Last visit was: 08 Jul 2025, 23:08 It is currently 08 Jul 2025, 23:08
Close
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
Your Progress

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.
Close
Request Expert Reply
Confirm Cancel
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 08 Jul 2025
Posts: 102,594
Own Kudos:
Given Kudos: 97,452
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,594
Kudos: 739,627
 [75]
3
Kudos
Add Kudos
72
Bookmarks
Bookmark this Post
Most Helpful Reply
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 08 Jul 2025
Posts: 21,064
Own Kudos:
26,112
 [8]
Given Kudos: 296
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 21,064
Kudos: 26,112
 [8]
5
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
General Discussion
User avatar
nick1816
User avatar
Retired Moderator
Joined: 19 Oct 2018
Last visit: 28 Jun 2025
Posts: 1,853
Own Kudos:
7,804
 [5]
Given Kudos: 707
Location: India
Posts: 1,853
Kudos: 7,804
 [5]
2
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
User avatar
Archit3110
User avatar
Major Poster
Joined: 18 Aug 2017
Last visit: 8 July 2025
Posts: 8,319
Own Kudos:
4,790
 [3]
Given Kudos: 243
Status:You learn more from failure than from success.
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1: 545 Q79 V79 DI73
GPA: 4
WE:Marketing (Energy)
GMAT Focus 1: 545 Q79 V79 DI73
Posts: 8,319
Kudos: 4,790
 [3]
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
total = M+E+S-2*all subjects
total = 40+50+35-2x
total = 125-2x
value will be minimized at value of x = 62 ; ie we then get = 125-124 ;1
IMO B

Bunuel
The Number of students learning three subjects are as follows

Maths = 40
English = 50
Science = 35

If the Number of students learning exactly two subjects is maximum and no student learns all the three subjects, then what is the minimum number of students learning exactly one subject?

A. 0
B. 1
C. 25
D. 35
E. 45


Are You Up For the Challenge: 700 Level Questions
User avatar
AnirudhaS
User avatar
LBS Moderator
Joined: 30 Oct 2019
Last visit: 25 Jun 2024
Posts: 812
Own Kudos:
848
 [1]
Given Kudos: 1,575
Posts: 812
Kudos: 848
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
nick1816
Assume number of students learning exactly two subjects is 'x', and number of students learning exactly one subject is 'y'
we have to minimize, y=40+50+35-2*x=125-2x
minimum value of y is 1 {odd-even= odd}, when x=62

Sorry where did you get this? Is is another formula?

The formula I am aware of is Total = A+B+C-(sum of exactly 2 overlap) -2(sum of all 3 overlap)+Neither

or, Total = 40+50+35-(sum of exactly 2 overlap) -2(0)+0
or total = 125 - (sum of exactly 2 overlap)
User avatar
nick1816
User avatar
Retired Moderator
Joined: 19 Oct 2018
Last visit: 28 Jun 2025
Posts: 1,853
Own Kudos:
7,804
 [3]
Given Kudos: 707
Location: India
Posts: 1,853
Kudos: 7,804
 [3]
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
N(maths)= a+b+d+e

N(English)= b+c+e+f

N(Science)= d+e+f+g

N(maths)+N(English)+N(Science)
= a+b+d+e+b+c+e+f+d+e+f+g
= a+c+g+2(b+d+f)+3e

Now we need to figure out students learning exactly one subject, that is a+c+g.

a+c+g= N(maths)+N(English)+N(Science)-2(b+d+f)-3e


It's always better to draw venn diagram and look for what you need to figure out. (Don't just cram the formulas)


AnirudhaS
nick1816
Assume number of students learning exactly two subjects is 'x', and number of students learning exactly one subject is 'y'
we have to minimize, y=40+50+35-2*x=125-2x
minimum value of y is 1 {odd-even= odd}, when x=62

Sorry where did you get this? Is is another formula?

