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Schools: INSEAD Aug'24 intake Oxford Said'25 Judge '25 Imperial'25 HEC Sep'24 Intake LBS '26 ISB '27
GMAT 1: 700 Q50 V35
Posts: 260
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08 Sep 2022, 11:47
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This topic is about understanding change in average without much calculations:
Let's assume A, B, C, D and E are 5 friends
They decided to organize a party and all of them gave whatever funds they could. Details are mentioned below:
A brought 100
B brought 80
C brought 120
D brought 90
E brought 110
Total funds brought by A, B, C, D, E is 500
Average fund= 500/5=100
Case I
Now let's assume there is a rift between A and the rest of the friends.
A says I am going back and I need my funds back.
Since, A was giving in the funds that were enough for himself only. Nothing more, nothing less.
Therefore, there is no effect on average when A leaves. Average remains same i.e. 100
Case II
Now let's assume there is a rift between B and the rest of the friends.
B says I am going back and I need my funds back. B takes his 120 back
Since B was giving 20 more than what was being spent per person. The extra 20 brought by him shall be taken back.
In this case, the entire average falls. Now we have to find out by what number does the average falls
Since, 20 is falling short, the said amount shall be distributed among the rest of the candidates i.e. 4
20/4 =5 is the change in average
Therefore, the new average is 100-5=95
Case III
Now let's assume there is a rift between C and the rest of the friends.
C says I am going back and I need my funds back. C takes his 80 back
Since C was giving 20 less than what was being spent per person. The extra 20 given to him shall be distributed among the rest of the candidates.
In this case, the entire average increases. Now we have to find out by what number does the average increases
Since, 20 is the extra amount, the said amount shall be distributed among the rest of the candidates i.e. 4
20/4 =5 is the change in average
Therefore, the new average is 100+5=105
Case IV
Now let's assume that B and D teams up and leave the rest of the friends.
B says I am going back and I need my funds back. B takes his 120 back
Since B was giving 20 more than what was being spent per person. The extra 20 brought by him shall be taken back.
D says I am going back and I need my funds back. D takes his 90 back
Since D was giving 10 less than what was being spent per person. The extra 10 given to him shall be taken back.
In this case, the entire average falls. Now we have to find out by what number does the average falls
Since, 20 is falling short and 10 is the extra amount, the net amount shall be distributed among the rest of the candidates i.e. 4
20-10/4 =10/4= 2.5 is the change in average
Therefore, the new average is 100-2.5=97.5
Also the average of B and D will be
120, 90
In this case, one thing we know that 90 is being given by both the candidates i.e. B and D. Therefore, the average must be greater than 90.
Now B is bringing extra 30 than the 90 (the common term between the two)
That 30 shall be divided between these 2 candidates
Therefore, Average = 90+30/2=90+15=105
Hope this helps with the averages questions. If it does, then let me know, i will share for other topics as well.
Let's assume A, B, C, D and E are 5 friends
They decided to organize a party and all of them gave whatever funds they could. Details are mentioned below:
A brought 100
B brought 80
C brought 120
D brought 90
E brought 110
Total funds brought by A, B, C, D, E is 500
Average fund= 500/5=100
Case I
Now let's assume there is a rift between A and the rest of the friends.
A says I am going back and I need my funds back.
Since, A was giving in the funds that were enough for himself only. Nothing more, nothing less.
Therefore, there is no effect on average when A leaves. Average remains same i.e. 100
Case II
Now let's assume there is a rift between B and the rest of the friends.
B says I am going back and I need my funds back. B takes his 120 back
Since B was giving 20 more than what was being spent per person. The extra 20 brought by him shall be taken back.
In this case, the entire average falls. Now we have to find out by what number does the average falls
Since, 20 is falling short, the said amount shall be distributed among the rest of the candidates i.e. 4
20/4 =5 is the change in average
Therefore, the new average is 100-5=95
Case III
Now let's assume there is a rift between C and the rest of the friends.
C says I am going back and I need my funds back. C takes his 80 back
Since C was giving 20 less than what was being spent per person. The extra 20 given to him shall be distributed among the rest of the candidates.
In this case, the entire average increases. Now we have to find out by what number does the average increases
Since, 20 is the extra amount, the said amount shall be distributed among the rest of the candidates i.e. 4
20/4 =5 is the change in average
Therefore, the new average is 100+5=105
Case IV
Now let's assume that B and D teams up and leave the rest of the friends.
B says I am going back and I need my funds back. B takes his 120 back
Since B was giving 20 more than what was being spent per person. The extra 20 brought by him shall be taken back.
D says I am going back and I need my funds back. D takes his 90 back
Since D was giving 10 less than what was being spent per person. The extra 10 given to him shall be taken back.
In this case, the entire average falls. Now we have to find out by what number does the average falls
Since, 20 is falling short and 10 is the extra amount, the net amount shall be distributed among the rest of the candidates i.e. 4
20-10/4 =10/4= 2.5 is the change in average
Therefore, the new average is 100-2.5=97.5
Also the average of B and D will be
120, 90
In this case, one thing we know that 90 is being given by both the candidates i.e. B and D. Therefore, the average must be greater than 90.
Now B is bringing extra 30 than the 90 (the common term between the two)
That 30 shall be divided between these 2 candidates
Therefore, Average = 90+30/2=90+15=105
Hope this helps with the averages questions. If it does, then let me know, i will share for other topics as well.
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