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The oldest member of a group of 20 people is 90 years old. He is repla

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Bunuel
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The oldest member of a group of 20 people is 90 years old. He is repla [#permalink] New post   17 Apr 2020, 04:22
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The oldest member of a group of 20 people is 90 years old. He is replaced by a new member and the average (arithmetic mean) age of the group is decreased by 4 years. What is the age of the new member ?

A. 10 years
B. 15 years
C. 20 years
D. 30 years
E. 40 years
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Re: The oldest member of a group of 20 people is 90 years old. He is repla [#permalink] New post   17 Apr 2020, 06:07
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The oldest member of a group of 20 people is 90 years old. He is replaced by a new member and the average (arithmetic mean) age of the group is decreased by 4 years. What is the age of the new member?

A. 10 years
B. 15 years
C. 20 years
D. 30 years
E. 40 years


The total reduction =20*4=80. Deduct 80 from the age of the oldest member. You will get 10, which is the age of the new entrant --- Ans. is A.
The answer arrived by a random hit and run guess and not by any rationale.
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Re: The oldest member of a group of 20 people is 90 years old. He is repla [#permalink] New post   17 Apr 2020, 04:39
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Let the initial Average = A.
The total sum of ages all 20 people = 20A
one man aged 90 replaced by new member of age x.
New total sum of ages all 20 people = 20A -90 +x
New Average = (20A -90 +x)/20 = old Average -4
Hence, (20A -90 +x)/20 = A-4
or, 20A -90 +x = 20A-80
or, x = 90-80 = 10

Hence, the age of new person = 10 years
Answer A

Bunuel wrote:
The oldest member of a group of 20 people is 90 years old. He is replaced by a new member and the average (arithmetic mean) age of the group is decreased by 4 years. What is the age of the new member ?

A. 10 years
B. 15 years
C. 20 years
D. 30 years
E. 40 years
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Re: The oldest member of a group of 20 people is 90 years old. He is repla [#permalink] New post   17 Apr 2020, 05:52
Let the Average age of group of 20 with 90 year old man = Y
And The sum of the remaining 19 members be X
So the average will be denoted as (X+90)/20=Y----(1)

Let the age of new member in the group be Z.
The total of age of 19 members be X+Z (age of new member)
So the average will be
(X+Z)/20=Y-4
[(X+Z)/20]+4=Y----(2)
Equating both.
[(X+90)/20]= [(X+Z)/20]+4
X+90=X+Z+80
Z=10

Therefore the age of new member is 10.
OA is A

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The oldest member of a group of 20 people is 90 years old. He is repla [#permalink] New post   17 Apr 2020, 09:20
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Bunuel wrote:
The oldest member of a group of 20 people is 90 years old. He is replaced by a new member and the average (arithmetic mean) age of the group is decreased by 4 years. What is the age of the new member ?

A. 10 years
B. 15 years
C. 20 years
D. 30 years
E. 40 years


One Step Explanation


Total people = 20

Change of average = 4 years

i.e. change of Sum of ages of 20 people = 20*4 = 80

90 years old gets replaced and total decreases by 80

i.e new person's age = 90-80 =10

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The oldest member of a group of 20 people is 90 years old. He is repla [#permalink] New post   19 Apr 2020, 05:03
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Bunuel wrote:
The oldest member of a group of 20 people is 90 years old. He is replaced by a new member and the average (arithmetic mean) age of the group is decreased by 4 years. What is the age of the new member ?

A. 10 years
B. 15 years
C. 20 years
D. 30 years
E. 40 years


Let x = the age of the new member and y = the average age of the original 20 people. We can create the equation:

(20y - 90 + x)/20 = y - 4

20y - 90 + x = 20y - 80

x = 10

Answer: A
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Re: The oldest member of a group of 20 people is 90 years old. He is repla [#permalink] New post   22 Apr 2020, 06:54
Let S be the sum of members:

\(\frac{ S-90+x}{20}=\frac{ S}{20}-4\)

S-90+x = S-80
x=10
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Re: The oldest member of a group of 20 people is 90 years old. He is repla [#permalink] New post   25 Apr 2021, 08:47
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Re: The oldest member of a group of 20 people is 90 years old. He is repla [#permalink]
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