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03 Sep 2024, 19:02
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Hello all,
Please help on the following
Question from GMAT Online bank:
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
d) 33
My initial approach was the following:
AVG_(Men + Women) = 35
AVG_Men = 38
AVG_Women = ?
AVG_(Men + Women) = 35 = (AVG_Men + AVG_Women)/2
35 = (38 + AVG_Women)/2
AVG_Women = 70 - 38 = 32 (wrong answer)
The correct solution is the following:
There were 22 + 26 = 48 men and women at the party and their average age was exactly 35 years, so the sum of all of their ages was (48)(35) = 1,680 years. The average age of the 22 men was exactly 38 years, so the sum of the men’s ages was (22)(38) = 836 years. Therefore, the sum of the women’s ages was 1,680 − 836 = 844 years, and their average age was ≈ 32.5 years.
OK I understand how this was approached and I get, but why the other way wouldn't lead me to the correct answer too???
I tested my approach using sets of data and it seems to work.
Example: Let T be the following set: 2,4,8,10,12,22
AVG T= (2+4+8+10+12+22)/6 = 58/6 = 29/3 ≈ 9.67
let U be subset of T such as: 2,4,8
AVG_U = (2+4+8)/3 = 14/3
let W be subset of T such as: 10,12,22
AVG_W = (10+12+22)/3 = 44/3
AVG_T = (AVG_U + AVG_W)/2
= (14/3 + 44/3)/2 ≈ 9.67
Thanks!
Please help on the following
Question from GMAT Online bank:
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
d) 33
My initial approach was the following:
AVG_(Men + Women) = 35
AVG_Men = 38
AVG_Women = ?
AVG_(Men + Women) = 35 = (AVG_Men + AVG_Women)/2
35 = (38 + AVG_Women)/2
AVG_Women = 70 - 38 = 32 (wrong answer)
The correct solution is the following:
There were 22 + 26 = 48 men and women at the party and their average age was exactly 35 years, so the sum of all of their ages was (48)(35) = 1,680 years. The average age of the 22 men was exactly 38 years, so the sum of the men’s ages was (22)(38) = 836 years. Therefore, the sum of the women’s ages was 1,680 − 836 = 844 years, and their average age was ≈ 32.5 years.
OK I understand how this was approached and I get, but why the other way wouldn't lead me to the correct answer too???
I tested my approach using sets of data and it seems to work.
Example: Let T be the following set: 2,4,8,10,12,22
AVG T= (2+4+8+10+12+22)/6 = 58/6 = 29/3 ≈ 9.67
let U be subset of T such as: 2,4,8
AVG_U = (2+4+8)/3 = 14/3
let W be subset of T such as: 10,12,22
AVG_W = (10+12+22)/3 = 44/3
AVG_T = (AVG_U + AVG_W)/2
= (14/3 + 44/3)/2 ≈ 9.67
Thanks!
03 Sep 2024, 19:42
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Hi
The question bank’s problem should be thought of as a weighted average problem.
Simplify the problem. If there were two men with heights 10 and 10, and one woman with a height of 20, would you say that the average of everyone (men plus woman) is 15 or 13.33?
In your example, in the final step, you essentially just rewrote the first summation
Posted from my mobile device
The question bank’s problem should be thought of as a weighted average problem.
Simplify the problem. If there were two men with heights 10 and 10, and one woman with a height of 20, would you say that the average of everyone (men plus woman) is 15 or 13.33?
In your example, in the final step, you essentially just rewrote the first summation
Posted from my mobile device
07 Sep 2024, 04:08
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Hi the easiest way to solve such problems is by a shortcut
Number of group 1 items/Number of group 2 items = (Average of group 2 - Average of Total group) / (Average of total group - Average of group 1)
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?
Let men be group 2 as their average is greater than combined average and women be group 1
26/22 = (38 - 35)/(35 - x)
26/22 = 3/(35-x)
13/11 = 3/(35-x)
13*(35-x) = 3*11
35 - x = (3*11)/13
x = 35 - [ (3*11)/13]
x = 35 - ~2.9
x = ~32 a little above 32 i.e. 32.5
Derivation of formula i used:
Weighted avg formula =
CombAvg = [(N1)(Avg 1) + N2(Avg 2) ]/ (N1 + N2)
Comb Avg * (N1 + N2) = (N1)(Avg 1) + N2(Avg 2)
CombAvg* N1 + CombAvg*N2 - (N1)*(Avg 1) - N2*(Avg 2) = 0
N1 (CombAvg - Avg1) = N2 ( Avg 2 - CombAvg)
N1/N2 = [( Avg 2 - CombAvg)]/ (CombAvg - Avg1)
The shortcut I used!
Also can you share more of such online qs on online bank to me ? Can help you with same. PM.
Number of group 1 items/Number of group 2 items = (Average of group 2 - Average of Total group) / (Average of total group - Average of group 1)
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?
Let men be group 2 as their average is greater than combined average and women be group 1
26/22 = (38 - 35)/(35 - x)
26/22 = 3/(35-x)
13/11 = 3/(35-x)
13*(35-x) = 3*11
35 - x = (3*11)/13
x = 35 - [ (3*11)/13]
x = 35 - ~2.9
x = ~32 a little above 32 i.e. 32.5
Derivation of formula i used:
Weighted avg formula =
CombAvg = [(N1)(Avg 1) + N2(Avg 2) ]/ (N1 + N2)
Comb Avg * (N1 + N2) = (N1)(Avg 1) + N2(Avg 2)
CombAvg* N1 + CombAvg*N2 - (N1)*(Avg 1) - N2*(Avg 2) = 0
N1 (CombAvg - Avg1) = N2 ( Avg 2 - CombAvg)
N1/N2 = [( Avg 2 - CombAvg)]/ (CombAvg - Avg1)
The shortcut I used!
Also can you share more of such online qs on online bank to me ? Can help you with same. PM.
