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Updated on: 15 Dec 2016, 15:35
Originally posted by HumptyDumpty on 14 Jan 2013, 06:16.
Last edited by stonecold on 15 Dec 2016, 15:35, edited 1 time in total.
Last edited by stonecold on 15 Dec 2016, 15:35, edited 1 time in total.
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
73% (01:17) correct
27%
(01:22)
wrong
based on 532
sessions
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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?
(A) 24
(B) 25
(C) 26
(D) 27
(E) 28
Source: Manhattan Advanced GMAT Quant
(A) 24
(B) 25
(C) 26
(D) 27
(E) 28
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?
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?
Source: Manhattan Advanced GMAT Quant
15 Jan 2013, 09:32
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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.
The first answer choice that makes sense is 27 years for the oldest sister leaving the middle and youngest to be 24.
15 Jan 2013, 09:59
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Dear sambam,
I would be glad if you've read the whole story before answering
.
Quote:
Solving the problem as such is not the purpose of my post.
I would be glad if you've read the whole story before answering
. 
