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
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.
Bunnel: Thanks for the explanation. But it becomes a bit confusing here. Looks like i have to extra vigilent for these type of statements.
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