A total of 22 men and 26 women were at a party, and the average (arithmetic mean)

[BTGModeratorVI]

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

Answer: D
Source: Official guide

[deloitte247]

Total men at party = 22
Total women at party = 26
Total people at party = men + women
= 22 + 26 = 48


The average age of people at party = 35
Sum of all age = 48 * 35 = 1680


The average age of men = 38
Total age of men = 38 * 22 = 836

Total age of women = 1680 - 836 = 844
$$Average\ age\ of\ women=\frac{total\ age\ of\ women}{number\ of\ women}$$
$$=\ \frac{844}{26}$$
$$\approx\ 32.5$$
$$Answer=\ D$$

[Brent@GMATPrepNow]

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

Answer: D
Source: Official guide

Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...

There are 48 people in total.
So, 22/48 = the proportion of women
And 26/48 = the proportion of men

Let x = average age of the women

So, plugging the information into the formula, we get: (22/48)(38) + (26/48)(x) = 35
Simplify: (11/24)(38) + (13/24)(x) = 35
Multiply both sides by 24 to get: (11)(38) + 13x = (35)(24)
Simplify: 418 + 13x = 840
Rearrange: 13x = 422
Solve: x = 422/13 ≈ 32.5

Answer: D

Cheers,
Brent