Last visit was: 13 Dec 2024, 07:52 It is currently 13 Dec 2024, 07:52
Home
GMAT
Messages
Tests
Schools
Reviews
Social
Chat
My Profile
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
doomedcat
User avatar
Joined: 24 Jun 2013
Last visit: 28 Nov 2021
Posts: 119
Own Kudos:
343
 []
Given Kudos: 124
Location: India
Schools: ISB '20 GMBA '20
GMAT 1: 680 Q47 V36
Schools: ISB '20 GMBA '20
GMAT 1: 680 Q47 V36
Posts: 119
Kudos: 343
 []
The median weight of students in class A comprising 25 students is 40 15 Feb 2021, 10:13
Kudos
Add Kudos
15
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

95% (hard)

Question Stats:

29% (02:48) correct 71% (02:39) wrong based on 109 sessions

History

Date
Time
Result
Not Attempted Yet
The median weight of students in class A comprising 25 students is 40 Kg. The median weight of students in class B comprising 65 students is 50 Kg. If 20 students leave class B and join class A, the median weights of class A and class B do not change. What is the maximum number of students in class A who now weigh more that 40 Kg but less than 50 Kg.?

A) 12
B) 13
C) 20
D) 22
E) 23
ShowHide Answer
Official Answer
A
User avatar
CrackverbalGMAT
User avatar
GMAT Club Legend
Joined: 03 Oct 2013
Last visit: 13 Dec 2024
Posts: 4,878
Own Kudos:
8,144
 []
Given Kudos: 224
Affiliations: CrackVerbal
Location: India
Posts: 4,878
Kudos: 8,144
 []
The median weight of students in class A comprising 25 students is 40 20 Feb 2021, 04:39
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
The median of an odd number of observations is the \(\frac{n+1}{2}\)th value.

In class A, 40kg is the weight of the 13th student and in class B, 50 kgs is the weight of the 33rd student.

So in Class A, there are 12 students greater than 40 kg, and since we want to maximize the number who are greater than 40 and less than 50kg, let us assume that all 12 fall in this category.

Now when 20 people leave class B, leaving its median unchanged, then 10 students ≤ 50 kg and 10 students ≥ 50 kg, would have left the class.

When these 20 joined class A, leaving it's median unchanged it means that 10 would have been ≥ 40 kg and 10 have to be ≤ 40 kg.

So, the 10 who are ≥ 50 kg go onto the right of the student weighing 40 kgs, and 10 students would go to the left of the student weigh who weighs 40 kg.

Therefore the maximum number of students > 40kg and < 50 kg does not change as the new students are all greater than or equal to 50 kgs which is 12.


Option A

Arun Kumar
avatar
Dvaishnav
avatar
Joined: 25 Sep 2019
Last visit: 05 Aug 2021
Posts: 40
Own Kudos:
29
Given Kudos: 85
GMAT 1: 730 Q50 V40
GMAT 1: 730 Q50 V40
Posts: 40
Kudos: 29
The median weight of students in class A comprising 25 students is 40 22 Feb 2021, 21:03
Kudos
Add Kudos
Bookmarks
Bookmark this Post
CrackVerbalGMAT
The median of an odd number of observations is the \(\frac{n+1}{2}\)th value.

In class A, 40kg is the weight of the 13th student and in class B, 50 kgs is the weight of the 33rd student.

So in Class A, there are 12 students greater than 40 kg, and since we want to maximize the number who are greater than 40 and less than 50kg, let us assume that all 12 fall in this category.

Now when 20 people leave class B, leaving its median unchanged, then 10 students ≤ 50 kg and 10 students ≥ 50 kg, would have left the class.

When these 20 joined class A, leaving it's median unchanged it means that 10 would have been ≥ 40 kg and 10 have to be ≤ 40 kg.

So, the 10 who are ≥ 50 kg go onto the right of the student weighing 40 kgs, and 10 students would go to the left of the student weigh who weighs 40 kg.

Therefore the maximum number of students > 40kg and < 50 kg does not change as the new students are all greater than or equal to 50 kgs which is 12.


Option A

Arun Kumar

I was thinking of the following case where I ended up with an answer of 22. Can you please check and explain what is my mistake?

