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

 It is currently 15 Jan 2019, 21:54

### 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

## Events & Promotions

###### Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### The winning strategy for a high GRE score

January 17, 2019

January 17, 2019

08:00 AM PST

09:00 AM PST

Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL.

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 29 Nov 2018
Posts: 59
Concentration: Marketing, Strategy
The ratio of the average age of the class without the teacher to the  [#permalink]

### Show Tags

10 Jan 2019, 07:00
4
00:00

Difficulty:

45% (medium)

Question Stats:

67% (02:25) correct 33% (02:18) wrong based on 18 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
Joined: 01 May 2017
Posts: 62
Location: India
The ratio of the average age of the class without the teacher to the  [#permalink]

### Show Tags

Updated on: 10 Jan 2019, 22:10
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, 17:55.
Last edited by Dare Devil on 10 Jan 2019, 22:10, edited 1 time in total.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8783
Location: Pune, India
Re: The ratio of the average age of the class without the teacher to the  [#permalink]

### Show Tags

10 Jan 2019, 20:13
1
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.

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

Karishma
Veritas Prep GMAT Instructor

Math Expert
Joined: 02 Aug 2009
Posts: 7199
Re: The ratio of the average age of the class without the teacher to the  [#permalink]

### Show Tags

10 Jan 2019, 20:47
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
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

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

### Show Tags

10 Jan 2019, 21:43
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
Joined: 01 May 2017
Posts: 62
Location: India
Re: The ratio of the average age of the class without the teacher to the  [#permalink]

### Show Tags

10 Jan 2019, 22:39
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.
Re: The ratio of the average age of the class without the teacher to the &nbs [#permalink] 10 Jan 2019, 22:39
Display posts from previous: Sort by