GMAT Club World Cup 2022 (DAY 10): On a joint company picnic, 160

Question

On a joint company picnic, 160 employees of Alpha Ltd, Beta Ltd and Gamma Ltd were engaged in several football matches. The average (arithmetic mean) number of goals scored by the employees of Alpha Ltd was 10, and the average (arithmetic mean) number of goals scored by the employees of Beta Ltd was 12.2. Was the average (arithmetic mean) number of goals scored by all 160 employees more than 11 ?

(1) The 75 employees of Gamma Ltd scored the average of 12 goals.
(2) The ratio of the number of employees of Alpha Ltd to Beta Ltd to Gamma Ltd was 16:1:15.

(1) The 75 employees comprising Gamma Ltd scored an average of 12 goals.

(2) The ratio of the number of employees of Alpha Ltd to Beta Ltd to Gamma Ltd was 16:1:15.

Bunuel · Accepted Answer

Official Solution:

On a joint company picnic, 160 employees of Alpha Ltd, Beta Ltd and Gamma Ltd were engaged in several football matches. The average (arithmetic mean) number of goals scored by the employees of Alpha Ltd was 10, and the average (arithmetic mean) number of goals scored by the employees of Beta Ltd was 12.2. Was the average (arithmetic mean) number of goals scored by all 160 employees more than 11 ?

(1) The 75 employees of Gamma Ltd scored the average of 12 goals.
(2) The ratio of the number of employees of Alpha Ltd to Beta Ltd to Gamma Ltd was 16:1:15.

The question  "Was the average (arithmetic mean) number of goals scored by all 160 employees more than 11?"  can be rephrased as  "Was the total number of goals scored by all 160 employees more than 160*11 = 1,760?"

(1) The 75 employees comprising Gamma Ltd scored an average of 12 goals.

The statement implies that the total number of goals scored by all the employees of Gamma Ltd was 900. The least number of goals the remaining 160 - 75 = 85 employees could have scored is if we minimize the number of employees of Beta Ltd (since they scored on average more than the employees of Alpha Ltd). The minimum number of employees Beta Ltd could have is 5 because the total number of goals scored by them must be an integer, so (number of employees)*12.2 must be an integer, which means the least value of the number of employees is 5. Thus, the least number of goals the remaining 85 employees could have scored is thus 80*10 + 5*12.2 = 861. This would make the total number of goals equal to 900 + 861 = 1,761, which is more than 1,760. Sufficient.

(2) The ratio of the number of employees of Alpha Ltd to Beta Ltd to Gamma Ltd was 16:1:15.

The statement implies that in Alpha Ltd, Beta Ltd, and Gamma Ltd there are 80, 5, and 75 employees, respectively. The total number of goals scored by Alpha Ltd and Beta Ltd would thus be 80*10 + 5*12.2 = 861. If the 75 employees of Gamma Ltd scored a total of 1 goal, then the answer to the question would be NO. However, if they scored a total of 1,000 goals, the answer would be YES. Not sufficient.

Answer: A

mainbhiankit · Answer

This was a fun question to solve, tbh.

Using statement 1, we have:

Alpha 
No. of employees: x (say)
Average Goals: 10

Beta 
No. of employees: 85-x
Average Goals: 12.2

Gamma 
No. of employees: 75
Average Goals: 12

Therefore, total no. of goals = 1937 - 2.2x
and, total no. of employees = 160 (given)

Since, the total no. of goals has to be a whole number, to calculate the lowest total average, the largest value we can assign to x = 80.

Putting x = 80, total no. of goals = 1937 - 176 = 1761
And the total no. of employees, as we know, is 160

Therefore, average = 1761/160 = 11. 00625, which is marginally greater than 11. Hence, this statement is sufficient.

Using statement 2,

This statement helps us calculate the number of employees for each of alpha, beta and gamma.

Alpha 
No. of employees: 80
Average Goals: 10

Beta 
No. of employees: 5
Average Goals: 12.2

Gamma 
No. of employees: 75
Average Goals: x (say)

Average goals for all employees will be = (800 + 70 + 75x)/160

We cannot say for certain that the average will be more than or less than 11 using statement 2. Hence, it is insufficient.

Answer is option A.

gmatophobia · Answer

Total score required = 160 * 11 = 1760

Average of Team Alpha = 10

Average of Team Beta = 12.2 ( Inference : The number of people in Team Beta is in multiples of 5 and the number of employees is greater than 0)

Statement 1

Number of employees of team gamma = 75

Average goals = 12

Total by team gamma = 900

Remaining points = 1760 - 900 = 860

Remaining Employees = 160 - 75 = 85

Case 1

Team Alpha has 80 members

Contribution by team alpha = 800

Team Beta has 5 members

Contribution by team beta = 61

Total = 861

Hence the avg > 11

Case 2

Team Alpha has 5 members

Contribution by team alpha = 50

Team Beta has 80 members

Contribution by team beta = 976

Total > 860

Hence Statement 1 is sufficient

Statement 2

Number of employees in Team Alpha =  \frac{16}{32}  * 160 = 80

Number of employees in Team Beta=  \frac{1}{32}  * 160 = 05

Number of employees in Team Gamma=  \frac{15}{32}  * 160 = 75

Case 1

Lets assume the average (arithmetic mean) number of goals scored by the employees of Team Gamma is 1

Total = 75 + 800 + 61 = 936

Therefore the average is < 11

Case 2

Lets assume the average (arithmetic mean) number of goals scored by the employees of Team Gamma is 100

The average is > 11.

