GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 May 2019, 06:30

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
Senior Manager
Joined: 25 Dec 2018
Posts: 296
Location: India
Concentration: General Management, Finance
GMAT Date: 02-18-2019
GPA: 3.4
WE: Engineering (Consulting)
Each of the hundred students in a class enrolled in at least one of  [#permalink]

### Show Tags

13 Apr 2019, 08:06
00:00

Difficulty:

45% (medium)

Question Stats:

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

### HideShow timer Statistics

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
Manager
Joined: 05 Oct 2017
Posts: 63
Re: Each of the hundred students in a class enrolled in at least one of  [#permalink]

### Show Tags

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!
_________________
Press Kudos if you liked my response!!!
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3386
Location: India
GPA: 3.12
Each of the hundred students in a class enrolled in at least one of  [#permalink]

### Show Tags

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)
_________________
You've got what it takes, but it will take everything you've got
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3386
Location: India
GPA: 3.12
Re: Each of the hundred students in a class enrolled in at least one of  [#permalink]

### Show Tags

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!
_________________
You've got what it takes, but it will take everything you've got
Re: Each of the hundred students in a class enrolled in at least one of   [#permalink] 14 Apr 2019, 02:41
Display posts from previous: Sort by