Averages

You can set up the equation as follows.

Average age of men: 38
Total men: 22
Sum of all the men's ages: 22*38

Average age of women: x
Total women: 26
Sum of all the women's ages: 26*x

Average age of men and women: 35
Total men and women: 22+26
Sum of all men and women's ages: 35*(22+26)


Equation:
Sum of men's age + Sum of women's age = Sum of men's and women's age

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

The question asks for the average age of women, which can be found by solving for x.

After some messy calcuation, you get to x=32.46 which is closest to D.

Thanks Tmmyc

Any shortcut to this question ? I am sure there must be ...[/list]

# of men/# of women= distance between overall mean-mean of women/distance between overall mean-mean of men

=>22/26=x/3
=>11/13=x/3
=>x=33/13=2.53
=>mean of women: 35-2.53=32.47~32.5

so D

Hi scoobydooby,

Kindly explain what wicked formula you employed to arrive at that answer. I've never seen this before:

# of men / # of women = mean of women / mean of men

According to your formula, "x" = 32.15, which, as you said, is a little less than 33. But is it closer to choice C, 32, than to D, 32.5.

If you use the weighted formula to workout the answer,

22/48*38 + 26/48*x = 35
x = 32.45, which is the exact answer to the nearest tenth. I, like others here, would like to know if there's a shorter way to arrive at this answer. The calculations were brutal.

hi linfongyu,

refer to Stuart's post in the link for the shortcut

(i had applied a wrong formula and have just edited it)

https://www.beatthegmat.com/what-fractio ... 11500.html