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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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21 Mar 2017, 04:02
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5% (low)

Question Stats:

93% (01:36) correct 7% (01:54) wrong based on 62 sessions

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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
[Reveal] Spoiler: OA

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Posts: 2058
Re: At a recent company meeting, there were 14 project managers and 10 eng [#permalink]

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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

[Reveal] Spoiler:
A

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

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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

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

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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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Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3326
Location: India
GPA: 3.5
Re: At a recent company meeting, there were 14 project managers and 10 eng [#permalink]

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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...
_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Re: At a recent company meeting, there were 14 project managers and 10 eng   [#permalink] 21 Mar 2017, 10:28
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