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The ratio of the number of employees of three companies X, Y

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The ratio of the number of employees of three companies X, Y  [#permalink]

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The ratio of the number of employees of three companies X, Y and Z is 3:4:8, respectively. Is the average age of all employees in these companies less than 40 years?

(1) The total age of all the employees in these companies is 600.

(2) The average age employees in X, Y, and Z, is 40, 20, and 50, respectively.

Originally posted by amitsurana on 14 Jun 2014, 20:03.
Last edited by Bunuel on 15 Jun 2014, 02:16, edited 1 time in total.
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Re: The ratio of the number of employees of three companies X, Y  [#permalink]

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New post 15 Jun 2014, 02:16
The ratio of the number of employees of three companies X, Y and Z is 3:4:8, respectively. Is the average age of all employees in these companies less than 40 years?

Given that the ratio of the number of employees is 3x:4x:8x, for some positive multiple x.

The questions asks whether (average age)=(total age)/(# of employees)<40, or whether (total age)/(3x+4x+8x)<40, which is the same as: is (total age)<600x?

(1) The total age of all the employees in these companies is 600. The question becomes: is 600<600x? Or is 1<x. We don't know that: f x=1, then the answer is NO but if x>1, then the answer is YES. Not sufficient.

(2) The average age employees in X, Y, and Z, is 40, 20, and 50, respectively. (total age)=40*3x+20*4x+50*8x=600x, so the answer to the question is NO. Sufficient.

Answer: B.
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Re: The ratio of the number of employees of three companies X, Y  [#permalink]

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New post 29 Dec 2014, 20:53
Hi Bunuel,

I didnt get the second point, why is it sufficient to answer the question??
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Re: The ratio of the number of employees of three companies X, Y  [#permalink]

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New post 30 Dec 2014, 02:12
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The ratio of the number of employees of three companies X, Y  [#permalink]

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New post 26 Feb 2015, 02:57
Hi,

I chose B for the same reasons, but now I have a question...

[1] Does not give us the number of employees, as these are 3x+4x+8x=15x.
[2] Gives us 40*3x+20*4x+50*8x=600x.

So, all sounds logical. But now I thought of this for [1] and got confused:

We know that 3x+4x+8x=15x is N (Number of emloyees).
And we know that the sum of the ages is 600.

Can we say then than \(Mage =\) \(\frac{Sage}{N}\) ??

Then, this could become \(M =\)\(\frac{600}{15x}\)


\(x =\) \(\frac{600}{15M}\)

\(x = 40M\)

I am sorry for not being clear, but I barely understand myself at this point... Any ideas about what is confusing me?
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Re: The ratio of the number of employees of three companies X, Y  [#permalink]

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New post 26 Feb 2015, 13:12
Hi pacifist85,

In this ratio question, we're dealing with numbers of employees. Since you CANNOT have a "fraction" of an employee, the ratio of 3:4:8 means that the number of employees at the first company MUST be a multiple of 3, the number at the second company MUST be an equivalent multiple of 4 and the number at the third company MUST be an equivalent multiple of 8.

So, we could have 3, 4 and 8 employees = 15 total
We could also have 6, 8 and 16 employees = 30 total
Etc.

In real basic terms, the total number of employees IS a positive multiple of 15. We just don't know WHICH positive multiple of 15.

We're asked if the average age of all the employees is UNDER 40. This is a YES/NO question.

Fact 1: Total age = 600

IF....
There are 15 employees, then the average age is 600/15 = 40 and the answer to the question is NO.

IF....
There are 30 employees, then the average age is 600/30 = 20 and the answer to the question is YES.
Fact 1 is INSUFFICIENT.

Fact 2: The average age at each company is 40, 20 and 50, respectively.

This information gives us an EXACT weighted average.

IF....
There are 15 employees, then the average is [3(40) + 4(20) + 8(50)]/15 = 600/15 = 40 and the answer to the question is NO.

Increasing the number of employees will NOT change the answer though, since the number of employees is based on the 3:4:8 ratio.

IF...
There are 30 employees, then the average is [6(40) + 8(20) + 16(50)]/30 = 1200/30 = 40 and the answer to the question is NO.
The answer to the question is ALWAYS NO.
Fact 2 is SUFFICIENT.

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Re: The ratio of the number of employees of three companies X, Y  [#permalink]

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New post 06 Aug 2019, 21:16
The average age employees in X, Y, and Z, is 40, 20, and 50, respectively. (total age)=40*3x+20*4x+50*8x=600x, so the answer to the question is NO.

B Sufficient.
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Re: The ratio of the number of employees of three companies X, Y   [#permalink] 06 Aug 2019, 21:16
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