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# Three sisters have an average (arithmetic mean) age of 25 ye

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Manager
Joined: 12 Dec 2012
Posts: 162
Location: Poland
Followers: 4

Kudos [?]: 164 [0], given: 67

Three sisters have an average (arithmetic mean) age of 25 ye [#permalink]

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14 Jan 2013, 06:16
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Difficulty:

35% (medium)

Question Stats:

69% (01:56) correct 31% (01:03) wrong based on 75 sessions

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This post is about a doubtful assumption, perhaps an error in the book, which however doesn't influence the answer to the original question.
Try-It 7-13:

Three sisters have an average (arithmetic mean) age of 25 years and a median age of 24 years. What is the minimum possible age, in years, of the oldest sister?

f = age of the first sister, etc.
M = Median = 24
m = mean

$$\frac{f+s+t}{3}=25=m$$

$$M=s=24$$

$$f+s=51$$

My assumption:
The problem says about the oldest sister, so I assumed that:

f≤s<t

In case the younger sisters were twins. The book explains: The youngest sister must be less than or equal to 24 years old. Agreed.

However, the book also assumes that:

s≤t:

Of course, the oldest sister must be at least as old as the middle sister (...) Not agreed. (Further implications concerning M=24 that turn the ≤ into the < possibility are correct.)

My thinking is: If there is one sister that is the oldest, she must not be the same age as the younger sister(s). Hypothetically, she could be 9 months older and still born in the same year, but I think it is impossible from the medical point of view. Or the sisters could be a step sisters, etc. Nevertheless, this situation is purely hypothetical and - even if the point was to mislead the thinker - in my opinion this is a bit too much, because the very natural assumption for expression of an age is it be an integer.

Moreover, if there were a hypothetical sets:

A={24,25,25},
OR
B={25,25,25},

none of the elements in each set were the greatest (oldest), because "the greatest" is an expression inherently relative to some other objects.

Disputably, in the A'={24,25} we could point 25 as "the greatest", because it's the greatest within the set, even though inside the set it is only "the greater" element, because there is only one other element to be relatively smaller (24).

If you have a one brother, you never say "I am his oldest brother" (unless you're joking).
Instead, you will say: "I am his older brother.". Ain't right?

And if you have two siblings, you will say: "I am the oldest one (of us three).", won't you?

OAs:
(A) 24
(B) 25
(C) 26
(D) 27
(E) 28
[Reveal] Spoiler: OA

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Manager
Joined: 18 Oct 2011
Posts: 90
Location: United States
Concentration: Entrepreneurship, Marketing
GMAT Date: 01-30-2013
GPA: 3.3
Followers: 2

Kudos [?]: 55 [0], given: 0

Re: Three sisters have an average (arithmetic mean) age of 25 ye [#permalink]

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15 Jan 2013, 09:32
This question is fairly simple. Note that in the question stem they do not say that each sister has a different age..meaning two could have the same age. If we have a median of 24 that means the middle sister is 24. If we have a mean of 25 that means that the total age of all 3 sisters is 75. If you take out the middle sisters age from the total you get 51...the youngest and oldest sisters must combine for 51 years.
The first answer choice that makes sense is 27 years for the oldest sister leaving the middle and youngest to be 24.
Manager
Joined: 12 Dec 2012
Posts: 162
Location: Poland
Followers: 4

Kudos [?]: 164 [0], given: 67

Re: Three sisters have an average (arithmetic mean) age of 25 ye [#permalink]

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15 Jan 2013, 09:59
Dear sambam,
Quote:
This post is about a doubtful assumption, perhaps an error in the book, which however doesn't influence the answer to the original question.

Solving the problem as such is not the purpose of my post.
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Re: Three sisters have an average (arithmetic mean) age of 25 ye   [#permalink] 15 Jan 2013, 09:59
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