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Three baseball teams, A, B, and C, play in a seasonal league

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kidderek
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Three baseball teams, A, B, and C, play in a seasonal league [#permalink] New post   Updated on: 06 Jul 2012, 01:51
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Three baseball teams, A, B, and C, play in a seasonal league. The ratio of the number of players on the three teams is 2:5:3, respectively. Is the average number of runs scored per player across all three teams collectively greater than 22?

(1) The average number of runs scored per player for each of the three teams, A, B, and C, is 30, 17, and 25, respectively.
(2) The total number of runs scored across all three teams collectively is at least 220.
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Originally posted by kidderek on 07 Nov 2006, 11:04.
Last edited by Bunuel on 06 Jul 2012, 01:51, edited 1 time in total.
Edited the question and added the OA.
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Re: Three baseball teams, A, B, and C, play in a seasonal league [#permalink] New post   06 Jul 2012, 02:13
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Three baseball teams, A, B, and C, play in a seasonal league. The ratio of the number of players on the three teams is 2:5:3, respectively. Is the average number of runs scored per player across all three teams collectively greater than 22?

Since the ratio of the number of players on the three teams is 2:5:3, respectively, then the # of players on the three teams would be \(2x\), \(5x\), and \(3x\), respectively (for some positive integer multiple x).

The average number of runs scored per player equals to total \(\frac{# \ of \ runs}{# \ of \ players}=\frac{# \ of \ runs}{10x}\). So, we are asked to find whether \(\frac{# \ of \ runs}{10x}>22\), or whether \(# \ of \ runs>220x\)

(1) The average number of runs scored per player for each of the three teams, A, B, and C, is 30, 17, and 25, respectively. The total # of runs for each team would be: \(30*2x=60x\), \(17*5x=85x\) and \(25*3x=75x\), so the total # of runs for all teams would be \(60x+85x+75=220x\). Sufficient.

(2) The total number of runs scored across all three teams collectively is at least 220. If the total # of runs is 220 and \(x=1\), then the answer will be NO but if the total # of runs is 230 and \(x=1\), then the answer will be YES. Not sufficient.

Answer: A.
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[#permalink] New post   07 Nov 2006, 11:40
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Three baseball teams, A, B, and C, play in a seasonal league. The ratio of the number of players on the three teams is 2:5:3, respectively. Is the average number of runs scored per player across all three teams collectively greater than 22?

(1) The average number of runs scored per player for each of the three teams, A, B, and C, is 30, 17, and 25, respectively.

(2) The total number of runs scored across all three teams collectively is at least 220.

number of players = 2x,5x,3x total = 10x

is number of runs / total number of players > 22

from one

total number of runs = 60x , 85x, 75x

average = 220x/10x = 22 suff

from two

assume that total number of runs = 220 / 10x = 22/x , x is positive intiger
it depends on x .........not suff

I say A
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Three baseball teams, A, B, and C, play in a seasonal league [#permalink] New post   Updated on: 18 Nov 2023, 02:12
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smartmanav wrote:
But the minimum value x will have will always be >= 1 ,so ofcourse the avg will be less than 22 .
No ??


The total number of runs is AT LEAST 220 which means it could very well be 300 too. If x = 1 and total number of runs is 220, the avg is 22. Is x > 1 and total number of runs is 220, avg is less than 22. If x = 1 and total number of runs is 300, avg is greater than 22.
Hence statement 2 is insufficient.

Weighted Avg Basics are discussed here:
Blog post: https://anaprep.com/arithmetic-weighted-averages/
Video: https://www.youtube.com/watch?v=_GOAU7moZ2Q

Originally posted by KarishmaB on 05 Jul 2012, 22:29.
Last edited by KarishmaB on 18 Nov 2023, 02:12, edited 1 time in total.
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Re: Three baseball teams, A, B, and C, play in a seasonal league [#permalink] New post   14 Aug 2016, 04:38
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Bunuel wrote:
Three baseball teams, A, B, and C, play in a seasonal league. The ratio of the number of players on the three teams is 2:5:3, respectively. Is the average number of runs scored per player across all three teams collectively greater than 22?

Since the ratio of the number of players on the three teams is 2:5:3, respectively, then the # of players on the three teams would be \(2x\), \(5x\), and \(3x\), respectively (for some positive integer multiple x).

The average number of runs scored per player equals to total \(\frac{# \ of \ runs}{# \ of \ players}=\frac{# \ of \ runs}{10x}\). So, we are asked to find whether \(\frac{# \ of \ runs}{10x}>22\), or whether \(# \ of \ runs>220x\)

(1) The average number of runs scored per player for each of the three teams, A, B, and C, is 30, 17, and 25, respectively. The total # of runs for each team would be: \(30*2x=60x\), \(17*5x=85x\) and \(25*3x=75x\), so the total # of runs for all teams would be \(60x+85x+75=220x\). Sufficient.

(2) The total number of runs scored across all three teams collectively is at least 220. If the total # of runs is 220 and \(x=1\), then the answer will be NO but if the total # of runs is 230 and \(x=1\), then the answer will be YES. Not sufficient.

Answer: A.


One doubt here, we have to prove whether total runs > 220x, correct.

In statement A, if we take x=1, we are getting 220, which is not > 220.

What I am trying to say is if we have 2,5,and 3 players. In that case total number of runs is 220 not greater than 220.
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Re: Three baseball teams, A, B, and C, play in a seasonal [#permalink] New post   01 Jun 2014, 21:18
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VeritasPrepKarishma wrote:
smartmanav wrote:
But the minimum value x will have will always be >= 1 ,so ofcourse the avg will be less than 22 .
No ??


