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Each of the hundred students in a class enrolled in at least one of

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New post 13 Apr 2019, 08:06
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Difficulty:

  45% (medium)

Question Stats:

63% (01:17) correct 38% (01:20) wrong based on 8 sessions

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Each of the hundred students in a class enrolled in at least one of the three activities: Singing, Dancing, and Theatre. If 40 participated in Singing, 50 participated in Dancing and 40 participated in Theatre and if 10 participated in all the three activities, how many students participated in at least two activities?

A. 10
B. 20
C. 24
D. 30
E. 32
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Re: Each of the hundred students in a class enrolled in at least one of  [#permalink]

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New post 14 Apr 2019, 01:40
mangamma wrote:
Each of the hundred students in a class enrolled in at least one of the three activities: Singing, Dancing, and Theatre. If 40 participated in Singing, 50 participated in Dancing and 40 participated in Theatre and if 10 participated in all the three activities, how many students participated in at least two activities?

A. 10
B. 20
C. 24
D. 30
E. 32

Hi,

Can someone post a detailed solution for this? My answer is coming no where close to the answer choices' figures. Not quite able to pin point my mistake in solving this.

Thanks!
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Each of the hundred students in a class enrolled in at least one of  [#permalink]

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New post 14 Apr 2019, 02:36
1
mangamma wrote:
Each of the hundred students in a class enrolled in at least one of the three activities: Singing, Dancing, and Theatre. If 40 participated in Singing, 50 participated in Dancing and 40 participated in Theatre and if 10 participated in all the three activities, how many students participated in at least two activities?

A. 10
B. 20
C. 24
D. 30
E. 32


Given data:
P(Total) = 100
P(S) = 40
P(D) = 50
P(T) = 40

From the question stem, we can deduce the following information, P(All 3) = 10 | P(Neither) = 0

Formula used: P(Total) = P(S) + P(D) + P(T) - P(Only 2) - 2*P(All 3) + P(Neither)

Substituting values, 100 = 40 + 50 + 40 - P(Only 2) - 2*10 + 0 -> x = 110 - 100 = 10

Therefore, the number of students who participated in atleast 2 activities is P(Only 2) + P(All 3) = 10 + 10 = 20(Option B)
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Re: Each of the hundred students in a class enrolled in at least one of  [#permalink]

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New post 14 Apr 2019, 02:41
1
neha283 wrote:
mangamma wrote:
Each of the hundred students in a class enrolled in at least one of the three activities: Singing, Dancing, and Theatre. If 40 participated in Singing, 50 participated in Dancing and 40 participated in Theatre and if 10 participated in all the three activities, how many students participated in at least two activities?

A. 10
B. 20
C. 24
D. 30
E. 32

Hi,

Can someone post a detailed solution for this? My answer is coming no where close to the answer choices' figures. Not quite able to pin point my mistake in solving this.

Thanks!


neha283 - I have posted a detailed solution for the question. Hope it helps!
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Re: Each of the hundred students in a class enrolled in at least one of   [#permalink] 14 Apr 2019, 02:41
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