Last visit was: 23 Apr 2026, 18:05 It is currently 23 Apr 2026, 18:05
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
cfc198
User avatar
CAT Forum Moderator
Joined: 29 Nov 2018
Last visit: 12 Apr 2020
Posts: 261
Own Kudos:
832
 [31]
Given Kudos: 50
Concentration: Marketing, Strategy
Posts: 261
Kudos: 832
 [31]
The ratio of the average age of the class without the teacher to the 10 Jan 2019, 08:00
Kudos
Add Kudos
31
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:

75% (hard)

Question Stats:

60% (02:52) correct 40% (02:32) wrong based on 146 sessions

History

Date
Time
Result
Not Attempted Yet
The ratio of the average age of the class without the teacher to the average age including the teacher is 8 : 9. If the ratio of the teacher’s age and the average age of the students is 3 : 1, find the number of students.

A. 8
B. 9
C. 10
D. 12
E. 15
ShowHide Answer
Official Answer
E
Most Helpful Reply
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 23 Apr 2026
Posts: 16,441
Own Kudos:
79,397
 [6]
Given Kudos: 484
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,441
Kudos: 79,397
 [6]
The ratio of the average age of the class without the teacher to the Updated on: 20 Oct 2022, 05:17
Originally posted by KarishmaB on 10 Jan 2019, 21:13.
Last edited by KarishmaB on 20 Oct 2022, 05:17, edited 1 time in total.
5
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
cfc198
The ratio of the average age of the class without the teacher to the average age including the teacher is 8 : 9. If the ratio of the teacher’s age and the average age of the students is 3 : 1, find the number of students.

A. 8
B. 9
C. 10
D. 12
E. 15
Show more


Solve it using the logical approach.

Avg Age of students : Avg age of students incl teacher = 8:9

Age of teacher : Avg age of students = 3:1 = 24 : 8 (to make it comparable to ratio above.)

Say if teacher's age is 24, the students avg age is 8 which becomes 9 when the teacher is added to the group. The increase of 1 is because of the excess 16 (24 - 8 = 16) that the teacher brought in to divide evenly among all students and herself. Since everyone got 1 (the avg increased by 1), there must have been total 16 people (15 students + 1 teacher).

Hence number of students must be 15.

Answer (E)
General Discussion
User avatar
Dare Devil
User avatar
Joined: 01 May 2017
Last visit: 17 Feb 2025
Posts: 65
Own Kudos:
36
 [2]
Given Kudos: 14
Location: India
Posts: 65
Kudos: 36
 [2]
The ratio of the average age of the class without the teacher to the Updated on: 10 Jan 2019, 23:10
Originally posted by Dare Devil on 10 Jan 2019, 18:55.
Last edited by Dare Devil on 10 Jan 2019, 23:10, edited 1 time in total.
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
The ratio of the average age of the class without the teacher to the average age including the teacher is 8 : 9. If the ratio of the teacher’s age and the average age of the students is 3 : 1, find the number of students.

Let number of students in the class = x
Let the average age of the students = y
Let the age of the teacher = z

Given,
1) ratio of the average age of the class without the teacher to the average age including the teacher = 8 : 9
Average age of students and teacher = \((No.Of Students*Avg Age + Age of teacher)/(No.of students + 1)\)
= \((x*y + z)/(x+1)\)
Given this ratio = 8:9
\(y/((x*y + z)/(x+1)) = 8/9\)
\(y(x+1)/(x*y + z) = 8/9\)
\(xy + 9y = 8z\) -----------------------equation 1

2) Ratio of the teacher’s age and the average age of the students is 3 : 1
\(z/y = 3/1\)
\(z = 3y\) --------------------------------- equation 2
equation 2 in equation 1 implies,
\(xy + 9y = 8(3z)\)
\(xy = 15y\)
\(y(x-15) =0\)
Since y avg age can't be zero
\(x = 15\)
Number of students = 15

Option E is correct
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 22 Apr 2026
Posts: 11,229
Own Kudos:
45,002
 [1]
Given Kudos: 335
Status:Math and DI Expert
Location: India
Concentration: Human Resources, General Management
GMAT Focus 1: 735 Q90 V89 DI81
Products:
My Reviews
Expert
Expert reply
GMAT Focus 1: 735 Q90 V89 DI81
Posts: 11,229
Kudos: 45,002
 [1]
The ratio of the average age of the class without the teacher to the 10 Jan 2019, 21:47
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
cfc198
The ratio of the average age of the class without the teacher to the average age including the teacher is 8 : 9. If the ratio of the teacher’s age and the average age of the students is 3 : 1, find the number of students.

A. 8
B. 9
C. 10
D. 12
E. 15
Show more

(A)A logical way..

(I) If s students are there, the strength with the addition of a teacher becomes s+1..
(II) However, teacher's age is 3 times the average of students average age, we can take instead of teacher we are adding the 3 students to total students, say s... so s+3

Therefore, final ratio 8:9 will be similar to ratio s=1 : s+3..
\(\frac{8}{9}=\frac{s+1}{s+3}.....9(s+1)=8(s+3)......9s+9=8s+24......s=24-9=15\)


(B)If you do not understand the reasoning behind the above solution..
# of students = s and average age = a... so total age = as
# after addition of teacher = s+1, and age of teacher = 3a...so total age = as+3a... average age now = \(\frac{as+3a}{s+1}=\frac{a(s+3)}{s+1}\)

Thus initial average age : average age after addition = a : \(\frac{a(s+3)}{s+1}\) = 8:9.....1 : \(\frac{(s+3)}{s+1}\) = 8:9..
\(9*1=\frac{(s+3)}{s+1}*8....9(s+1)=8(s+3)......9s+9=8s+24......s=24-9=15.\)

E
avatar
Bharat1993
avatar
Joined: 07 Jan 2019
Last visit: 03 Oct 2019
Posts: 1
Own Kudos:
1
 [1]
Given Kudos: 12
Posts: 1
Kudos: 1
 [1]
The ratio of the average age of the class without the teacher to the 10 Jan 2019, 22:43
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Dare Devil
The ratio of the average age of the class without the teacher to the average age including the teacher is 8 : 9. If the ratio of the teacher’s age and the average age of the students is 3 : 1, find the number of students.

Let number of students in the class = x
Let the average age of the students = y
Let the age of the teacher = z

Given,
1) ratio of the average age of the class without the teacher to the average age including the teacher = 8 : 9
Average age of students and teacher = \((No.Of Students*Avg Age + Age of teacher)/(No.of students + 1)\)
= \((x*y + z)/(x+1)\)
Given this ratio = 8:9
\((x*y + z)/(x+1) = 8/9\)
\(xy + 9y = 8z\) -----------------------equation 1

2) Ratio of the teacher’s age and the average age of the students is 3 : 1
\(z/y = 3/1\)
\(z = 3y\) --------------------------------- equation 2
equation 2 in equation 1 implies,
\(xy + 9y = 8(3z)\)
\(xy = 15y\)
\(y(x-15) =0\)
Since y avg age can't be zero
\(x = 15\)
Number of students = 15

Option E is correct
Show more

Thank you for the solution. I have a small question to ask. I see no element of average age of students without teacher being used while deriving the 1st equation. I see that the ratio has been directly equated to the equation of new average age with teacher. However the solution is correct. Where am I thinking wrong? Or what am I missing here. Can you kindly help me out? Thanks in advance

Posted from my mobile device
User avatar
Dare Devil
User avatar
Joined: 01 May 2017
Last visit: 17 Feb 2025
Posts: 65
Own Kudos:
36
Given Kudos: 14
Location: India
Posts: 65
Kudos: 36
The ratio of the average age of the class without the teacher to the 10 Jan 2019, 23:39
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bharat1993


Thank you for the solution. I have a small question to ask. I see no element of average age of students without teacher being used while deriving the 1st equation. I see that the ratio has been directly equated to the equation of new average age with teacher. However the solution is correct. Where am I thinking wrong? Or what am I missing here. Can you kindly help me out? Thanks in advance

Posted from my mobile device
Show more

Hey Bharat, I did the problem basically on the paper first So I wrote the final step after resolving the equation as equation 1 ...you are right I missed avg of students.. I arrived at the right answer..including the avg of students. I have edited it, inline in the first post with the correct steps and thanks for pointing out the mistake.
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,964
Own Kudos:
1,117
Posts: 38,964
Kudos: 1,117
The ratio of the average age of the class without the teacher to the 09 Nov 2025, 07:20
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.
Moderators:
Bunuel
Math Expert
109785 posts
Krunaal
Tuck School Moderator
853 posts