Last visit was: 21 Jul 2024, 01:22 It is currently 21 Jul 2024, 01:22
Toolkit
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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

# In a class of 345 students, equal number of students enrolled in Engli

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 94433
Own Kudos [?]: 642638 [21]
Given Kudos: 86715
Director
Joined: 25 Oct 2015
Posts: 516
Own Kudos [?]: 897 [1]
Given Kudos: 74
Location: India
GMAT 1: 650 Q48 V31
GMAT 2: 720 Q49 V38 (Online)
GPA: 4
GMAT Club Legend
Joined: 03 Oct 2013
Affiliations: CrackVerbal
Posts: 4918
Own Kudos [?]: 7807 [1]
Given Kudos: 221
Location: India
GMAT Club Legend
Joined: 03 Jun 2019
Posts: 5318
Own Kudos [?]: 4239 [0]
Given Kudos: 161
Location: India
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Re: In a class of 345 students, equal number of students enrolled in Engli [#permalink]
Bunuel wrote:
In a class of 345 students, equal number of students enrolled in English club, Math club and Science club. 30 students enrolled both in English club and Math club, 26 students enrolled both in Math club and Science club, 28 students enrolled both in Science club and English club and 14 students enrolled in all three clubs. If there are 43 students who didn’t enroll in any of the three clubs, how many students enrolled in both English and Math clubs but not in Science club?

A. 108
B. 124
C. 178
D. 246
E. 286

Are You Up For the Challenge: 700 Level Questions

Given:
1. In a class of 345 students, equal number of students enrolled in English club, Math club and Science club.
2. 30 students enrolled both in English club and Math club, 26 students enrolled both in Math club and Science club, 28 students enrolled both in Science club and English club and 14 students enrolled in all three clubs.

Asked: If there are 43 students who didn’t enroll in any of the three clubs, how many students enrolled in both English and Math clubs but not in Science club?

Please see the solution in attached image.

Number of students enrolled in both English and Math clubs but not in Science club = 80 + 82 + 16 = 178

IMO C
Attachments

Screenshot 2020-04-25 at 11.55.21 PM.png [ 47 KiB | Viewed 6465 times ]

Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 19175
Own Kudos [?]: 22685 [1]
Given Kudos: 286
Location: United States (CA)
Re: In a class of 345 students, equal number of students enrolled in Engli [#permalink]
1
Bookmarks
Bunuel wrote:
In a class of 345 students, equal number of students enrolled in English club, Math club and Science club. 30 students enrolled both in English club and Math club, 26 students enrolled both in Math club and Science club, 28 students enrolled both in Science club and English club and 14 students enrolled in all three clubs. If there are 43 students who didn’t enroll in any of the three clubs, how many students enrolled in both English and Math clubs but not in Science club?

A. 108
B. 124
C. 178
D. 246
E. 286

Are You Up For the Challenge: 700 Level Questions

We can create an equation using the following formula:

Total = N(E) + N(M) + N(S) - N(E and M) - N(M and S) - N(E and S) + N(all three) + N(none)

345 = n + n + n - 30 - 26 - 28 + 14 + 43

345 = 3n - 84 + 57

345 = 3n - 27

372 = 3n

124 = n

The number of students enrolled in either the English club or the Math club but not in the Science club is:

Total - N(S) - N(none)

345 - 124 - 43 = 178

Intern
Joined: 11 Dec 2017
Posts: 30
Own Kudos [?]: 7 [0]
Given Kudos: 25
Location: India
Concentration: Strategy, General Management
GMAT 1: 710 Q50 V38
GMAT 2: 760 Q49 V44
GPA: 3.2
WE:Consulting (Consulting)
In a class of 345 students, equal number of students enrolled in Engli [#permalink]
CrackVerbalGMAT wrote:
In a question on Venn diagrams, we try to evaluate the word problem in small chunks without trying to consume the whole question in one go.
When the Venn diagram is being drawn, we try to populate the common regions first followed by the exclusive regions i.e. we proceed outwards from the inner regions.
We also ensure that we don’t ignore the numbers that can be outside the circles but inside the rectangle.

