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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You have to specify what part was unclear for you.
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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

The x can't small than 1 right? the # of people at each company has to be integer...

For statement 1, the average is only 40 if there are 15 people, hence Bunuel's x = 1.

But if x = 2 the number of employees is no longer 15 but 3(2):4(2):8(2) = 30

Then the average will be 600/30 = 20 so statement 1 is insufficient
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Given that the ratio of the number of employees is 3x:4x:8x3x:4x:8x, for some positive multiple xx.

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

(1) The total age of all the employees in these companies is 600. The question becomes: is 600<600x600<600x? Or is 1<x1<x. We don't know that: if x=1x=1, then the answer is NO but if x>1x>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(total age)=40∗3x+20∗4x+50∗8x=600x, so the answer to the question is NO. Sufficient.

My solution
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1) not sufficient
2) lets take minimum ratio 3:4:8
total age= 3*40+4*20+8*50 =600
so average= 600 /15 =40 (for minimum ratio)
40 is not less than 40 wrong

take next ratio multiplied by 2
lets take minimum ratio 6:8:16
then we get ratio < 40 correct
two different solutions so answer is E even if we combine both two cases 1 &2
Please correct me if i am wrong

Hi. Why is the first statement insufficient? We basically have been given total age. Dividing that with the sum of ratio given is enough to deduce that the avg age of all employees = 40 yrs.

I answered it as D.

Interesting question. I answered D assuming the number of employees as 15 i.e x=1 in the first option. Now i get what i missed to consider.

Correct answer is B
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