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Practice Question #3-Each employee of a certain company

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Director
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Joined: 16 May 2014
Posts: 597
GRE 1: 326 Q165 V161
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Practice Question #3-Each employee of a certain company [#permalink] New post 29 May 2014, 08:18
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0% (00:00) correct 100% (00:08) wrong based on 1 sessions
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
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Director
Director
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Joined: 16 May 2014
Posts: 597
GRE 1: 326 Q165 V161
Followers: 72

Kudos [?]: 313 [1] , given: 64

Re: Practice Question #3 [#permalink] New post 29 May 2014, 08:21
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Solution


One strategy for answering this kind of question is to find the least and/or greatest possible value. Clearly the average salary is between $25,000 and $35,000, and all of the answer choices are in this interval. Since you are told that there are more employees with the lower average salary, the average salary of all employees must be less than the average of $25,000 and $35,000, which is $30,000. If there were exactly twice as many employees in Department X as in Department Y, then the average salary for all employees would be, to the nearest dollar, the following weighted mean,

\frac{(2)(25,000)+(1)(35000)}{(2+1)}= 28,333

where the weight for $25,000 is 2 and the weight for $35,000 is 1. Since there are more than twice as many employees in Department X as in Department Y, the actual average salary must be even closer to $25,000 because the weight for $25,000 is greater than 2. This means that $28,333 is the greatest possible average. Among the choices given, the possible values of the average are therefore $26,000 and $28,000. Thus, the correct answer consists of Choices A ($26,000) and B ($28,000).

Intuitively, you might expect that any amount between $25,000 and $28,333 is a possible value of the average salary. To see that $26,000 is possible, in the weighted mean above, use the respective weights 9 and 1 instead of 2 and 1. To see that $28,000 is possible, use the respective weights 7 and 3.
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Re: Practice Question #3   [#permalink] 29 May 2014, 08:21
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Practice Question #3-Each employee of a certain company

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