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When 52-year old Jane joined a group of professionals

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Director
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Status: Manager
Joined: 27 Oct 2018
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When 52-year old Jane joined a group of professionals  [#permalink]

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New post 26 Dec 2018, 10:57
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Difficulty:

  75% (hard)

Question Stats:

41% (02:38) correct 59% (02:25) wrong based on 22 sessions

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When 52-year old Jane joined a group of professionals, the average (arithmetic mean) age of the group increased by ten percent. If the average age of the group before Jane joined was 26 years, how many professionals are there in the group now?

A) 9

B) 10

C) 11

D) 12

E) 13

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Re: When 52-year old Jane joined a group of professionals  [#permalink]

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New post 26 Dec 2018, 13:08
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Mahmoudfawzy83 wrote:
When 52-year old Jane joined a group of professionals, the average (arithmetic mean) age of the group increased by ten percent. If the average age of the group before Jane joined was 26 years, how many professionals are there in the group now?

A) 9

B) 10

C) 11

D) 12

E) 13


X = ORIGINAL SUM
N = ORIGINAL NUMBER

26 = X/N
X = 26N

After new member addition

26*1.1 = (X + 52)/(N+1)
Put X = 26N and solve for N
N=9

Now 9+1= 10 members

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Re: When 52-year old Jane joined a group of professionals  [#permalink]

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New post 26 Dec 2018, 18:20
Mahmoudfawzy83 wrote:
When 52-year old Jane joined a group of professionals, the average (arithmetic mean) age of the group increased by ten percent. If the average age of the group before Jane joined was 26 years, how many professionals are there in the group now?

A) 9

B) 10

C) 11

D) 12

E) 13


You can treat this as a weighted averages problem!

You're averaging one 52-year-old (Jane), and an unknown number of 26-year-olds. (It doesn't matter that they might all have different ages; what we care about is that their average age is 26.)

The result is an average that's 10% higher than 26. So, the new average is 1.1(26), which equals 28.6.

Here's what we have:

professionals: 26 -------- average: 28.6 ---------------------------------------------- Jane: 52

Start by finding how far each group is from the average. The 26-year-olds are 2.6 years below the average, while Jane is 52-28.6 = 23.4 years above the average. That's a ratio of 2.6:23.4, or 26:234, or 1:9.

Since Jane's age is 9 times further from the average than everyone else's, there must be 9 times as many other people. So, there were 9 people in the group before Jane arrived, and now there are 10.
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Re: When 52-year old Jane joined a group of professionals   [#permalink] 26 Dec 2018, 18:20
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