Last visit was: 23 Apr 2026, 20:23 It is currently 23 Apr 2026, 20:23
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
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 23 Apr 2026
Posts: 109,785
Own Kudos:
810,878
 [33]
Given Kudos: 105,853
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,785
Kudos: 810,878
 [33]
A class has 4 sections P, Q, R and S and the average weights of the st 29 Jun 2017, 04:25
4
Kudos
Add Kudos
29
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

85% (hard)

Question Stats:

53% (02:43) correct 47% (03:07) wrong based on 266 sessions

History

Date
Time
Result
Not Attempted Yet
A class has 4 sections P, Q, R and S and the average weights of the students in the sections are 45lb, 50lb, 55lb and 65lb respectively. What is the maximum possible number of students in section R if there are 40 students in all sections combined and the average weight of the all students across all the sections is 55lb? It is known that each section has at least one student.

(A) 18
(B) 20
(C) 25
(D) 35
(E) 37
ShowHide Answer
Official Answer
D
Most Helpful Reply
User avatar
Luckisnoexcuse
User avatar
Current Student
Joined: 18 Aug 2016
Last visit: 31 Mar 2026
Posts: 513
Own Kudos:
684
 [9]
Given Kudos: 198
Concentration: Strategy, Technology
Schools: Kenan-Flagler '20 (M)
GMAT 1: 630 Q47 V29
GMAT 2: 740 Q51 V38
Products:
My Reviews
Schools: Kenan-Flagler '20 (M)
GMAT 2: 740 Q51 V38
Posts: 513
Kudos: 684
 [9]
A class has 4 sections P, Q, R and S and the average weights of the st 29 Jun 2017, 04:33
3
Kudos
Add Kudos
5
Bookmarks
Bookmark this Post
Bunuel
A class has 4 sections P, Q, R and S and the average weights of the students in the sections are 45lb, 50lb, 55lb and 65lb respectively. What is the maximum possible number of students in section R if there are 40 students in all sections combined and the average weight of the all students across all the sections is 55lb? It is known that each section has at least one student.

(A) 18
(B) 20
(C) 25
(D) 35
(E) 37
Show more

Average is 55
P : Q :R :S
45 : 50 : 55 : 65
We need to minimize the number of students in each section (Each will have one atleast)

R is mean

P has 1 : 10 away from mean
Q has 1 : 5 away from mean

Then S will have 3 students : 3*5 to maintain the mean of overall population

Leftover students in R (Maximum) : 40 - 1- 1-3 = 35
D
avatar
gopeshkhare
avatar
Joined: 12 Apr 2016
Last visit: 17 Mar 2019
Posts: 3
Own Kudos:
7
 [7]
Given Kudos: 14
Posts: 3
Kudos: 7
 [7]
A class has 4 sections P, Q, R and S and the average weights of the st 01 Aug 2017, 01:48
6
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel
A class has 4 sections P, Q, R and S and the average weights of the students in the sections are 45lb, 50lb, 55lb and 65lb respectively. What is the maximum possible number of students in section R if there are 40 students in all sections combined and the average weight of the all students across all the sections is 55lb? It is known that each section has at least one student.

(A) 18
(B) 20
(C) 25
(D) 35
(E) 37
Show more


We've 45 50 55 65 and the average is 55. Now, around the mean the distribution is -10 (for 45) and -5(for 50) = -15 on the left AND 0(55) and 10(65) = +10 on the right.

We must now try and balance both sides in such a manner so as to maximize number of students for R.
On the right the increment is in steps of 10, next biggest = 20. This means we will give 2 students to section S (10 X 2)
AND on the left we will increment one student in Q. This implies that 2 students in Q [(-10 X 1) + (-5 X 2)]. Therefore, both sides are balanced.

We will get, P has 1; Q has 2 and S has 2. Therefore, Number of students in R = 40 - 1 - 2 - 2 = 35.
General Discussion
User avatar
Heseraj
User avatar
Current Student
Joined: 04 Jan 2016
Last visit: 01 Nov 2022
Posts: 157
Own Kudos:
121
 [6]
Given Kudos: 421
Location: United States (NY)
Schools: W. P. Carey Arizona State '18 Goizueta '18 Carlson '18 Wharton '20 (A)
GMAT 1: 620 Q44 V32
GMAT 2: 600 Q48 V25
GMAT 3: 660 Q42 V39
GPA: 3.48
Schools: W. P. Carey Arizona State '18 Goizueta '18 Carlson '18 Wharton '20 (A)
GMAT 3: 660 Q42 V39
Posts: 157
Kudos: 121
 [6]
A class has 4 sections P, Q, R and S and the average weights of the st 01 Jul 2017, 17:57
4
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
In order to maximize the mean we need to equalize the difference of numbers between the two poles of the data set.

