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Overlapping Set Problems

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Intern
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Joined: 10 Aug 2017
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Overlapping Set Problems [#permalink]

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New post 15 Oct 2017, 15:13
Question:
Total= 100 students, Physics=40, Sociology=30, Music=60. All courses=6. P+S=12, S+M=10, M+P=15. How many take none?

If we do this with formula: Total= P+S+C - (PS+PM+SM) - 2(All) + Neither, we get 19.
100=130-37-12+N
100=81+N
N=19

But if we do this with Venn Diagram we get 1. (As shown in the attached photo)

N= 100- P-S-M
N= 100- (19+14+41+6+6+4+9)
N= 1

Can anyone get the same answer with both methods?
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Re: Overlapping Set Problems [#permalink]

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New post 16 Oct 2017, 01:15
NomanSaleem wrote:
Question:
Total= 100 students, Physics=40, Sociology=30, Music=60. All courses=6. P+S=12, S+M=10, M+P=15. How many take none?

If we do this with formula: Total= P+S+C - (PS+PM+SM) - 2(All) + Neither, we get 19.
100=130-37-12+N
100=81+N
N=19

But if we do this with Venn Diagram we get 1. (As shown in the attached photo)

N= 100- P-S-M
N= 100- (19+14+41+6+6+4+9)
N= 1

Can anyone get the same answer with both methods?


We will get 1 in both the methods.
(P U S U M) = P + S + M - (PS + PM + SM) + PSM + Neither
100 = 40 + 30 + 60 - (12 + 15 + 10) + 6 + Neither
100 = 136 - 37 + Neither
Neither = 1

You made a mistake by doubling and subtracting the overlap (among the three) instead of just adding, hence the mismatch between formula and Venn diagram.

Kudos [?]: 3 [0], given: 54

Re: Overlapping Set Problems   [#permalink] 16 Oct 2017, 01:15
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Overlapping Set Problems

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