Official Solution:


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

The questions asks whether \((average \ age)=\frac{(total \ age)}{(number \ of \ employees)} \lt 40\), or whether \(\frac{(total \ age)}{3x+4x+8x} \lt 40\), which is the same as: is \((total \ age) \lt 600x\)?

(1) The total age of all the employees in these companies is 600. The question becomes: is \(600 \lt 600x\)? Or is \(1 \lt x\). We don't know that: if \(x=1\), then the answer is NO but if \(x \gt 1\), 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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This is an Yes/No DS question. In a Yes/No Data Sufficiency questions, statement(s) is sufficient if the answer is “always yes” or “always no” while a statement(s) is insufficient if the answer is "sometimes yes" and "sometimes no".

The question asks: is the average age of all employees in these companies less than 40 years? As shown in the solution this is the same as asking is \((total \ age) \lt 600x\)? The second statement says that \((total \ age)=600x\), thus the asnwer to the question is NO.

Hope it's clear.
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(1) The total age of all the employees in these companies is 600. The question becomes: is 600 \lt 600x? Or is 1 \lt x. We don't know that: if x=1, then the answer is NO but if x \gt 1, then the answer is YES. Not sufficient.

I dont understand why you ruled out Statement 1. We know that x>1 since there is a given ratio for the employees. isnt that sufficient?

I did this way

B) The ratio of the employees are 3:4:8 and the average age are 40,20 and 50.
If you look, more no. of people are above 40 years old. So obviously average will be greater than 40 so the answer has to be N0.

B is the answer

If \(x=1\) (so if the number of employees is 15), then the answer is NO but if \(x \gt 1\) (so if the number of employees is 30, 45, ...), then the answer is YES.
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Thanks for explaining this. I solved this correctly but your method is much clearer and takes less time.
I think for anyone else having trouble solving this quickly, one needs to always have a clear and organized workspace. Recognizing the two concepts in play - the unknown ratio multiplier, and how to calculate an average and a total - is crucial, but writing them down and then solving for them is even more important.

(1) says (total age) = 600
(2) says (total age) = 600x

There is a huge difference between 600 and 600x.
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