A total of 22 men

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A total of 22 men

by shahfahad » Thu Nov 26, 2015 1:58 am
A total of 22 men and 26 women were at a party, and the average (arithmetic mean) age of all of the adults at the party was exactly 35 years. If the average age of the men was exactly 38 years, which of the following was closest to the average age, in years of the women?

(A) 31
(B) 31.5
(C) 32
(D) 32.5
(E) 33

I tried solving it with the weighted average formula but my answer was incorrect. In OG, it is solved by first taking the sum of total members - sum of men ages which is equal of sum of women ages and divide it by number of women to get the average. Can we solve it another way? With the weighted average formula?
Last edited by shahfahad on Thu Nov 26, 2015 11:24 am, edited 1 time in total.

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by [email protected] » Thu Nov 26, 2015 10:59 am
Hi shahfahad,

Can you post your steps? It would help to see where you may have made a mistake.

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by shahfahad » Thu Nov 26, 2015 11:06 am
The formula i applied was:

Weighted Average = Population A/Total * Average of A + Population B/Total * Average of B

35 = 22/48 * (38) + 26/48 * x

x = 35*48/22*38*26

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by Brent@GMATPrepNow » Thu Nov 26, 2015 11:22 am
Be CAREFUL when transcribing questions. The answer choices and your solution suggest that the average of all adults is 35 (not 25)
shahfahad wrote:A total of 22 men and 26 women were at a party, and the average (arithmetic mean) age of all of the adults at the party was exactly 35 years. If the average age of the men was exactly 38 years, which of the following was closest to the average age, in years of the women?

(A) 31
(B) 31.5
(C) 32
(D) 32.5
(E) 33
Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...

The weighted average of groups combined = 35

Men comprise 22/48 of the attendees
Average age of men = 38

Women comprise 26/48 of the attendees
Let average age of women = w

Plug in values to get: 35 = (22/48)(38) + (26/48)(w)
This is an AWFUL equation to solve for w!

Simplify: 35 = (11/24)(38) + (13/24)(w)
Multiply both sides by 24 to get: 840 = 418 + 13w
Solve: w = 32.46

Answer: D

For more information on weighted averages, you can watch this free GMAT Prep Now video: https://www.gmatprepnow.com/module/gmat- ... ics?id=805

Here are some additional practice questions related to weighted averages:
- https://www.beatthegmat.com/weighted-ave ... 17237.html
- https://www.beatthegmat.com/weighted-ave ... 14506.html
- https://www.beatthegmat.com/average-weig ... 57853.html
- https://www.beatthegmat.com/averages-que ... 87118.html

Cheers,
Brent
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by Brent@GMATPrepNow » Thu Nov 26, 2015 11:23 am
shahfahad wrote:The formula i applied was:

Weighted Average = Population A/Total * Average of A + Population B/Total * Average of B

35 = 22/48 * (38) + 26/48 * x (PERFECT)

x = 35*48/22*38*26 ?????
See my calculations in the post above.

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by shahfahad » Thu Nov 26, 2015 11:28 am
Thanks Brent. Yes i have corrected my post by making the average 35.

Ok so i made the equation correct.

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by Matt@VeritasPrep » Fri Nov 27, 2015 12:04 am
shahfahad wrote:Thanks Brent. Yes i have corrected my post by making the average 35.

Ok so i made the equation correct.
I make these sort of transcription errors a lot myself, and they've taught me that if my logic seems sound, I probably wrote the problem down wrong or made a simple arithmetic mistake somewhere. This seems to bedevil me the most on problems that are hard to set up: I use up all my brainpower figuring out how to start the problem, and don't have enough brains left over to check the simple stuff!