Bunuel wrote:
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
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.