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Math Expert V
Joined: 02 Sep 2009
Posts: 59588

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Difficulty:   55% (hard)

Question Stats: 55% (01:45) correct 45% (02:03) wrong based on 305 sessions

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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.

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

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Math Expert V
Joined: 02 Sep 2009
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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.

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Intern  B
Joined: 28 Aug 2014
Posts: 8
GMAT 1: 620 Q48 V27 ### Show Tags

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?
Math Expert V
Joined: 02 Sep 2009
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sriharsha63 wrote:
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?

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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Intern  B
Joined: 28 Aug 2014
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GMAT 1: 620 Q48 V27 ### Show Tags

thanks Bunuel, it makes sense now. I wasnt aware about the yes/no DS question!!
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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?
Math Expert V
Joined: 02 Sep 2009
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kritiu wrote:
(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?

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

Bunuel wrote:
kritiu wrote:
(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?

We don't know whether x > 1. The ratio could be 3:4:8, which is if x = 1.
Intern  B
Joined: 12 Mar 2017
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Schools: Ross '20 (S)
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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.

Math Expert V
Joined: 02 Sep 2009
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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.

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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Senior Manager  G
Joined: 31 May 2017
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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.

Intern  B
Joined: 12 Jan 2017
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Location: United States (NY)
Schools: Booth '21 (D)
GMAT 1: 710 Q47 V41 GPA: 3.48

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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.

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.
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Joined: 16 Oct 2015
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there is no difference between statements 1 and 2..they are saying that the sum of ages is 600....how can B be the answer? what if x > 1...i think answer has to be E
Math Expert V
Joined: 02 Sep 2009
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dandiv1989 wrote:
there is no difference between statements 1 and 2..they are saying that the sum of ages is 600....how can B be the answer? what if x > 1...i think answer has to be E

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

There is a huge difference between 600 and 600x.
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# M25-18

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