lenagmat wrote:In a certain company, the average wages of employees in Town A is X, the average wages of employees in Town B is Y. If both types of employees are added together, is the new average salary smaller than (X + Y)/2?
(1) There are more employees in Town A than B
(2) Y-X = 4200
Let's assume no of Employees from town A to be a, and no of employees from town B to be b.
Hence,
Total of wages for Town A = aX (No of Employees X Avg. wages)
Total of wages for Town B = bY
Total wages for town A and B = aX + bY
Total no of Employees = a+b
New Average = ( Total Wages of Employees in Town A and B ) / (Total no of Employees in Town A and B)
= (aX+bY) / (a+b)
The stem asks us to check whether,
= (aX+bY) / (a+b) <. (X+Y)/2 - Cross Multiply and apply FOIL
= 2aX + 2bY < aX + aY + bX + bY. - Taking like terms on each side
= 2bY-bY-bX < aY + aX - 2aX
= bY - bX < aY- aX
= b(Y-X) < a(Y-X). - So, if this is true than the New Average is less than ( X + Y ) / 2 )
Statement 1: - There are more Employees i n Town A than in Town B, Hence a > b
If Y- X is positive then b(Y-X) < a(Y-X) holds true.
But if Y-X is negative then b(Y-X) > a ( Y-X) note that the sign flips hence the original inequality we are testing does not hold true
As there are two possible outcomes :
Insufficient - Eliminate AD
Statement 2 :- (Y-X) = 4200
This does not tell us about a and b hence :
Insufficent : Eliminate B
Both, a > b and Y-X = 4200 and hence positive we can conclude that,
b(Y-X) < a (Y-X)
Correct Answer C [/b]
