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# Venn Diagram Question

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Intern
Joined: 20 May 2009
Posts: 1
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Kudos [?]: 0 [0], given: 0

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20 May 2009, 08:01
Of the 300 patients who suffered from at least one symptom of A, B, and C, 35% sufffered from A, 45% suffered from B, 40% suffered from C, 10% suffered from exactly 2 of them. How many people suffered from eactly one symptom?

The answer is 255 but I don't know how to solve this. Appreciate the help.
Senior Manager
Joined: 08 Jan 2009
Posts: 329
Followers: 2

Kudos [?]: 156 [0], given: 5

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20 May 2009, 23:19
We know that AuBuC = A + B + C - ( AnB + BnC+ CnB) - 2 ( AnBnC)

So 100 % = 35 + 40 + 45 + - ( 10 ) - 2 ( AnBnC)

So exactly 3 of them AnBnC = 5 % so 5 % of 300 = 15

Exactly two of tem = 300 * 10% = 30

eactly one symptom = 300 - 30 -15 = 255.
Current Student
Joined: 25 May 2010
Posts: 52
Location: Taiwan
GMAT 1: 720 Q50 V38
GPA: 3.59
WE: Supply Chain Management (Manufacturing)
Followers: 0

Kudos [?]: 8 [0], given: 22

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20 Mar 2011, 08:01
tkarthi4u wrote:
We know that AuBuC = A + B + C - ( AnB + BnC+ CnB) - 2 ( AnBnC)

So 100 % = 35 + 40 + 45 + - ( 10 ) - 2 ( AnBnC)

So exactly 3 of them AnBnC = 5 % so 5 % of 300 = 15

Exactly two of tem = 300 * 10% = 30

eactly one symptom = 300 - 30 -15 = 255.

--------------

I'm sorry, but I'm a little confused, where do you get the 2 from 2 ( AnBnC)?
Manager
Joined: 05 Jan 2011
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Kudos [?]: 134 [1] , given: 8

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20 Mar 2011, 09:45
1
KUDOS
tingjojo wrote:
tkarthi4u wrote:
We know that AuBuC = A + B + C - ( AnB + BnC+ CnB) - 2 ( AnBnC)

So 100 % = 35 + 40 + 45 + - ( 10 ) - 2 ( AnBnC)

So exactly 3 of them AnBnC = 5 % so 5 % of 300 = 15

Exactly two of tem = 300 * 10% = 30

eactly one symptom = 300 - 30 -15 = 255.

--------------

I'm sorry, but I'm a little confused, where do you get the 2 from 2 ( AnBnC)?

Have a look at http://gmatclub.com/forum/formulae-for-3-overlapping-sets-69014.html#p522537
Current Student
Joined: 25 May 2010
Posts: 52
Location: Taiwan
GMAT 1: 720 Q50 V38
GPA: 3.59
WE: Supply Chain Management (Manufacturing)
Followers: 0

Kudos [?]: 8 [0], given: 22

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21 Mar 2011, 03:22
Onell wrote:
tingjojo wrote:
tkarthi4u wrote:
We know that AuBuC = A + B + C - ( AnB + BnC+ CnB) - 2 ( AnBnC)

So 100 % = 35 + 40 + 45 + - ( 10 ) - 2 ( AnBnC)

So exactly 3 of them AnBnC = 5 % so 5 % of 300 = 15

Exactly two of tem = 300 * 10% = 30

eactly one symptom = 300 - 30 -15 = 255.

--------------

I'm sorry, but I'm a little confused, where do you get the 2 from 2 ( AnBnC)?

Have a look at http://gmatclub.com/forum/formulae-for-3-overlapping-sets-69014.html#p522537

Thanks a lot!! Kudos to you!
SVP
Joined: 16 Nov 2010
Posts: 1671
Location: United States (IN)
Concentration: Strategy, Technology
Followers: 33

Kudos [?]: 528 [0], given: 36

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22 Mar 2011, 05:07
A + AB + AC + B + BC + C + ABC = 300

A + B + C = ?

A + AB + AC + ABC = 35/100 * 300 = 105

B + BC + AB + ABC = 45/100 * 300 = 135

C + AC + BC + ABC = 40/100 * 300 = 120

AB + BC + AC = 10/100 * 300 = 30

A + B + C + 60 + 3ABC = 360

=> A + B + C + 3ABC = 300

A + B + C + ABC = 300 - 30 = 270

=> ABC = 30/2= 15

So A + B +C = 300 - 30 - 15 = 255

or 2 (A+B+C) = 810 - 300 = 510 => (A+B+C) = 510/2 = 255
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Re: Venn Diagram Question   [#permalink] 22 Mar 2011, 05:07
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