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Bunuel
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In a tournament, there are two groups of teams. Group A has 20 teams 20 Apr 2020, 05:16
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22% (03:33) correct 78% (02:53) wrong based on 89 sessions

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In a tournament, there are two groups of teams. Group A has 20 teams and Group B has 25 teams. The average (arithmetic mean) scores of teams in Group A and B are 20 and 25, respectively. The highest and lowest scores in Group A are 25 and 15, respectively and the highest and lowest scores in Group B are 32 and 24, respectively. What can be the minimum and maximum value of Group A’s average if 5 teams are transferred from Group B to Group A?

A. 20.8 and 22.8
B. 20.8 and 22.4
C. 20.8 and 21.8
D. 20.8 and 21.6
E. 20.6 and 22.6


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In a tournament, there are two groups of teams. Group A has 20 teams 20 Apr 2020, 05:43
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Answer should be B
Average of Group A is 400 [A=20*20]
The lowerst score of group B team is 24.
Let's suppose there were 5 members in team B with 24 (minimum) score and they are transferred.
So 400+24*5=400+120=520
New Average=520/25=20.8

Now suppose there were 5 members in team B with 32 (maximum) score and they are transferred.
So 400+32*5=400+160=560
New Average=560/25=22.4

Even if the score Exceeds 24 or is short from 32.
The range will nearly lie between 20.8-22.4

So answer should be B

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In a tournament, there are two groups of teams. Group A has 20 teams 23 Apr 2020, 06:48
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Bunuel
In a tournament, there are two groups of teams. Group A has 20 teams and Group B has 25 teams. The average (arithmetic mean) scores of teams in Group A and B are 20 and 25, respectively. The highest and lowest scores in Group A are 25 and 15, respectively and the highest and lowest scores in Group B are 32 and 24, respectively. What can be the minimum and maximum value of Group A’s average if 5 teams are transferred from Group B to Group A?

A. 20.8 and 22.8
B. 20.8 and 22.4
C. 20.8 and 21.8
D. 20.8 and 21.6
E. 20.6 and 22.6


Are You Up For the Challenge: 700 Level Questions
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...................A......B
# of teams....20...25
Average........20...25

5 teams are to be transferred from B to A..
Let Group B score be such that 5 teams have highest possible score 32, 5 teams have lowest score 24 and remaining 15 hare adjusted accordingly..
32, 32, 32, 32, 32, .

MAX average of A after transfer..


All 5 have maximum possible, so take remaining 20 as minimum possible = 24. Total of these 20 teams = 20*24=480.
Thus, maximum possible score of these 5 teams = 25*25-24*20=145, and average= \(\frac{20*20+145}{25}=\frac{545}{25}=21.8\)

MIN average of A after transfer..


All 5 have minimum possible, that is 24, so NEW average of A= \(\frac{20*20+24*5}{25}=\frac{520}{25}=20.8\)

So Min and Max = 20.8 and 21.8

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In a tournament, there are two groups of teams. Group A has 20 teams 23 Apr 2020, 06:50
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yashikaaggarwal
Answer should be B
Average of Group A is 400 [A=20*20]
The lowerst score of group B team is 24.
Let's suppose there were 5 members in team B with 24 (minimum) score and they are transferred.
So 400+24*5=400+120=520
New Average=520/25=20.8

Now suppose there were 5 members in team B with 32 (maximum) score and they are transferred.
So 400+32*5=400+160=560
New Average=560/25=22.4

Even if the score Exceeds 24 or is short from 32.
The range will nearly lie between 20.8-22.4

So answer should be B

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Hi,
You cannot have a case where all 5 have 32, because then the average will be > 25. You have to check whether values fit for the average or not.
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In a tournament, there are two groups of teams. Group A has 20 teams 23 Apr 2020, 07:56
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chetan2u
yashikaaggarwal
Answer should be B
Average of Group A is 400 [A=20*20]
The lowerst score of group B team is 24.
Let's suppose there were 5 members in team B with 24 (minimum) score and they are transferred.
So 400+24*5=400+120=520
New Average=520/25=20.8

Now suppose there were 5 members in team B with 32 (maximum) score and they are transferred.
So 400+32*5=400+160=560
New Average=560/25=22.4

Even if the score Exceeds 24 or is short from 32.
The range will nearly lie between 20.8-22.4

So answer should be B

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Hi,
You cannot have a case where all 5 have 32, because then the average will be > 25. You have to check whether values fit for the average or not.
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I thought so too, but I put it like this because the minimum no. Has taken the lowest no. Into consideration only. I agree with your statement though. Will rectify it. Thank You.
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In a tournament, there are two groups of teams. Group A has 20 teams 23 May 2023, 00:32
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Bunuel
In a tournament, there are two groups of teams. Group A has 20 teams and Group B has 25 teams. The average (arithmetic mean) scores of teams in Group A and B are 20 and 25, respectively. The highest and lowest scores in Group A are 25 and 15, respectively and the highest and lowest scores in Group B are 32 and 24, respectively. What can be the minimum and maximum value of Group A’s average if 5 teams are transferred from Group B to Group A?

A. 20.8 and 22.8
B. 20.8 and 22.4
C. 20.8 and 21.8
D. 20.8 and 21.6
E. 20.6 and 22.6


Are You Up For the Challenge: 700 Level Questions

...................A......B
# of teams....20...25
Average........20...25

5 teams are to be transferred from B to A..
Let Group B score be such that 5 teams have highest possible score 32, 5 teams have lowest score 24 and remaining 15 hare adjusted accordingly..
32, 32, 32, 32, 32, .

MAX average of A after transfer..


All 5 have maximum possible, so take remaining 20 as minimum possible = 24. Total of these 20 teams = 20*24=480.
Thus, maximum possible score of these 5 teams = 25*25-24*20=145, and average= \(\frac{20*20+145}{25}=\frac{545}{25}=21.8\)

MIN average of A after transfer..


All 5 have minimum possible, that is 24, so NEW average of A= \(\frac{20*20+24*5}{25}=\frac{520}{25}=20.8\)

So Min and Max = 20.8 and 21.8

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Thank you for this (Max part).

I did a hit-trial to find that there'd be three 32 and two values close to 32. Got an approximate answer.
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In a tournament, there are two groups of teams. Group A has 20 teams 05 Oct 2025, 19:34
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