Quote:
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.
This was a fun question to solve, tbh.
Using statement 1, we have:
AlphaNo. of employees: x (say)
Average Goals: 10
BetaNo. of employees: 85-x
Average Goals: 12.2
GammaNo. 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.
AlphaNo. of employees: 80
Average Goals: 10
BetaNo. of employees: 5
Average Goals: 12.2
GammaNo. 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.