Class A weight distribution: student number 13 to student number 23 --> All are 40 kg.
Class B weight distribution: student number 33 to student number 43 --> All are 50 kg.
Next, we move 20 students from class B whose weight is above 40 and less than 50 (so basically 20 of the first 32 students in class B).
Now, class B has a strength of 65 - 20 = 45 and the median is still 50 (the 43rd student of the original class B).
class A has a strength of 25 + 20 = 45. The median is still 40 kg (the 23rd student of the original class A)
ANSWER: In class A, all of the students above the median (24th to 45th) can have weight between 40 and 50. Hence, my answer was 22.
avatar
sthahvi
avatar
Joined: 30 Nov 2018
Last visit: 24 Jan 2022
Posts: 63
Own Kudos:
9
 []
Given Kudos: 194
Posts: 63
Kudos: 9
 []
The median weight of students in class A comprising 25 students is 40 09 Mar 2021, 05:40
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Dvaishnav
CrackVerbalGMAT
The median of an odd number of observations is the \(\frac{n+1}{2}\)th value.

In class A, 40kg is the weight of the 13th student and in class B, 50 kgs is the weight of the 33rd student.

So in Class A, there are 12 students greater than 40 kg, and since we want to maximize the number who are greater than 40 and less than 50kg, let us assume that all 12 fall in this category.

Now when 20 people leave class B, leaving its median unchanged, then 10 students ≤ 50 kg and 10 students ≥ 50 kg, would have left the class.

When these 20 joined class A, leaving it's median unchanged it means that 10 would have been ≥ 40 kg and 10 have to be ≤ 40 kg.

So, the 10 who are ≥ 50 kg go onto the right of the student weighing 40 kgs, and 10 students would go to the left of the student weigh who weighs 40 kg.

Therefore the maximum number of students > 40kg and < 50 kg does not change as the new students are all greater than or equal to 50 kgs which is 12.


Option A

Arun Kumar

I was thinking of the following case where I ended up with an answer of 22. Can you please check and explain what is my mistake?

Class A weight distribution: student number 13 to student number 23 --> All are 40 kg.
Class B weight distribution: student number 33 to student number 43 --> All are 50 kg.
Next, we move 20 students from class B whose weight is above 40 and less than 50 (so basically 20 of the first 32 students in class B).
Now, class B has a strength of 65 - 20 = 45 and the median is still 50 (the 43rd student of the original class B).
class A has a strength of 25 + 20 = 45. The median is still 40 kg (the 23rd student of the original class A)
ANSWER: In class A, all of the students above the median (24th to 45th) can have weight between 40 and 50. Hence, my answer was 22.

yes that is why my answer is also 22
User avatar
Harsh9676
User avatar
Joined: 18 Sep 2018
Last visit: 27 Feb 2023
Posts: 252
Own Kudos:
212
Given Kudos: 322
Location: India
Concentration: Finance, International Business
GMAT 1: 690 Q49 V36
GPA: 3.72
WE:Investment Banking (Finance: Investment Banking)
Products:
My Reviews
GMAT 1: 690 Q49 V36
Posts: 252
Kudos: 212
The median weight of students in class A comprising 25 students is 40 09 Mar 2021, 12:11
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Dvaishnav
CrackVerbalGMAT
The median of an odd number of observations is the \(\frac{n+1}{2}\)th value.

In class A, 40kg is the weight of the 13th student and in class B, 50 kgs is the weight of the 33rd student.

So in Class A, there are 12 students greater than 40 kg, and since we want to maximize the number who are greater than 40 and less than 50kg, let us assume that all 12 fall in this category.

Now when 20 people leave class B, leaving its median unchanged, then 10 students ≤ 50 kg and 10 students ≥ 50 kg, would have left the class.

When these 20 joined class A, leaving it's median unchanged it means that 10 would have been ≥ 40 kg and 10 have to be ≤ 40 kg.

So, the 10 who are ≥ 50 kg go onto the right of the student weighing 40 kgs, and 10 students would go to the left of the student weigh who weighs 40 kg.

Therefore the maximum number of students > 40kg and < 50 kg does not change as the new students are all greater than or equal to 50 kgs which is 12.


Option A

Arun Kumar

I was thinking of the following case where I ended up with an answer of 22. Can you please check and explain what is my mistake?

Class A weight distribution: student number 13 to student number 23 --> All are 40 kg.
Class B weight distribution: student number 33 to student number 43 --> All are 50 kg.
Next, we move 20 students from class B whose weight is above 40 and less than 50 (so basically 20 of the first 32 students in class B).
Now, class B has a strength of 65 - 20 = 45 and the median is still 50 (the 43rd student of the original class B).
class A has a strength of 25 + 20 = 45. The median is still 40 kg (the 23rd student of the original class A)
ANSWER: In class A, all of the students above the median (24th to 45th) can have weight between 40 and 50. Hence, my answer was 22.


