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# M25-18

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Math Expert
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16 Sep 2014, 00:23
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55% (hard)

Question Stats:

51% (01:13) correct 49% (01:16) wrong based on 437 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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16 Sep 2014, 00:23
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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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19 Oct 2014, 23:50
I didnt get the solution right! can you elaborate more with any other example.
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20 Oct 2014, 03:13
sriharsha63 wrote:
I didnt get the solution right! can you elaborate more with any other example.

You have to specify what part was unclear for you.
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20 Oct 2014, 03:20
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?
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20 Oct 2014, 03:28
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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20 Oct 2014, 04:21
thanks Bunuel, it makes sense now. I wasnt aware about the yes/no DS question!!
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22 Oct 2014, 21:11
(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?
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22 Oct 2014, 22:58
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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22 Dec 2014, 09:45
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.
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13 Nov 2015, 06:07
Hello Bunuel,

Don't you think OA needs to be edited for this question:

Question Stem:

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?

Analysis:

Ratio of number of employees:
X : Y: Z
3x: 4x: 8x = 15x -------- (A)

Age Average/Individual: Unknown

Is average age less than 40????

Statements are as follows:

(1) The total age of all the employees in these companies is 600

Average age = Total age/ N

Here N needs to be at least 15 because X can not be less than 01. So 600/15 =40

Hence average age needs to be 40 or more.

Answer to the question "Is the average age of all employees in these companies less than 40 years" is obviously NO.

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

Analysis for this statement already done by you.

So the answer to this question needs to be D.

Please suggest that whether my analysis for statement 01 is correct.

Thanks
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13 Nov 2015, 19:56
The x can't small than 1 right? the # of people at each company has to be integer...
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13 Nov 2015, 21:28
Right, that's what make statement 01 sufficient I guess
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29 Dec 2015, 05:26
WillGetIt wrote:
Right, that's what make statement 01 sufficient I guess

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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29 Dec 2015, 05:30
WillGetIt wrote:
Hello Bunuel,

Don't you think OA needs to be edited for this question:

Question Stem:

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?

Analysis:

Ratio of number of employees:
X : Y: Z
3x: 4x: 8x = 15x -------- (A)

Age Average/Individual: Unknown

Is average age less than 40????

Statements are as follows:

(1) The total age of all the employees in these companies is 600

Average age = Total age/ N

Here N needs to be at least 15 because X can not be less than 01. So 600/15 =40

Hence average age needs to be 40 or moreLESS.

Answer to the question "Is the average age of all employees in these companies less than 40 years" is obviously NO MAYBE.

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

Analysis for this statement already done by you.

So the answer to this question needs to be D.

Please suggest that whether my analysis for statement 01 is correct.

Thanks

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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03 Jan 2017, 10:12
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
--------------
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
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04 Jan 2017, 00:33
ashokingmat wrote:
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
--------------
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

How did you get the red part? (40∗6+20∗8+50∗16)/(6 + 8 + 16) = 40, not less than 40.
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12 Jul 2017, 02:45
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.

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12 Jul 2017, 05:15
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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13 Mar 2018, 16:57
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.

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# M25-18

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