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At a recent company meeting, there were 14 project managers and 10 eng

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At a recent company meeting, there were 14 project managers and 10 eng  [#permalink]

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At a recent company meeting, there were 14 project managers and 10 engineers in attendance, with an overall average age of 31. If the average age of the project managers was 36, what was the average age of the engineers?

A. 24
B. 25
C. 26
D. 28
E. 30

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Re: At a recent company meeting, there were 14 project managers and 10 eng  [#permalink]

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New post 21 Mar 2017, 07:46
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Bunuel wrote:
At a recent company meeting, there were 14 project managers and 10 engineers in attendance, with an overall average age of 31. If the average age of the project managers was 36, what was the average age of the engineers?

A. 24
B. 25
C. 26
D. 28
E. 30


This is a nice weighted averages question.

Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...

So: average age of COMBINED workers = (proportion of project managers)(average age of project managers) + (proportion of engineers)(average age of engineers)

We have a total of 24 workers (14 project managers + 10 engineers = 24 workers)
So, the proportion of project managers = 14/24 = 7/12
The proportion of engineers = 10/24 = 5/12
Let E = average age of engineers

Now, plug everything into the formula to get:
31 = (7/12)(36) + (5/12)(E)
Simplify: 31 = 21 + 5E/12
Subtract 21 from both sides: 10 = 5E/12
Multiply both sides by 12 to get: 120 = 5E
Solve: E = 24

Answer:

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Re: At a recent company meeting, there were 14 project managers and 10 eng  [#permalink]

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New post 21 Mar 2017, 07:46
Bunuel wrote:
At a recent company meeting, there were 14 project managers and 10 engineers in attendance, with an overall average age of 31. If the average age of the project managers was 36, what was the average age of the engineers?

A. 24
B. 25
C. 26
D. 28
E. 30


Hey,

PFB the solution. :)

    • Number of Project Managers = 14
    • Average Age of Project Managers = 36
    • Number of Engineers = 10
    • Average Age of Engineers = X (assume)
    • Overall Average = 31

Thus, we can write

Overall Average = [(Number of Project Managers *Average Age of Project Managers + Number of Engineers*Average Age of Engineers)/[Number of Project Managers+Number of Engineers]

\(31 = \frac{(14*36 + 10X)}{(14+10)}\)

\(10X = 24 * 31 - 14 *36 = 24*31 - 24 * 21\)

\(10 X = 10 * 24\)

\(X = 24\)

Thus, the correct answer is Option A


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Re: At a recent company meeting, there were 14 project managers and 10 eng  [#permalink]

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New post 21 Mar 2017, 10:28
Bunuel wrote:
At a recent company meeting, there were 14 project managers and 10 engineers in attendance, with an overall average age of 31. If the average age of the project managers was 36, what was the average age of the engineers?

A. 24
B. 25
C. 26
D. 28
E. 30


\(24*31 = 14*36 + 10*e\)

\(Or, 12*31 = 7*36 +5e\)

\(Or, 372 = 252 + 5e\)

\(Or, 120 = 5e\)

\(Or, e = 24\)

Thus, the average age of the engineers is (A) 24 years...
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Re: At a recent company meeting, there were 14 project managers and 10 eng  [#permalink]

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New post 21 Mar 2017, 10:28
Bunuel wrote:
At a recent company meeting, there were 14 project managers and 10 engineers in attendance, with an overall average age of 31. If the average age of the project managers was 36, what was the average age of the engineers?

A. 24
B. 25
C. 26
D. 28
E. 30


\(24*31 = 14*36 + 10*e\)

\(Or, 12*31 = 7*36 +5e\)

\(Or, 372 = 252 + 5e\)

\(Or, 120 = 5e\)

\(Or, e = 24\)

Thus, the average age of the engineers is (A) 24 years...
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Abhishek....

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At a recent company meeting, there were 14 project managers and 10 eng  [#permalink]

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New post 17 Jul 2018, 09:40
Bunuel wrote:
At a recent company meeting, there were 14 project managers and 10 engineers in attendance, with an overall average age of 31. If the average age of the project managers was 36, what was the average age of the engineers?

A. 24
B. 25
C. 26
D. 28
E. 30


We are given that the average age of the 14 project managers was 36. Now, the 10 engineers
in attendance will have to reduce the total by \(14*5 = 70\) (such that the overall average to 31)

Therefore, the average age of the engineers is \(\frac{70}{10}\) or \(7\) less than 31, which is 24(Option A)
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At a recent company meeting, there were 14 project managers and 10 eng &nbs [#permalink] 17 Jul 2018, 09:40
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