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

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Re: The ratio of the number of employees of three companies X, Y [#permalink]
Shree9975 wrote:
Hi Bunuel,

I didnt get the second point, why is it sufficient to answer the question??

The question asks whether (total age) < 600x. (2) says that (total age) = 600x, thus the answer to the question is NO.
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Re: The ratio of the number of employees of three companies X, Y [#permalink]
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]
1
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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]
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]
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Re: The ratio of the number of employees of three companies X, Y [#permalink]
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