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# There are 32 students in a certain class. The students chose

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VP
Joined: 13 Jun 2004
Posts: 1115
Location: London, UK
Schools: Tuck'08
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There are 32 students in a certain class. The students chose [#permalink]

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17 Oct 2004, 20:57
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There are 32 students in a certain class. The students chose some clubs to take part in, 10 students did not choose any club, 15 students chose A, 20 students chose B. How many students chose only one club?
Manager
Joined: 18 Sep 2004
Posts: 151
Location: Dallas, TX
Followers: 1

Kudos [?]: 11 [0], given: 0

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17 Oct 2004, 21:37
32-10 = 22 Students in one or two clubs

# In A + # In B =
15 + 20 = 35

35 - 22 = 13 In both A and B The overlap

22 - 13 = 9 In only one
VP
Joined: 13 Jun 2004
Posts: 1115
Location: London, UK
Schools: Tuck'08
Followers: 7

Kudos [?]: 45 [0], given: 0

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17 Oct 2004, 22:58
Correct.

I have the same result

A + B - Both + Excluded = 32
15+20-both+10=32
35-Both=22
Both=13

in A -> 15-13 = 2 students chose only A
in b -> 20-13 = 7 students chose only B

So total, 9 students only chose one club.

Good job Nzgmat
Intern
Joined: 07 Oct 2004
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18 Oct 2004, 22:39
as 10 students are not in any clubs
=> n(AUB) =32 - 10 =22

we have formula n(AUB) =n(A) + n(B) -n(A intersection B)

//**simple sets formula(cudn't find intersection's sign which is inverted U)..kindly adjust...

=>n(A intersection B)=15 + 20 - 22 = 13

so, only A=15 - 13 =2
and, only B=20 -13 =7

so only A& B = 2+7 =9
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VP
Joined: 13 Jun 2004
Posts: 1115
Location: London, UK
Schools: Tuck'08
Followers: 7

Kudos [?]: 45 [0], given: 0

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19 Oct 2004, 01:34
For me, exactly the same way than you guys to find that result is 9
Just wanted to confirm my first result because I didn't have any official answer attached with the problem
CIO
Joined: 09 Mar 2003
Posts: 463
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20 Oct 2004, 08:18
Who's up for a good Venn diagram?

Ans: 9
Manager
Joined: 31 Aug 2004
Posts: 162
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21 Oct 2004, 12:39
Same answer as everyone else, 9 people.

21 Oct 2004, 12:39
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