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guys this question is more specific related to english and math together then math only,i am studying GRE tasks(quantity variant) and want to be acquainted every term and trick related to math problem,for example,let's take this task:

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?

i have question related to this fragment from problem: there are more then twice as many employees in department X as in department Y. so there is two way to translate this stattment into mathematics term.first:if in department X there is $a$ person,then in $Y$ department there is $2*a$ employee,second variant is this ,first leave as we introduced,but in $Y$ department there is $a+2*a=3*a$ employee,which one is correct one?it is very crucial for passing test successfuly,so i need to be clarified in such terms,thanks a lot of

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1 Answer 1

up vote 2 down vote accepted

Let $a$ denote the number of employees in $X$ and $b$ the number for $Y$. Your attempt was to set $b=2a$, but that translates as *"In department $Y$ there are exactly twice as many employees as in department $X$". So there are two things wrong: You swapped the role of $X$ and $Y$ and you replaced "more than " by "exactly". The correct tranlation of the given condition about employee counts is $$a>2b.$$ This might mean that $a=3b$ or $a=100b$ or just that $a=2b+1$.

Note that I didn't write $a\ge 2b$ because that would be the translation for "at least twice as many", while the problem statement says "more than twice as many".

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this is why i have posted question,because sometimes it is difficult exactly what is written to understand,now it is clear,i will try to solve this problem and if any question,i will post here now only for mathemaical solutions,thanks a lot of –  dato datuashvili Oct 24 '12 at 6:32
    
by the way,total number of employees would be $a+b$ right? –  dato datuashvili Oct 24 '12 at 6:40

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