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Baseball teams

by SaraLotfy » Thu Sep 19, 2013 1:28 am
Three baseball teams, A, B and C, play in a seasonal league. The ratio of the number of players on the three teams is 2:3:5 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 team collectively is at least 220
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Source: — Data Sufficiency |
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by theCodeToGMAT » Thu Sep 19, 2013 1:38 am
Sara i would request you to post the answers as well.

The ANSWER is [spoiler][A]
[/spoiler]

Statement 1:
Since we have the ratio as 2:3:5
Lets have
A TEAM = 2x
B TEAM = 3x
C TEAM = 5x
Total Number of players = 10x


So, Average per player
= ( 30 * 2x + 17 * 3x + 25 * 5x ) / 10x
= (60 + 51 + 125)/10
= 23.6
SUFFICIENT

Statement 2:
The lowest possible number of players : 2 + 3 + 5 = 10

The Average Runs per player
220/10 = 22

Since, 220 is the least .. it can be 221 ,222, etc.. so the average will increase
So, average >= 22..

so INSUFFICIENT
Last edited by theCodeToGMAT on Thu Sep 19, 2013 2:25 am, edited 1 time in total.
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by SaraLotfy » Thu Sep 19, 2013 1:52 am
Rahul, unfortunately I do not have OAs for these questions! I post them to discuss and find out the correct answers since the source does not provide answers along with the questions. Sorry! :(

As for discussing the solution,

I understood from requirement that we are looking for the overall average. ie total runs for all 3 teams / # of players in all three teams 2x+3x+5x

St1 Gives individual averages for each team

Team A = (total runs for team A) / # of players in A = 30
Team B = (total runs for team B) / # of players in B = 17
Team C = (total runs for team C) / # of players in C = 25

Since we don't have the each team's number of players nor total runs, therefore we can not compute the requirement Insufficient

St2 Gives us the total runs across all teams which is the numerator in the required equation but nothing more.

If we combine both 1&2 we will conclude that the average per player has to be greater than 22.


let me know what you think
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by theCodeToGMAT » Thu Sep 19, 2013 2:27 am
SaraLotfy wrote:Rahul, unfortunately I do not have OAs for these questions! I post them to discuss and find out the correct answers since the source does not provide answers along with the questions. Sorry! :(

As for discussing the solution,

I understood from requirement that we are looking for the overall average. ie total runs for all 3 teams / # of players in all three teams 2x+3x+5x

St1 Gives individual averages for each team

Team A = (total runs for team A) / # of players in A = 30
Team B = (total runs for team B) / # of players in B = 17
Team C = (total runs for team C) / # of players in C = 25

Since we don't have the each team's number of players nor total runs, therefore we can not compute the requirement Insufficient

St2 Gives us the total runs across all teams which is the numerator in the required equation but nothing more.

If we combine both 1&2 we will conclude that the average per player has to be greater than 22.


let me know what you think


Ah.. thats ok :)

Regarding the Solution:

Statement 1:
Since we have the ratio as 2:3:5
Lets have
A TEAM = 2x
B TEAM = 3x
C TEAM = 5x
Total Number of players = 10x

So, Average per player
= ( 30 * 2x + 17 * 3x + 25 * 5x ) / 10x
= (60 + 51 + 125)/10
= 23.6
HENCE SUFFICIENT.


Statement 2:
We know the ratio of denominator= 10x (lets keep x = 1)
The Question says the score is minimum 220
that implies, 220/10 = 22
230/10 = 23
hence We cannot comment whether the average is always greater than 22.
HENCE INSUFFICIENT.


ANSWER [A]
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by GMATGuruNY » Thu Sep 19, 2013 2:36 am
The ratio in the question stem should read as posted below:
SaraLotfy 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 team collectively is at least 220
Let the number of players on A = 2x, the number of players on B = 5x, and the number of players on C = 3x.
Total number of players = 2x + 5x + 3x = 10x.
If the average number of runs per player = 22, then the total number of runs = (total number of players)(average number of runs per player) = (10x)(22) = 220x.
Thus, for the average to be GREATER than 22, the TOTAL must be greater than 220x.

Question rephrased: Is the total number of runs greater than 220x?

Statement 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.
Total number of runs for A = 30 * 2x = 60x.
Total number of runs for B = 17 * 5x = 85x.
Total number of runs for C = 25 * 3x = 75x.
Total number of runs for all 3 teams = 60x + 85x + 75x = 220x.
Thus, the total number of runs is NOT greater than 220x.
SUFFICIENT.

Statement 2: The total number of runs scored across all three teams collectively is at least 220.
Case 1: Total number of runs = 220 and x=1.
Here, the total number of runs is EQUAL to 220x.
Case 2: Total number of runs = 22,000 and x=1.
Here, the total number of runs is GREATER than 220x.
INSUFFICIENT.

The correct answer is A.
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