Considering all the above, we can draw a Venn diagram for the given question which looks like the one below:

Attachment:
25th April 2020 - Reply 4 - 1.jpg

The question says that equal number of students enrolled for the English, Math and Science clubs. This essentially means that the total number of people in each of these circles should be the same.
Therefore,

a + 44 = b + 42 which gives us a = b – 2

c + 40 = b + 42 which gives us c = b + 2.

Total number of people inside the circles = 345 – People who opted for none of the clubs = 345 – 43 = 302.

Therefore, a + b + c + 14 + 16 + 14 + 12 = 302 OR a + b + c = 246.

Substituting the values of a and c in the above equation and simplifying, we get b = 82, a = 80 and c = 84.
We do not want the students enrolled in the Science Club, therefore, we consider the regions outside the Science circle (marked in red) i.e. a+16 + b = 80 + 16 + 82 = 178.

Attachment:
25th April 2020 - Reply 4 - 2.jpg

The correct answer option is C
.
Hope that helps!

Thanks for the solution, Sir. I understood what you have done. However, I have a doubt about how the question is phrased - "BOTH English and Maths but not Science. Should the answer then not be 16? That is the only area where students are enrolled in both but not in the third subject.

CrackVerbal
ArvindCrackVerbal

Originally posted by iammanas on 23 Aug 2020, 04:57.
Last edited by iammanas on 05 Sep 2020, 01:28, edited 1 time in total.
Intern
Joined: 17 Jan 2020
Posts: 28
Own Kudos [?]: 9 [1]
Given Kudos: 7
Re: In a class of 345 students, equal number of students enrolled in Engli [#permalink]
1
Kudos
iammanas wrote:
CrackVerbalGMAT wrote:
In a question on Venn diagrams, we try to evaluate the word problem in small chunks without trying to consume the whole question in one go.
When the Venn diagram is being drawn, we try to populate the common regions first followed by the exclusive regions i.e. we proceed outwards from the inner regions.
We also ensure that we don’t ignore the numbers that can be outside the circles but inside the rectangle.

Considering all the above, we can draw a Venn diagram for the given question which looks like the one below:

Attachment:
25th April 2020 - Reply 4 - 1.jpg

The question says that equal number of students enrolled for the English, Math and Science clubs. This essentially means that the total number of people in each of these circles should be the same.
Therefore,

a + 44 = b + 42 which gives us a = b – 2

c + 40 = b + 42 which gives us c = b + 2.

Total number of people inside the circles = 345 – People who opted for none of the clubs = 345 – 43 = 302.

Therefore, a + b + c + 14 + 16 + 14 + 12 = 302 OR a + b + c = 246.

Substituting the values of a and c in the above equation and simplifying, we get b = 82, a = 80 and c = 84.
We do not want the students enrolled in the Science Club, therefore, we consider the regions outside the Science circle (marked in red) i.e. a+16 + b = 80 + 16 + 82 = 178.

Attachment:
25th April 2020 - Reply 4 - 2.jpg

The correct answer option is C
.
Hope that helps!

Thanks for the solution, Sir. I understood what you have done. However, I have a doubt with how the question is phrased - "BOTH E and M but not S. Should the reason not be 16? That is the only area where students are enrolled in both but not in the third subject.

Absolutely!!....The question is not asking for the number of students enrolled in Math or English but not Science, it is saying Math AND English but not Science. So the answer should be 16.
Manager
Joined: 08 Jun 2022
Posts: 53
Own Kudos [?]: 18 [0]
Given Kudos: 47
Location: India
Re: In a class of 345 students, equal number of students enrolled in Engli [#permalink]
I understood the solution but my doubt is : Isn't the final statement confusing? ; "how many students enrolled in both English and Math clubs but not in Science club?". Doesn't this mean E Int M-E int M int S.?
Re: In a class of 345 students, equal number of students enrolled in Engli [#permalink]
Moderator:
Math Expert
94433 posts