Hi Dvaishnav

The problem with your case is highlighted. Even if we assume that the weight of all students in Class B is 50. The 20 students we are moving to class A would be = 50. Hence the Answer would Still be 12.

However, the case you are referring to is :

Class A - Containing students with weight = 40

Class B - Containing Students with <= 40 till 33rd student and = 50 from 33rd student.

If we move the 20 students from below we get 22.
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 12 Dec 2024
Posts: 19,867
Own Kudos:
24,279
 []
Given Kudos: 288
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 19,867
Kudos: 24,279
 []
The median weight of students in class A comprising 25 students is 40 09 Mar 2021, 14:16
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
doomedcat
The median weight of students in class A comprising 25 students is 40 Kg. The median weight of students in class B comprising 65 students is 50 Kg. If 20 students leave class B and join class A, the median weights of class A and class B do not change. What is the maximum number of students in class A who now weigh more that 40 Kg but less than 50 Kg.?

A) 12
B) 13
C) 20
D) 22
E) 23
Solution:

We know that class A has 12 students ≤ 40 kg, 1 student at the median of 40 kg, and 12 students ≥ 40 kg.

We know that class B has 32 students ≤ 50 kg, 1 student at the median of 50 kg, and 32 students ≥ 50 kg.

From class B, we move 10 students weighing less than 50 kg (let’s call them “lightweights”) and 10 students weighing more than 50 kg (let’s call them “heavyweights”). This maintains the median of class B at 50 kg.

In order for the median of class A to remain at 40 kg, the 10 “lightweights” who came from class B must actually weigh less than 40 kg. And since the “heavyweights” who came from class B all weigh more than 50 kg, we see that the only students in class A who could possibly weigh between 40 and 50 kg, exclusive, are the 12 original members of class A who were above the median weight of 40 kg.

And since we are looking for the maximum number of students between 40 and 50 kg, exclusive, we see that if all of those 12 original members above the median were all between 40 and 50 kg, exclusive, then that maximum number would be 12.

Answer: A
User avatar
760Abhi
User avatar
Joined: 25 Apr 2022
Last visit: 01 Dec 2022
Posts: 15
Own Kudos:
2
Given Kudos: 90
Posts: 15
Kudos: 2
The median weight of students in class A comprising 25 students is 40 06 May 2022, 05:22
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Dvaishnav
CrackVerbalGMAT
The median of an odd number of observations is the \(\frac{n+1}{2}\)th value.

In class A, 40kg is the weight of the 13th student and in class B, 50 kgs is the weight of the 33rd student.

So in Class A, there are 12 students greater than 40 kg, and since we want to maximize the number who are greater than 40 and less than 50kg, let us assume that all 12 fall in this category.

Now when 20 people leave class B, leaving its median unchanged, then 10 students ≤ 50 kg and 10 students ≥ 50 kg, would have left the class.

When these 20 joined class A, leaving it's median unchanged it means that 10 would have been ≥ 40 kg and 10 have to be ≤ 40 kg.

So, the 10 who are ≥ 50 kg go onto the right of the student weighing 40 kgs, and 10 students would go to the left of the student weigh who weighs 40 kg.

Therefore the maximum number of students > 40kg and < 50 kg does not change as the new students are all greater than or equal to 50 kgs which is 12.


Option A

Arun Kumar

I was thinking of the following case where I ended up with an answer of 22. Can you please check and explain what is my mistake?

Class A weight distribution: student number 13 to student number 23 --> All are 40 kg.
Class B weight distribution: student number 33 to student number 43 --> All are 50 kg.
Next, we move 20 students from class B whose weight is above 40 and less than 50 (so basically 20 of the first 32 students in class B).
Now, class B has a strength of 65 - 20 = 45 and the median is still 50 (the 43rd student of the original class B).
class A has a strength of 25 + 20 = 45. The median is still 40 kg (the 23rd student of the original class A)
ANSWER: In class A, all of the students above the median (24th to 45th) can have weight between 40 and 50. Hence, my answer was 22.


[quote="Bunuel"] Bunuel
Can you please identify the error in this solution?
Moderator:
Bunuel
Math Expert
97871 posts