The total number of runs is AT LEAST 220 which means it could very well be 300 too. If x = 1 and total number of runs is 220, the avg is 22. Is x > 1 and total number of runs is 220, avg is less than 22. If x = 1 and total number of runs is 300, avg is greater than 22.
Hence statement 2 is insufficient.


Hi

Can we use weighted average for statement 1.
Ratio of players is 2:5:3
Weighted average/player = (2/10)*30 + (5/10)*17 + (3/10)*25 = 6 + 8.5 + 7.5 = 22
Hence sufficient.
Is my logic right? Please let me know.
Thanks.

YK
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[#permalink] New post   07 Nov 2006, 11:42
My Pick is A
1. we know ratio for number of players in each team and we know average runs scored per team we can total runs scored by each team and then divide by the number of players

2. Insuff
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Re: Three baseball teams, A, B, and C, play in a seasonal [#permalink] New post   05 Jul 2012, 17:52
But the minimum value x will have will always be >= 1 ,so ofcourse the avg will be less than 22 .
No ??
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Re: Three baseball teams, A, B, and C, play in a seasonal [#permalink] New post   01 Jun 2014, 22:24
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khanym wrote:
VeritasPrepKarishma wrote:
smartmanav wrote:
But the minimum value x will have will always be >= 1 ,so ofcourse the avg will be less than 22 .
No ??


The total number of runs is AT LEAST 220 which means it could very well be 300 too. If x = 1 and total number of runs is 220, the avg is 22. Is x > 1 and total number of runs is 220, avg is less than 22. If x = 1 and total number of runs is 300, avg is greater than 22.
Hence statement 2 is insufficient.


Hi

Can we use weighted average for statement 1.
Ratio of players is 2:5:3
Weighted average/player = (2/10)*30 + (5/10)*17 + (3/10)*25 = 6 + 8.5 + 7.5 = 22
Hence sufficient.
Is my logic right? Please let me know.
Thanks.

YK


Yes, your logic is correct.
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Re: Three baseball teams, A, B, and C, play in a seasonal league [#permalink] New post   14 Aug 2016, 06:19
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viksingh15 wrote:
Bunuel wrote:
Three baseball teams, A, B, and C, play in a seasonal league. The ratio of the number of players on the three teams is 2:5:3, respectively. Is the average number of runs scored per player across all three teams collectively greater than 22?

Since the ratio of the number of players on the three teams is 2:5:3, respectively, then the # of players on the three teams would be \(2x\), \(5x\), and \(3x\), respectively (for some positive integer multiple x).

The average number of runs scored per player equals to total \(\frac{# \ of \ runs}{# \ of \ players}=\frac{# \ of \ runs}{10x}\). So, we are asked to find whether \(\frac{# \ of \ runs}{10x}>22\), or whether \(# \ of \ runs>220x\)

(1) The average number of runs scored per player for each of the three teams, A, B, and C, is 30, 17, and 25, respectively. The total # of runs for each team would be: \(30*2x=60x\), \(17*5x=85x\) and \(25*3x=75x\), so the total # of runs for all teams would be \(60x+85x+75=220x\). Sufficient.

(2) The total number of runs scored across all three teams collectively is at least 220. If the total # of runs is 220 and \(x=1\), then the answer will be NO but if the total # of runs is 230 and \(x=1\), then the answer will be YES. Not sufficient.

Answer: A.


One doubt here, we have to prove whether total runs > 220x, correct.

In statement A, if we take x=1, we are getting 220, which is not > 220.

What I am trying to say is if we have 2,5,and 3 players. In that case total number of runs is 220 not greater than 220.


Yes, so we have a definite NO answer to the question whether total runs > 220x, which is sufficient.
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Re: Three baseball teams, A, B, and C, play in a seasonal league [#permalink] New post   14 Aug 2016, 09:56
kidderek wrote:
Three baseball teams, A, B, and C, play in a seasonal league. The ratio of the number of players on the three teams is 2:5:3, respectively. Is the average number of runs scored per player across all three teams collectively greater than 22?

(1) The average number of runs scored per player for each of the three teams, A, B, and C, is 30, 17, and 25, respectively.
(2) The total number of runs scored across all three teams collectively is at least 220.




Analyzing statement 1 : Let Na , Nb , Nc represent the number of players in teams A,B,C respectively

According to the ratio , Na = 2k , Nb = 5k , Nc = 3k , K is a positive integer
From the average given ,
Number of runs scored by A,B,C will be 60k , 85k , 75k

Average of runs scored per player collectively in all 3 teams = Total # of runs scored collectively / total # of players in A,B,C
= (60k+ 85k+75k ) / 10k = 22, which is not greater than 22
Sufficient to answer

Analyzing statement 2 ,

Average = Number of runs scored / 10k

Lets take kmin = 1 and minimum # of runs scored i.e 220

Average = 220/10 = 22 , which is not greater than 22
Lets take total runs scored as 300 , k=1

Average = 300 /10 = 30 , which is greater than 22

So , we do not have sufficient info to arrive at a unique result
statement 2 is insufficent

answer : A
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Re: Three baseball teams, A, B, and C, play in a seasonal league [#permalink] New post   09 Jan 2023, 09:55
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Re: Three baseball teams, A, B, and C, play in a seasonal league [#permalink]
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