Explanation to a GMATPrep Question please..

[Boosteda4]

"What is the average height of the n people in a certain group?"

(1) The average height of the n/3 tallest people is 6 feet 2.5 inches and the average height of the rest of the people is 5ft 10in.
(2) Sum of the heights of n people is 178ft 9 inches.

Correct answer is (A) Statement 1 is sufficient. I'm not sure I fully understand why?

Is it because since we know n must be an integer (since it is the number of people) and that statement 1 uses n/3, n must be either 1, 2, or 3? But since '1' would be 'person' (not the term 'people') and 3/3 equals 1, then n must be '2'? Thus, you can now calculate the average height.

[Rahul@gurome]

(1) Average height of the n people = [(n/3)*6ft 2.5in + (2n/3)*5ft 10in] / n
= (6ft 2.5in)/3 + (2*5ft 10in )/3, which can be calculated further.
So, (1) is SUFFICIENT.

(2) Number of people, n, should be known to find the average height of the n people.
So, (2) is NOT SUFFICIENT.

The correct answer is [spoiler](A)[/spoiler].

[gmatmachoman]

Basically tests the weighted average concept

(n1 * A1 + n2 * A2)/ n = Average

(n/3*A1 + 2n/3 * A2 )/n

" n" cancels out..U can find the average

Pick A