Latest GRE Aptitude Question SOLUTION: Question Each employee of a certain company is in either Department X or Department Y, and there are more than twice as many employees in Department X as in Department Y. The avera

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(#M40151707) GRE Numerical Ability question Arithmetic mean salary Keep an EYE

Question
Each employee of a certain company is in either Department X or Department Y, and there are more than twice as many employees in Department X as in Department Y. The average (arithmetic mean) salary is $25,000 for the employees in Department X and $35,000 for the employees in Department Y. Which of the following amounts could be the average salary for all of the employees of the company? Indicate all such amounts.
(a) $26,000
(b) $28,000
(c) $29,000
(d) $30,000
(e) $31,000
(f) $32,000
(g) $34,000

Asked In GRE Aashu (9 years ago)

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Abhigyan Chakraborty  (6 years ago)

If there are "a" number of employees in X
then there are "2a or 3a or more" number of employees in Y
Now lets assume a= 1
thererfore 2a= 2
3a= 3
Case-1: (when Dept X and Dept Y has 1,2 employees respectively)
then average salary =((25000*2)+35000)/(2+1) = 28333.33
Case-2: (when Dept X and Dept Y has 1,3 employees respectively)
then average salary =((25000*3)+35000)/(3+1) = 27500
So we can see that as the employees in X increases the total average salary decreases below 28333.33.
So all the options having value more than 28333.33 are not correct.
So we are left with two options 26000 and 28000.
But in order to have an average salary =26000, Dept X needs to have more than 8 times as many employees as in Dept Y. and if that was the case then it would have been mentioned in the question.
So 26000 is also wrong.
So the correct answer is (b) $28,000

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