Hence this statement is insufficient

IMO A

houston1980 · Answer

IMO,  Option A  is the answer.
 
Statement I Alone. 
From the question, Beta members must be a minimum of 5 members. Average is 12.2. Beta employee goals 12.2*5 = 61 goals 
Alpha members will be a maximum of 80 members. 80*10 = 800 goals
Gamma Employees goals = 75*12 = 900 goals.

Total goals = 900+800+61 = 1761 goals
Average is = 1761/160 . Average is greater than 11 because 1760/160 =11
1761 is the minimum total number of goals possible based on the information in the question and in statement 1.
Therefore Statement I alone is sufficient.
 
Statement II Alone. 
The ratio of the number of employees of Alpha Ltd to Beta Ltd to Gamma Ltd was 16:1:15. Or 
The number of employees of Alpha Ltd to Beta Ltd to Gamma Ltd was 80:5:75.
We do not know about the scores of each member of Gamma. It is possible each member of Gamma scores 100. The average will be greater than 11.
On the other hand, if each member of Gamma scores 0 goal, the average will be smaller than 11. 
Therefore Statement II alone is NOT sufficient.

Therefore IMO,  Option A  is the answer.

Kushchokhani · Answer

Total no. of employees of A, B and G combined = 160
Average goals of A = 10
Average goals of B = 12.2
Ques: was average goals of all 160 employees more than 11 i.e. was total goals of all 160 employees more than 1760?

Statement 1: Average goals of 75 employees of G = 12
So, total goals of G = 900
If total goals of A and B combined is more than 1760-900=860, the answer to the ques would be a definite YES.
No. of employees of A and B combined is 160-75=85
If we assume that B scored bare min. goals, then total goals of B = 12.2*5=61 (should be a whole number)
So, total goals of A = 10*80 = 800
So, total goals of A and B combined = 861. Answer is a definite YES.
This statement alone is sufficient.

Statement 2: By using the ratio of no. of employees, we come to know that no. of empl of A/B/G = 80/5/75 respectively.
We can calculate total goals of A and B = 800+61 = 861
However, we don't know either average or total goals of G. Just knowing no. of employees of G won't help us to arrive at the answer.
Hence, this statement alone is not sufficient.

Answer is A.

pintukr · Answer

On a joint company picnic, 160 employees of Alpha Ltd, Beta Ltd and Gamma Ltd were engaged in several football matches. The average (arithmetic mean) number of goals scored by the employees of Alpha Ltd was 10, and the average (arithmetic mean) number of goals scored by the employees of Beta Ltd was 12.2. Was the average (arithmetic mean) number of goals scored by all 160 employees more than 11 ?

(1) The 75 employees of Gamma Ltd scored the average of 12 goals.
(2) The ratio of the number of employees of Alpha Ltd to Beta Ltd to Gamma Ltd was 16:1:15.

(1) The 75 employees of Gamma Ltd scored the average of 12 goals.
(2) The ratio of the number of employees of Alpha Ltd to Beta Ltd to Gamma Ltd was 16:1:15.

Using (1)

Min goals scored by Beta (atleast 5 players) = 12.2 *5 = 61 (No of Goals will be an integer)
Goals scored by 75 players of Gamma = 900
Goals scored by at most 80 players of Alpha = 800

Total = 1761
Average = 1761/160 > 11

YES is the unique answer..SUFFICIENT

Using (2)

Employees of Alpha , Beta and Gamma will be 80, 5 , and 75
Goals scored by 80 players of Alpha = 800
Goals scored by 05 players of Beta = 61
Goals scored by 75 players of Beta = (no information about the average of these players)

So, overall average can not be ascertained

NOT SUFFICIENT

Hence, (A) is the correct answer

Bunuel · Answer

This one turned out to be 800+ Level question!!! Posted a solution.

tanishqgirotra · Answer

lovely question! request you to post more such questions on the club...

Bunuel · Answer

Thank you! This is a GMAT Club Tests' question. Arguably one of the best sources of DS and PS questions on the market. I see you are already a subscriber, so you can check more there.

colfer · Answer

Option A. Alpha and Beta together average (10+12.2)/2 =11.1 and Gamma averages 12. Combined average will definitely be greater than 11.1

A is sufficient.

Option B: There are 80, 15 and 75 employess respectively in Alpha, Beta and Gamma.  Average of Alpha and Beta is 11.1. But without how many goals Gamma scored or their average we cant say for sure what the average is.

Not sufficient

HarishD · Answer

Very good question.

Oppenheimer1945 · Answer

S1) Is n*10+12.2*(85-n)+75*12>160*11?
Is 1937-2.2n>1760, n max is 85, the ineq always hold true. (suff)

S2) we know of players are 80,5,75, we don't know about score of gamma, hence Insuff

A)

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