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

It is currently 25 Jun 2019, 13:00

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

The ratio of the average age of the class without the teacher to the

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

 
Manager
Manager
avatar
P
Joined: 29 Nov 2018
Posts: 200
Concentration: Marketing, Strategy
The ratio of the average age of the class without the teacher to the  [#permalink]

Show Tags

New post 10 Jan 2019, 08:00
8
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

59% (02:26) correct 41% (02:36) wrong based on 30 sessions

HideShow timer Statistics


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
Manager
Manager
avatar
B
Joined: 01 May 2017
Posts: 82
Location: India
The ratio of the average age of the class without the teacher to the  [#permalink]

Show Tags

New post Updated on: 10 Jan 2019, 23:10
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

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.
Veritas Prep GMAT Instructor
User avatar
D
Joined: 16 Oct 2010
Posts: 9364
Location: Pune, India
Re: The ratio of the average age of the class without the teacher to the  [#permalink]

Show Tags

New post 10 Jan 2019, 21:13
3
cfc198 wrote:
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



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)

To read more on this approach, check: https://www.veritasprep.com/blog/2012/0 ... etic-mean/
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7763
Re: The ratio of the average age of the class without the teacher to the  [#permalink]

Show Tags

New post 10 Jan 2019, 21:47
cfc198 wrote:
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


(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
_________________
Intern
Intern
avatar
B
Joined: 07 Jan 2019
Posts: 1
Re: The ratio of the average age of the class without the teacher to the  [#permalink]

Show Tags

New post 10 Jan 2019, 22:43
1
Dare Devil wrote:
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


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
Manager
Manager
avatar
B
Joined: 01 May 2017
Posts: 82
Location: India
Re: The ratio of the average age of the class without the teacher to the  [#permalink]

Show Tags

New post 10 Jan 2019, 23:39
Bharat1993 wrote:

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


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.
GMAT Club Bot
Re: The ratio of the average age of the class without the teacher to the   [#permalink] 10 Jan 2019, 23:39
Display posts from previous: Sort by

The ratio of the average age of the class without the teacher to the

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


cron

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne