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

Using the “trick” from greg’s video i could get that the ration is that x:3.

But how do i know if x:3 is the ratio of men:women or women:men? (since x is not known, how do i know which out of x and 3 is larger?)

Firstly, to make average smaller, age of women has to be smaller.

Using Greg’s trick it can be solved in this manner

Women’s age -----x---- 35 ----3---- 38

Let difference in Mean and women’s age be x

Difference between Mean and men’s age is 3

Ratio is given as 22:26, flip it - 26:22

x/3 = 26/22

x=2.53 or 2.5

We get women’s age as 32.5

Check it

(26x32.5 + 22x38) / (22+26) = 35.02

Hey, thanks for the reply, my question had to do with why we had to flip the ratio.

But yes, I realized it does makes sense to flip it since the number of women are greater and therefore 35 will have to be closer to the women’s age than men’s age (and so x will be smaller than 3).