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

Source: Manhattan Advanced GMAT Quant

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<tIn 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 object

s.

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

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