Last visit was: 21 Apr 2026, 17:25 It is currently 21 Apr 2026, 17:25
Home
Messages
Tests
Schools
Events
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
User avatar
rn1112
User avatar
Joined: 16 Jul 2022
Last visit: 21 Mar 2025
Posts: 321
Own Kudos:
227
 [15]
Given Kudos: 7
Products:
My Reviews
Posts: 321
Kudos: 227
 [15]
In a class of 100 students, the students are given a choice to select 30 Jun 2023, 09:42
Kudos
Add Kudos
15
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

55% (hard)

Question Stats:

69% (03:20) correct 31% (03:10) wrong based on 65 sessions

History

Date
Time
Result
Not Attempted Yet
In a class of 100 students, the students are given a choice to select up to two hobbies from A and B. The ratio of students choosing no hobbies and two hobbies is 1:3, and the ratio of students selecting A as a hobby to those selecting B is 5:7. If the number of students choosing only B as their hobby is 20 more than those choosing only A, find the probability of a randomly selected student taking up only A as his/her hobby.

A. 4/7
B. 2/7
C. 2/3
D. 3/4
E. 1/5
ShowHide Answer
Official Answer
E
User avatar
gmatophobia
User avatar
Quant Chat Moderator
Joined: 22 Dec 2016
Last visit: 19 Apr 2026
Posts: 3,173
Own Kudos:
11,439
 [2]
Given Kudos: 1,862
Location: India
Concentration: Strategy, Leadership
Posts: 3,173
Kudos: 11,439
 [2]
In a class of 100 students, the students are given a choice to select 30 Jun 2023, 10:11
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
rn1112
In a class of 100 students, the students are given a choice to select up to two hobbies from A and B. The ratio of students choosing no hobbies and two hobbies is 1:3, and the ratio of students selecting A as a hobby to those selecting B is 5:7. If the number of students choosing only B as their hobby is 20 more than those choosing only A, find the probability of a randomly selected student taking up only A as his/her hobby.

A. 4/7
B. 2/7
C. 2/3
D. 3/4
E. 1/5
Show more

We can use a 2*2 matrix to plot the information.

The ratio of students choosing no hobbies and two hobbies is 1:3

  • The number of students with no hobbies = x
  • The number of students with exact two hobbies = 3x

This information is plotted in the matrix in red.

The ratio of students selecting A as a hobby to those selecting B is 5:7

  • The number of students who select A as their hobby = 5y
  • The number of students who select B as their hobby = 7y

This information is plotted in the matrix in green.

The number of students choosing only B as their hobby is 20 more than those choosing only A

Using the plotted information, the number of students who choose only A as their hobby = 5y - 3x

Therefore the number of students who choose only B as their hobby = 5y - 3x + 20

This information is plotted in blue.

Let's complete the matrix -

  • The number of students who do not choose B as their hobby = 5y - 2x
  • The number of students who do not choose A as their hobby = 5y - 2x + 20

Using the matrix created, we can find the values of x and y.

5y + 20 = 7y
y = 10 --- (1)

10y - 2x + 20 = 100
Using the value of y obtained in equation (1)
x = 10 --- (2)

The number of students selecting only A as his / her hobby = 5y - 3x = 20

Required probability = \(\frac{20}{100} = \frac{1}{5}\)

Option E
Attachments

Screenshot 2023-06-30 223021.jpg
Screenshot 2023-06-30 223021.jpg [ 32.06 KiB | Viewed 3193 times ]

User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,956
Own Kudos:
1,117
Posts: 38,956
Kudos: 1,117
In a class of 100 students, the students are given a choice to select 15 Sep 2025, 11:30
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
User avatar
Naseeb007
User avatar
Joined: 01 Jun 2025
Last visit: 06 Oct 2025
Posts: 11
Own Kudos:
30
 [1]
Posts: 11
Kudos: 30
 [1]
In a class of 100 students, the students are given a choice to select 29 Sep 2025, 01:53
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
In a class of 100 students, the students are given a choice to select upto two hobbies from A and B. The ratio of students choosing no hobbies and two hobbies is 1:3, and the ratio of students selecting A as a hobby to those selecting B is 5:7. If the number of students choosing only B as their hobby is 20 more than those choosing only A, find the probability of a randomly selected student taking up only A as their hobby.

A 4/7
B 1/7
C 1/2
D 1/3
E 1/5

Show Spoiler
Attachment:
Screenshot 2025-09-29 2.22.02 PM.png
Screenshot 2025-09-29 2.22.02 PM.png [ 62.89 KiB | Viewed 705 times ]
User avatar
Shreyaarora
User avatar
Joined: 14 Nov 2024
Last visit: 29 Nov 2025
Posts: 52
Own Kudos:
40
 [1]
Given Kudos: 121
Location: India
Concentration: Leadership, Entrepreneurship
Schools: ISB '26 IIM NUS HEC Sept '26
GPA: 3.11
Schools: ISB '26 IIM NUS HEC Sept '26
Posts: 52
Kudos: 40
 [1]
In a class of 100 students, the students are given a choice to select 29 Sep 2025, 02:36
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
e-> 1/5. Explanation:

x+3X+a+b =100 (a=A only & b is B only)

A/B= a+3x / b+3x = 5/7
cross multiply->
7a+6x=5b ---1


b=a+20
so,

4x+2a+20= 100
2x+a= 40 ---2

7a+6x=5(a+20)
2a+6x= 100
3x+a=50--3

solve 2 & 3,

x=10.
a=20

hence-> 20/100= 1/5

Naseeb007
In a class of 100 students, the students are given a choice to select upto two hobbies from A and B. The ratio of students choosing no hobbies and two hobbies is 1:3, and the ratio of students selecting A as a hobby to those selecting B is 5:7. If the number of students choosing only B as their hobby is 20 more than those choosing only A, find the probability of a randomly selected student taking up only A as their hobby.
A 4/7
B 1/7
C 1/2
D 1/3
E 1/5
Show more
Moderators:
Bunuel
Math Expert
109728 posts
Krunaal
Tuck School Moderator
853 posts