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150 students at seward high school. 66 play baseball, 45

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CEO
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Schools: Chicago (Booth) - Class of 2011
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Re: PS: high school sports [#permalink]

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New post 16 Jun 2008, 21:46
66+45+42-27-6+x=150 ---> x=30

This equation is constructed by following principle: How we can come from (66+45+42) to 150.

1. we have to subtract 27 as we count it twice in (66+45+42)
2. we have to subtract 2*3 as we count it three times in (66+45+42)
3. we have to add x (none) as we do not count it in (66+45+42)
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Re: PS: high school sports [#permalink]

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New post 24 Oct 2009, 23:22
30 too

150 - x = 150 - [66 + 45 + 42 - N2 - 2(3)]

PS: N2 is subtracted only once because any two pairs are counted exactly twice.
N3 is subtracted twice because all three are counted exactly three times.
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Re: 150 students at seward high school. 66 play baseball, 45 [#permalink]

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New post 13 Nov 2011, 11:04
These are the two formulas required in this ques:

1. Three sets A, B, and C, then
P(AuBuC) = P(A) + P(B) + P(C) – P(AnB) – P(AnC) – P(BnC) + P(AnBnC)

2. Number of people in exactly two of the sets =
P(AnB) + P(AnC) + P(BnC) – 3P(AnBnC)

Using 2,
27 = P(AnB) + P(AnC) + P(BnC) - 3 (3)

Hence, P(AnB) + P(AnC) + P(BnC) = 36

Put this in 1
P(AuBuC) = P(A) + P(B) + P(C) – P(AnB) – P(AnC) – P(BnC) + P(AnBnC)
or
P(AuBuC) = P(A) + P(B) + P(C) – [P(AnB) + P(AnC) + P(BnC)] + P(AnBnC)
=> P(AuBuC) = 66 + 42 + 45 - 36 + 3 = 120

Hence, NONE of sports is
Total - P(AuBuC) = 150-120 = 30

C is the Answer
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Re: 150 students at seward high school. 66 play baseball, 45 [#permalink]

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New post 09 Jun 2018, 20:39
ArvGMAT wrote:
150 students at seward high school. 66 play baseball, 45 basketball and 42 soccer. 27 play exactly 2 sports and 3 play all 3 sports. How many of the 150 play none of the 3 sports?


Here is the formula for overlapping sets:

Total - None = total baseball(A) + total basketball(B) + total soccer(C) - {exactly 2} - 2{All the three}

150 - None = 66 + 45 + 42 - {27} - 2{3}

150 - None = 153 - 27 - 6

None = 30
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Re: 150 students at seward high school. 66 play baseball, 45 [#permalink]

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New post 10 Jun 2018, 01:09
ArvGMAT wrote:
150 students at seward high school. 66 play baseball, 45 basketball and 42 soccer. 27 play exactly 2 sports and 3 play all 3 sports. How many of the 150 play none of the 3 sports?


150 - x = 66+45+42-27-2(3)

150-x = 153-33

x = 150-120 = 30
Re: 150 students at seward high school. 66 play baseball, 45   [#permalink] 10 Jun 2018, 01:09

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150 students at seward high school. 66 play baseball, 45

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