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Re: Overlapping Sets Problem [#permalink]
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27 Aug 2011, 11:22
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those who play single instrument = 20 those who don't play a single instrument (play 2 or 3) = 3520 = 15 those who play 2 instruments = 153 = 12 (3 play all three instruments)
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Re: Overlapping Sets Problem [#permalink]
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06 Sep 2011, 11:43
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).



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Re: Overlapping Sets Problem [#permalink]
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06 Sep 2011, 20:57
MBAhereIcome wrote: those who play single instrument = 20 those who don't play a single instrument (play 2 or 3) = 3520 = 15
those who play 2 instruments = 153 = 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 5176 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.
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Re: Of a group of people, 10 play piano, 11 play guitar, 14 play [#permalink]
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05 Feb 2012, 01:18
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.



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Re: Of a group of people, 10 play piano, 11 play guitar, 14 play [#permalink]
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05 Feb 2012, 01:47
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. 2620=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.



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Re: Overlapping Sets Problem [#permalink]
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05 Feb 2012, 02:19
VeritasPrepKarishma wrote: MBAhereIcome wrote: those who play single instrument = 20 those who don't play a single instrument (play 2 or 3) = 3520 = 15
those who play 2 instruments = 153 = 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.



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Of a group of people, 10 play piano, 11 play guitar, 14 play [#permalink]
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05 Feb 2012, 02:47
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 3520=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 153=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: http://gmatclub.com/forum/formulaefor ... ml#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. Attachment:
Union_3sets.gif [ 11.63 KiB  Viewed 5071 times ]
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Of a group of people, 10 play piano, 11 play guitar [#permalink]
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22 Aug 2012, 08:49
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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
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Re: Of a group of people, 10 play piano, 11 play guitar, 14 play [#permalink]
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15 Aug 2013, 14:18
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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 = 103 +113 +143 = 359 = 26 1 instruments player = 20 so 2 instruments player = 2620 = 6 =B
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Re: Overlapping Sets Problem [#permalink]
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15 Aug 2013, 19:05
VeritasPrepKarishma wrote: MBAhereIcome wrote: those who play single instrument = 20 those who don't play a single instrument (play 2 or 3) = 3520 = 15
those who play 2 instruments = 153 = 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???
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Re: Overlapping Sets Problem [#permalink]
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15 Aug 2013, 21:26
jaituteja wrote: VeritasPrepKarishma wrote: MBAhereIcome wrote: those who play single instrument = 20 those who don't play a single instrument (play 2 or 3) = 3520 = 15
those who play 2 instruments = 153 = 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.
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Re: Of a group of people, 10 play piano, 11 play guitar, 14 play [#permalink]
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18 Aug 2013, 10:36
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 103=7 Play only guitar 113=8 Play only violin 143=11 so, 20=7+8+112overlapping set 2overlapping set=2620=6 so, the best answer is (B) Posted by Abdul Mannan Mian



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Re: Of a group of people, 10 play piano, 11 play guitar, 14 play [#permalink]
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14 Sep 2013, 02:09
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..



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Re: Tough Overlapping Set Problem Veritas [#permalink]
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20 Dec 2013, 08:15
35 TOTPeople  20 individual instr  3 ABC = 12 remain for 2 instr / 2 instr = ANS:6 people play 2



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Re: Of a group of people, 10 play piano, 11 play guitar, 14 play [#permalink]
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05 Feb 2014, 10:24
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 2620 = 6 = People playing two instruments Hit Kudos if you found this helpful. Cheers and good luck



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Re: Of a group of people, 10 play piano, 11 play guitar, 14 play [#permalink]
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24 Sep 2014, 07:36
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.



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Of a group of people, 10 play piano, 11 play guitar, 14 play [#permalink]
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24 Sep 2014, 07:37
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 2620 = 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.



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Of a group of people, 10 play piano, 11 play guitar, 14 play [#permalink]
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01 Aug 2015, 20:17
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. 35209 = 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).



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Re: Of a group of people, 10 play piano, 11 play guitar, 14 play [#permalink]
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23 Aug 2015, 12:47
AHHH!! The key seems to be the 'play two instrument's' in the question. Was breaking my head over why not 3.



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Re: Of a group of people, 10 play piano, 11 play guitar, 14 play [#permalink]
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19 Mar 2016, 03:27
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. Please correct me.




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