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

Question

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.

Bunuel · Accepted Answer

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.

yezz · Answer

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

yogeshsheth · Answer

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

smartmanav · Answer

But the minimum value x will have will always be >= 1 ,so ofcourse the avg will be less than 22 . 
No ??

KarishmaB · Answer

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

khanym · Answer

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

KarishmaB · Answer

Yes, your logic is correct.

viksingh15 · Answer

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.

Bunuel · Answer

Yes, so we have a definite NO answer to the question whether total runs > 220x, which is sufficient.

ujjwaldheer · Answer

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

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards