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
A total of 22 men and 26 women were at a party, and the average
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Say the average age of women = x yearsBTGModeratorVI wrote: ↑Fri Jun 05, 2020 11:41 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
Thus, we have 22*38 + 26*x = 35*(22 + 26)
=> x = ~32.5 years
The correct answer: D
Hope this helps!
-Jay
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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 Jun 05, 2020 11:41 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
Cheers,
Brent
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Solution:BTGModeratorVI wrote: ↑Fri Jun 05, 2020 11:41 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
1) Since there are 48 people (22 men and 26 women) and the average age of all of them is 35, the total ages of all the people at the party is 48(35).
2) Since there are 22 men and their average age is 38, the sum of all the men's ages is 22(38).
3) There are 26 women; letting their average age be x, the sum of all the women's ages is 26x.
Since the sum of the ages of all 48 people must be equal to the sum of the ages of the 22 men plus the sum of the ages of the 26 women, we have
48(35) = 22(38) + 26x
1680 = 836 + 26x
26x = 844
x = 844/26
x = 32 12/26 ≈ 32.5
Answer: D
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