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
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A total of 22 men and 26 women were at a party, and the average (arithmetic mean)
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BTGModeratorVI
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deloitte247
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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
$$Average\ age\ of\ women=\frac{total\ age\ of\ women}{number\ of\ women}$$
$$=\ \frac{844}{26}$$
$$\approx\ 32.5$$
$$Answer=\ D$$
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
$$Average\ age\ of\ women=\frac{total\ age\ of\ women}{number\ of\ women}$$
$$=\ \frac{844}{26}$$
$$\approx\ 32.5$$
$$Answer=\ D$$
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Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...BTGModeratorVI wrote: ↑Fri Jul 03, 2020 7:14 amA 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
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
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