2: Q V
Followers: 13
Kudos [?]:
456
[1] , given: 48
|
Re: Overlapping Sets Problem [#permalink]
27 Aug 2011, 12:22
1
This post received
KUDOS
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
Download Valuable Collection of Percentage Questions (PS/DS)
|
|
|
|
|
|
Intern
Joined: 29 Aug 2011
Posts: 24
Followers: 1
Kudos [?]:
1
[0], given: 3
|
Re: Overlapping Sets Problem [#permalink]
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: 3104
Location: Pune, India
Followers: 567
Kudos [?]:
1993
[0], given: 92
|
Re: Overlapping Sets Problem [#permalink]
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 2447 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
My Blog
Save 10% on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.
Veritas Prep Reviews
|
|
|
|
|
|
Intern
Joined: 29 Aug 2011
Posts: 24
Followers: 1
Kudos [?]:
1
[0], given: 3
|
Re: Of a group of people, 10 play piano, 11 play guitar, 14 play [#permalink]
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: 75
Followers: 1
Kudos [?]:
11
[0], given: 2
|
Re: Of a group of people, 10 play piano, 11 play guitar, 14 play [#permalink]
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: 190
Location: India
Concentration: Finance, International Business
WE: Information Technology (Investment Banking)
Followers: 3
Kudos [?]:
14
[0], given: 1
|
Re: Overlapping Sets Problem [#permalink]
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.
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11506
Followers: 1791
Kudos [?]:
9523
[1] , given: 826
|
Re: Of a group of people, 10 play piano, 11 play guitar, 14 play [#permalink]
05 Feb 2012, 03:47
1
This post received
KUDOS
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: Attachment: 
Union_3sets.gif [ 11.63 KiB | Viewed 2281 times ]
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. Answer: B. Detailed analysis of this concept is here: formulae-for-3-overlapping-sets-69014.html#p729340subhajeet 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.
_________________
PLEASE READ AND FOLLOW: 11 Rules for Posting!!!
RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory
COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. NEW!!!
DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
|
Re: Of a group of people, 10 play piano, 11 play guitar, 14 play
[#permalink]
05 Feb 2012, 03:47
|
|
|
|
|
|
|
|
|
|
|
close
