Problem Solving

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

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