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

Question

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

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

BrentGMATPrepNow · Accepted Answer

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: A

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EgmatQuantExpert · Answer

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 = 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 e-GMAT Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts

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Abhishek009 · Answer

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...

Abhishek009 · Answer

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...

pushpitkc · Answer

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)

ScottTargetTestPrep · Answer

Solution:

Letting n = the average age of the engineers, we can create the equation:

(14 x 36 + 10n) / 24 = 31

504 + 10n = 744

10n = 240

n = 24

Answer: A

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

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