Problem Solving

Hi shahfahad,

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

GMAT assassins aren't born, they're made,
Rich

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

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.

Cheers,
Brent