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The average (arithmetic mean) ages, in years, of the people in group A

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Bunuel
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The average (arithmetic mean) ages, in years, of the people in group A [#permalink] New post   27 Nov 2018, 00:34
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The average (arithmetic mean) ages, in years, of the people in group A and group B are 41 and 36, respectively. The average age, in years, of the people in the two groups combined is 38. If there are no people in both group A and group B, what fraction of the people in the two groups combined are in group B?

A. 2/5
B. 1/2
C. 3/5
D. 2/3
E. 3/4
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gulsam
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Re: The average (arithmetic mean) ages, in years, of the people in group A [#permalink] New post   09 Nov 2019, 12:46
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Maybe it is more understandable?

Let A, B be the number of groups

41A + 36B = 38 (A + B)
41A + 36B = 38A + 38B
3A = 2B
B: A = 3: 2
problem: B / (A + B) = 3 / ( 2+3)=3/5
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Re: The average (arithmetic mean) ages, in years, of the people in group A [#permalink] New post   27 Nov 2018, 05:58
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Bunuel wrote:
The average (arithmetic mean) ages, in years, of the people in group A and group B are 41 and 36, respectively. The average age, in years, of the people in the two groups combined is 38. If there are no people in both group A and group B, what fraction of the people in the two groups combined are in group B?

A. 2/5
B. 1/2
C. 3/5
D. 2/3
E. 3/4



using allegation method:

41 - 38 = 3

36 - 38 = 2. negative sign must be ignored.

Ratio of the people A and B respectively : 2: 3.

fraction required : 3/ 5.

C is the correct answer.
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Re: The average (arithmetic mean) ages, in years, of the people in group A [#permalink] New post   28 Nov 2018, 09:51
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ParthSanghavi wrote:
Bunuel wrote:
The average (arithmetic mean) ages, in years, of the people in group A and group B are 41 and 36, respectively. The average age, in years, of the people in the two groups combined is 38. If there are no people in both group A and group B, what fraction of the people in the two groups combined are in group B?

A. 2/5
B. 1/2
C. 3/5
D. 2/3
E. 3/4


selim

I did not understand the 2nd half the question. Could you please elaborate on it?



**No people belong to both group.

***we are looking for fraction

*** what fraction of the people in the two groups combined are in group B

Mark these color parts.

In simple words we are looking for the number of people belong to Group B out of all the people who belong to Both A and B.

\(\frac{B}{A + B}\)
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Re: The average (arithmetic mean) ages, in years, of the people in group A [#permalink] New post   28 Nov 2018, 14:49
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selim wrote:
Bunuel wrote:
The average (arithmetic mean) ages, in years, of the people in group A and group B are 41 and 36, respectively. The average age, in years, of the people in the two groups combined is 38. If there are no people in both group A and group B, what fraction of the people in the two groups combined are in group B?

A. 2/5
B. 1/2
C. 3/5
D. 2/3
E. 3/4



using allegation method:

41 - 38 = 3

36 - 38 = 2. negative sign must be ignored.

Ratio of the people A and B respectively : 2: 3.

fraction required : 3/ 5.

C is the correct answer.



selim if A = 41 - 38 = 3 and B = 36 - 38 = 2.

the why ratio is 3/5 and not 2/5 ?
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The average (arithmetic mean) ages, in years, of the people in group A [#permalink] New post   Updated on: 28 Nov 2018, 07:07
Bunuel wrote:
The average (arithmetic mean) ages, in years, of the people in group A and group B are 41 and 36, respectively. The average age, in years, of the people in the two groups combined is 38. If there are no people in both group A and group B, what fraction of the people in the two groups combined are in group B?

A. 2/5
B. 1/2
C. 3/5
D. 2/3
E. 3/4



GMATinsight :

Sir how to solve this question ? can this be solved using venn diagram?

Originally posted by Archit3110 on 27 Nov 2018, 11:02.
Last edited by Archit3110 on 28 Nov 2018, 07:07, edited 2 times in total.
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Re: The average (arithmetic mean) ages, in years, of the people in group A [#permalink] New post   28 Nov 2018, 06:21
Bunuel wrote:
The average (arithmetic mean) ages, in years, of the people in group A and group B are 41 and 36, respectively. The average age, in years, of the people in the two groups combined is 38. If there are no people in both group A and group B, what fraction of the people in the two groups combined are in group B?

A. 2/5
B. 1/2
C. 3/5
D. 2/3
E. 3/4


selim

I did not understand the 2nd half the question. Could you please elaborate on it?
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Re: The average (arithmetic mean) ages, in years, of the people in group A [#permalink] New post   28 Nov 2018, 09:09
Even i did not get the second part of question. Bunuel could you please explain it.
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The average (arithmetic mean) ages, in years, of the people in group A [#permalink] New post   28 Nov 2018, 16:24
dave13 wrote:
selim wrote:
Bunuel wrote:
The average (arithmetic mean) ages, in years, of the people in group A and group B are 41 and 36, respectively. The average age, in years, of the people in the two groups combined is 38. If there are no people in both group A and group B, what fraction of the people in the two groups combined are in group B?

A. 2/5
B. 1/2
C. 3/5
D. 2/3
E. 3/4



using allegation method:

41 - 38 = 3

36 - 38 = 2. negative sign must be ignored.

Ratio of the people A and B respectively : 2: 3.

fraction required : 3/ 5.

C is the correct answer.



selim if A = 41 - 38 = 3 and B = 36 - 38 = 2.

the why ratio is 3/5 and not 2/5 ?



coz 2 persons belong to group A. but we are looking for B . \(\frac{B}{A+B}\)
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The average (arithmetic mean) ages, in years, of the people in group A [#permalink] New post   11 Nov 2019, 21:06
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Bunuel wrote:
The average (arithmetic mean) ages, in years, of the people in group A and group B are 41 and 36, respectively. The average age, in years, of the people in the two groups combined is 38. If there are no people in both group A and group B, what fraction of the people in the two groups combined are in group B?

A. 2/5
B. 1/2
C. 3/5
D. 2/3
E. 3/4



41x + 36(1-x) = 38
41x + 36 - 36x = 38
5x = 2
x = 2/5
1- x = 3/5

The correct answer is (C).
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Re: The average (arithmetic mean) ages, in years, of the people in group A [#permalink] New post   26 Dec 2023, 02:20
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Re: The average (arithmetic mean) ages, in years, of the people in group A [#permalink]
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