45 has a difference of 10 from 55 and
50 has difference of 5 from 55 therefore, the left side of the mean has a total difference of 15 at the least.

65 has a difference of 10 from the mean, the least difference possible. Therefore, the least average of combined weight to the left should be equal to the least combined weight of the right.

\((1)10 + 2 (5) = 2 (10) ==> 10 + 10= 20\)

Therefore, a total of 5 students in other sections which bring the number of students in Section R to 25.
User avatar
rocko911
User avatar
Joined: 11 Feb 2017
Last visit: 12 Apr 2018
Posts: 157
Own Kudos:
37
 [1]
Given Kudos: 206
Posts: 157
Kudos: 37
 [1]
A class has 4 sections P, Q, R and S and the average weights of the st 01 Aug 2017, 08:47
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel
A class has 4 sections P, Q, R and S and the average weights of the students in the sections are 45lb, 50lb, 55lb and 65lb respectively. What is the maximum possible number of students in section R if there are 40 students in all sections combined and the average weight of the all students across all the sections is 55lb? It is known that each section has at least one student.

(A) 18
(B) 20
(C) 25
(D) 35
(E) 37
Show more



Can someone explain me this question in the most easiest way to understand?
avatar
vtlinhbui
avatar
Joined: 19 Jun 2017
Last visit: 27 Nov 2017
Posts: 5
Own Kudos:
3
 [3]
Given Kudos: 32
Posts: 5
Kudos: 3
 [3]
A class has 4 sections P, Q, R and S and the average weights of the st 08 Aug 2017, 07:30
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Call p,q,r,s are the number of students in each section respectively. We have p+q+r+s= 40
Total W=45p+50q+55r+65s=55*40
Rewrite the W with respect to average weight of R (55) W=(55-10)p+(55-5)q+55r+(55+10)s=55(p+q+r+s)+10s-5q-10p=W+10s-5q-10p
---> 10s-5q-10p=0 hence s:q:p=2:1:2
Each section must have at least 1 student and max r --> min q =1 --> min s = min p=2 --> max r = 40 -5=35 -->D
User avatar
pk123
User avatar
Joined: 16 Sep 2011
Last visit: 26 Apr 2020
Posts: 104
Own Kudos:
122
 [3]
Given Kudos: 158
Products:
My Reviews
Posts: 104
Kudos: 122
 [3]
A class has 4 sections P, Q, R and S and the average weights of the st 07 Oct 2018, 02:09
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
A class has 4 sections P, Q, R and S and the average weights of the students in the sections are 45lb, 50lb, 55lb and 65lb respectively. What is the maximum possible number of students in section R if there are 40 students in all sections combined and the average weight of the all students across all the sections is 55lb? It is known that each section has at least one student.

(A) 18
(B) 20
(C) 25
(D) 35
(E) 37
Show more

What to look in an average problem is distance of a object from its average... so here average is 55lb which is section R

distance of P from section R= -10lb (negative as I consider R as centre since average lies at R)
distance of Q from R = - 5lb (negative as I consider R as centre since average lies at R)
distance of S from R = 10lb

Given: Each section has at least one student ..
So 37 is ruled out since if we take 1 from P, 1 from Q, 1 from S and 37 from R....average will not be 55lb....Lets see how?
1 from P = -10 distance from R.....1 from S = +10 distance from R...so both negate each other but we have additional -5 from P...so average will be slightly below 55lb now

Lets take another case 1 from P = -10lb
2 from Q = 2*-5lb = -10lb
and 2 from S= 2*+10lb= 20lb

So overall 1 from P + 2from Q = 2 from S...and average still remains at 55lb in section R

So total students taken= 1from P + 2 from Q + 2 from S = 5

Remaning students in R = 40-5= 35, which is the answer

Please give kudos if it is useful for you to understand..
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,960
Own Kudos:
1,117
Posts: 38,960
Kudos: 1,117
A class has 4 sections P, Q, R and S and the average weights of the st 16 Jul 2024, 21:37
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