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When a person aged 39 is added to a group of n people, the average age
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13 Aug 2021, 09:51
13 Aug 2021, 09:51
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When a person aged 39 is added to a group of n people, the average age increases by 2. When a person aged 15 is added instead, the average age decreases by 1. What is the value of n?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
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Re: When a person aged 39 is added to a group of n people, the average age
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13 Aug 2021, 09:59
13 Aug 2021, 09:59
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Carcass wrote:
When a person aged 39 is added to a group of n people, the average age increases by 2. When a person aged 15 is added instead, the average age decreases by 1. What is the value of n?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Let m = mean of ORIGINAL n people
This means the SUM of the ages of the ORIGINAL n people = nm
When a person aged 39 is added to a group of n people, the average age increases by 2
In other words: new mean (with extra person) of n+1 people = original mean + 2
Rewrite as: (nm + 39)/(n+1) = m + 2
Cross multiply to get: nm + 39 = (n + 1)(m + 2)
Simplify: nm + 39 = nm + 2n + m + 2
Simplify: 39 = 2n + m + 2
Rearrange to get: 2n+ m = 37
When a person aged 15 is added instead, the average age decreases by 1
In other words: new mean (with extra person) of n+1 people = original mean - 1
Rewrite as: (nm + 15)/(n+1) = m - 1
Cross multiply to get: nm + 15 = (n + 1)(m - 1)
Simplify: nm + 15 = nm - n + m - 1
Simplify: 15 = -n + m - 1
Rearrange to get: -n + m = 16
We now have the following system:
2n+ m = 37
-n + m = 16
Subtract the bottom equation from the top equation to get: 3n = 21
Solve: n = 7
Answer: A
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Re: When a person aged 39 is added to a group of n people, the average age [#permalink]
13 Aug 2021, 09:59
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