M25-18

Question

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

Bunuel · Accepted Answer

Official Solution:

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 question asks whether the average age, which is equal to  \frac{(total \ age)}{(number \ of \ employees)} < 40 . This is equivalent to asking whether  \frac{(total \ age)}{3x+4x+8x} < 40 , or in other words: is  (total \ age) < 600x ?
 
(1) The total age of all the employees in these companies is 600 years.
 
The question simplifies to: is  600 < 600x ? Or equivalently, is  1 < x ? 
 
We do not know that: if  x=1 , then the answer is NO, but if  x > 1 , then the answer is YES. Not sufficient.
 
(2) The average age of employees in X, Y, and Z, is 40, 20, and 50 years, respectively. 
 
The above implies that  (total \ age)=40*3x+20*4x+50*8x=600x , so the answer to the question is NO. Sufficient.

Answer: B

sriharsha63 · Answer

the second statement in particular;
(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.

we cannot find the answer from this statement, so how come we say its sufficient.

i opted for E because its not possible to get a single solution from both the statements.

how come the answer is B?

Bunuel · Answer

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.

sriharsha63 · Answer

thanks Bunuel, it makes sense now. I wasnt aware about the yes/no DS question!!

kritiu · Answer

(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?

Bunuel · Answer

We don't know whether x > 1. The ratio could be 3:4:8, which is if x = 1.

mathurvarun · Answer

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

maryamtheleadr · Answer

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.

Bunuel · 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.

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

BottomJee · Answer

I think this is a  high-quality  question and I agree with explanation.

Gemmie · Answer

Given information:

The ratio of employees in companies X, Y, and Z is 3:4:8.

Let the number of employees in companies X, Y, and Z be 3k, 4k, and 8k respectively.

Statement (1): The total age of all employees in these companies is 600 years.

This statement gives us the total age, but does not provide direct information about the average age.

However, we can use statement (1) to find the average age if we know the number of employees. The number of employees can be calculated as: 3k + 4k + 8k = 15kSo, the average age is: Avg=  \frac{600}{15k} = \frac{40}{k}

Since k can vary, we cannot definitively determine whether Avg < 40 without additional information.

Therefore, statement (1) alone is not sufficient.

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

Avg =  \frac{3k * 40 + 4k * 20 + 8k * 50}{15k} = \frac{600k}{15k} = 40

Therefore, statement (1) alone is sufficient.

=> Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

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M25-18

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