Avg q3

When 5 students each with highest score of 22 has transferred from class A and When 5 new students are transferred from B to A with high score of 31 of Class b THEN,

Average of B will decrease when avg of class A decreases But B's average increases from previous after second operation and then A's average decreases.


When lowest score of Transferred class is Taken i.e 23 of B and 18 of A THEN ,

A's avg increases then B's avg decreases .
B's average increases from previous then after second operation A's average increases from previous
I said "don't care about cases" and you continue to show me your cases. Why? I am trying to help you to actually solve this problem. Showing cases is not a solution. It may help you to find the solution, but I don't see it working in this thread.

Again.
What happens to B average when we replace 5 scores in such a way that each new score is lower than the old score?
 
Let's make the problem you're currently asking about easier to find:

There are 3 classes having 20, 25 and 30 students respectively having average marks in​
an examination as 20,25 and 30 respectively. The three classes are represented by A, B and C and you have the following information about the three classes.​
a. In class A highest score is 22 and lowest score is 18​
b. In class B highest score is 31 and lowest score is 23​
c. In class C highest score is 33 and lowest score is 26​
1639144094634.png

In this situation, you are interchanging 5 students from A and 5 from B; that is, each of the students in A is replaced by one from B, and vice versa. You know all of the latter have higher scores than any of the former. So it is as if 5 people in A all increase their scores, and 5 in B decrease their scores. What must happen to each average?

(Incidentally, the word "independent" in the problem is not really appropriate; they should have said something like "mutually exclusive". Also, when we have the answer, we will find that a second choice can also be considered true, though only in a technical sense.)
 
we will find that a second choice can also be considered true, though only in a technical sense.

Case 1 : B's Avg = 24.5 , 23.2

A's Avg = 19 1/3 , 22.25


Case 2 : B's Avg = 23.833 , 23.99

A's Avg = 20.66 , 21.24


B's avg decreases always .


But what can be said about A's avg?
 
Case 1 : B's Avg = 24.5 , 23.2

A's Avg = 19 1/3 , 22.25


Case 2 : B's Avg = 23.833 , 23.99

A's Avg = 20.66 , 21.24
As you've been told repeatedly, you don't need cases. And specific numbers don't help in determining what always happens. (Where did those numbers come from, anyway?)

Why in the world are you not learning anything from us? Why should we bother answering you when you don't pay attention? If there's something we say that you don't understand, then ask us specifically about that, rather than going back to what you were doing.

B's avg decreases always .
That's true. Do you understand why?
But what can be said about A's avg?
You tell me! It's the very same kind of thinking. If you understand the reasoning behind the first statement, you should know what to say here.

On the other hand, do you really need to answer this for the problem? You have the solution already.

I'll add the point I mentioned at the end of #42, which may possibly be why you ask this: If answer (b) is true, then answer (d) is also, though less precise.

Do you understand that? Knowing, for example, that all people breathe, I can correctly say that if you are standing, you are breathing. (You are also breathing if you are not standing, but I didn't happen to mention that.) Logically, the statement "if A then B" is true as long as B is true whenever A is true, regardless of what happens when A is false.

So the problem doesn't appear to have been written by a logician, or a mathematician generally.
 
That's true. Do you understand why?
I came to conclusion after performing the approach of two cases which sounds logical to me .
But after seeing B's value in both cases I came to conclusion B's avg decreases always irrespective of A's avg value.

B's Avg = 24.5 , 23.2

A's Avg = 19 1/3 , 22.25


Case 2 : B's Avg = 23.833 , 23.99

A's Avg = 20.66 , 21.24


There is some mistakes in #20

B's value for 25 students after 2nd operation = 23.2

A's final average with 20 students is 22.25 Not 17.8
These are the corrections


Where did those numbers come from, anyway?)
Just see #20?
Case 2 I haven't written but same process as case 1.




If you understand the reasoning behind the first statement, you should know what to say here.
A's average is increasing . So either (b) or (d).

Yes if then proposition I need to understand. I have almost forgotten.

Now its 3am in India .
 
Please reread #41. Don't use cases (by which you apparently mean "examples", not "cases" in the sense that we can use in proofs). I never said to.

You can experiment with particular numbers in order to get a feel for what happens, but then, in order to convince yourself about what always happens, you need to set those aside and think. Don't use them to try to convince others -- especially without any explanation why the result generalizes.
 
What happens to B average when we replace 5 scores in such a way that each new score is lower than the old score?
You are saying when Any 5 students of B are getting replaced by 5 students of A (overall strength = 25 ) or Any 5 students of A are joining class B (Overall strength =30)

In the latter case it will lead to decrease in avg of B .

But this is just the first operation only and then there will be loss of B and gain of A of 5 students
 
You are saying when Any 5 students of B are getting replaced by 5 students of A (overall strength = 25 ) or Any 5 students of A are joining class B (Overall strength =30)

In the latter case it will lead to decrease in avg of B .

But this is just the first operation only and then there will be loss of B and gain of A of 5 students
There is only one operation. Replace 5 students in B with 5 students from A. Hope this clears up any confusion.
 
You are saying when Any 5 students of B are getting replaced by 5 students of A (overall strength = 25 ) or Any 5 students of A are joining class B (Overall strength =30)

In the latter case it will lead to decrease in avg of B .

But this is just the first operation only and then there will be loss of B and gain of A of 5 students
Read the problem again. It refers to the transfers as "this operation". Singular. One operation.
 
Replace 5 students in B with 5 students from A. Hope this clears up any confusion.
just tell me when it is said that students are being transferred from one class to another class B that means "replaced " or addition of 5 students to already 25 students of class B which makes it 30 put together .
 
just tell me when it is said that students are being transferred from one class to another class B that means "replaced " or addition of 5 students to already 25 students of class B which makes it 30 put together .
You are in a store buying some shirts. You need size medium. Right before paying you realize you picked up one with size small. You tell the cashier "I need to REPLACE this one". Then you go and TRANSFER a small size shirt from your cart to the shelf and TRANSFER a medium size shirt from the shelf to your cart.
Question: did you lie to the cashier when you said you needed to replace a shirt?
 
You are in a store buying some shirts. You need size medium. Right before paying you realize you picked up one with size small. You tell the cashier "I need to REPLACE this one". Then you go and TRANSFER a small size shirt from your cart to the shelf and TRANSFER a medium size shirt from the shelf to your cart.
Question: did you lie to the cashier when you said you needed to replace a shirt?
So let's go step by step in solving the sum .
ok, so after first transfer class B now has 30 students and A has 15 students .
Then after second transfer from B to A class B has 25 students (20 from B & 5 from A) and class A has 20 students (15 from A & 5 from B).

It refers to the transfers as "this operation". Singular. One operation.
These two transfers are just one operation only ?
 
So let's go step by step in solving the sum .
ok, so after first transfer class B now has 30 students and A has 15 students .
Then after second transfer from B to A class B has 25 students (20 from B & 5 from A) and class A has 20 students (15 from A & 5 from B).


These two transfers are just one operation only ?
Asked and answered.
 
Before 1st transfer : 625 marks for Class b


After 1st transfer

Avg is the average marks of 5 transferred students from class A.

Average marks of class B after 1st transfer (Avg4 ) = ( 25 * 25 + Avg * 5 ) / 30

After 2nd transfer ,
Avg2 = Average marks per student out of 25 students in B class after 5 students left.

Sum of marks of B after independent set of 5 people left= Avg2 * 25

Avg marks per student of class B ( Avg2)= (20 * Avg3 + 5* Avg) / 25

Avg3 is the average marks per student of 20 original students of class B

Avg2 * 25 = Avg3 * 20 + Avg * 5


Now what Comparison?
 
Before 1st transfer : 625 marks for Class b


After 1st transfer

Avg is the average marks of 5 transferred students from class A.

Average marks of class B after 1st transfer (Avg4 ) = ( 25 * 25 + Avg * 5 ) / 30

After 2nd transfer ,
Avg2 = Average marks per student out of 25 students in B class after 5 students left.

Sum of marks of B after independent set of 5 people left= Avg2 * 25

Avg marks per student of class B ( Avg2)= (20 * Avg3 + 5* Avg) / 25

Avg3 is the average marks per student of 20 original students of class B

Avg2 * 25 = Avg3 * 20 + Avg * 5


Now what Comparison?
There is no such thing as "After 1st transfer". I asked for "B's average before and after the transfers". Plural.
If you do not accept that the 2 transfers are one operation I'm done.

Average = Total/N.
What is B average before and after replacement? What in Total/N remains the same? What changes? Changes how? How does it affect the average?
 
Before transfer : 625 marks for Class b and Avg was 25

After : Avg marks per student of class B ( Avg2)= (20 * Avg3 + 5* Avg) / 25

The average will decrease Always after operation as it has 5 students with lesser score .

But why did drp said
If answer (b) is true, then answer (d) is also, though less precise.
I understood if then operation quite well but how (d) can be a less precise answer.

But what can be said about A's avg? It always increases
 
But why did drp said

I understood if then operation quite well but how (d) can be a less precise answer.

But what can be said about A's avg? It always increases
Which part of that explanation (example with breathing) did you not understand?
 
Top