The formula I am aware of is Total = A+B+C-(sum of exactly 2 overlap) -2(sum of all 3 overlap)+Neither

or, Total = 40+50+35-(sum of exactly 2 overlap) -2(0)+0
or total = 125 - (sum of exactly 2 overlap)

Attachments

Untitled.png
Untitled.png [ 7.3 KiB | Viewed 13668 times ]

User avatar
NischalP
Joined: 26 Nov 2019
Last visit: 20 Dec 2022
Posts: 61
Own Kudos:
44
 [1]
Given Kudos: 76
Concentration: Technology, Strategy
GMAT 1: 650 Q49 V31
Products:
GMAT 1: 650 Q49 V31
Posts: 61
Kudos: 44
 [1]
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Still not clear with the explanation.
avatar
livfcind
Joined: 03 Aug 2019
Last visit: 29 Mar 2022
Posts: 62
Own Kudos:
Given Kudos: 171
Location: India
Concentration: Operations, Strategy
GPA: 4
WE:Operations (Aerospace and Defense)
Posts: 62
Kudos: 75
Kudos
Add Kudos
Bookmarks
Bookmark this Post
AnirudhaS
nick1816
Assume number of students learning exactly two subjects is 'x', and number of students learning exactly one subject is 'y'
we have to minimize, y=40+50+35-2*x=125-2x
minimum value of y is 1 {odd-even= odd}, when x=62

Sorry where did you get this? Is is another formula?

The formula I am aware of is Total = A+B+C-(sum of exactly 2 overlap) -2(sum of all 3 overlap)+Neither

or, Total = 40+50+35-(sum of exactly 2 overlap) -2(0)+0
or total = 125 - (sum of exactly 2 overlap)

I have the same question
User avatar
bhupendersingh27
Joined: 02 Jan 2020
Last visit: 23 Dec 2020
Posts: 26
Own Kudos:
36
 [1]
Given Kudos: 45
Posts: 26
Kudos: 36
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Maths = 40
English = 50
Science = 35

Total number of students = 125
maximum how many students can be assigned two subjects: 2 x (125/2) = 2 X(62.5) ~ 2 x (62) = 124.
so 1 student left when number of students learning exactly two subjects is maximum.
User avatar
naveenban2
Joined: 24 Jul 2018
Last visit: 17 Nov 2021
Posts: 8
Own Kudos:
Given Kudos: 5
Posts: 8
Kudos: 13
Kudos
Add Kudos
Bookmarks
Bookmark this Post
bhupendersingh27
Maths = 40
English = 50
Science = 35

Total number of students = 125
maximum how many students can be assigned two subjects: 2 x (125/2) = 2 X(62.5) ~ 2 x (62) = 124.
so 1 student left when number of students learning exactly two subjects is maximum.

bhupendersingh27 Total number of students is not 125. Number of students in individual subjects contain the number the number of students common to other subjects.
Can you please explain the Formula used by you ? 2 x (125/2) = 2 X(62.5) ~ 2 x (62) = 124.
User avatar
effatara
Joined: 09 Nov 2015
Last visit: 17 Jul 2024
Posts: 196
Own Kudos:
Given Kudos: 96
Posts: 196
Kudos: 424
Kudos
Add Kudos
Bookmarks
Bookmark this Post
nick1816

Could you draw a venn diagram specifying the distribution of the subject combinations showing how B works?
User avatar
adewale223
Joined: 07 Oct 2022
Last visit: 8 July 2025
Posts: 119
Own Kudos:
57
 [2]
Given Kudos: 45
Location: Nigeria
Posts: 119
Kudos: 57
 [2]
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Very simple way to solve the problem

Let a be sum of only one

b sum of only two

c sum of only three

a + 2b + 3c = 125

Since c = 0

a + 2b = 125

Since 2b is even, maximum number for 2b will be 124

So a is 1

Answer choice B
User avatar
deepa1405
Joined: 28 Dec 2024
Last visit: 17 Jun 2025
Posts: 1
Given Kudos: 2
Posts: 1
Kudos: 0
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi Nick, the formula you are referring to provides us with the total population value. However, considering we are focusing on "exactly one subject" we will subtract the remaining "sum of exactly 2 overlap" from the population. giving us A+B+C -2x
AnirudhaS
nick1816
Assume number of students learning exactly two subjects is 'x', and number of students learning exactly one subject is 'y'
we have to minimize, y=40+50+35-2*x=125-2x
minimum value of y is 1 {odd-even= odd}, when x=62

Sorry where did you get this? Is is another formula?

The formula I am aware of is Total = A+B+C-(sum of exactly 2 overlap) -2(sum of all 3 overlap)+Neither

or, Total = 40+50+35-(sum of exactly 2 overlap) -2(0)+0
or total = 125 - (sum of exactly 2 overlap)
Moderators:
Math Expert
102594 posts
PS Forum Moderator
679 posts