Bunuel wrote:
What is the average (arithmetic mean) height of the n people in a certain group?(1) The average height of the n/3 tallest people in the group is 6 feet \(2 \frac{1}{2}\) inches, and the average height of the rest of the people in the group is 5 feet 10 inches.
The average height of the n/3 tallest people is 74.5 inches;
The average height of the remaining n - n/3 = 2n/3 people is 70 inches.
(The average height of the group) = (The sum of the heights)/n \(= \frac{74.5*\frac{n}{3}+70*\frac{2n}{3}}{n}\)
Reduce by n:
\(= 74.5*\frac{1}{3}+70*\frac{2}{3}\).
Sufficient.
(2) The sum of the heights of the n people is 178 feet 9 inches.
We don't know the number of students, in the group, n, so cannot get the average. Not sufficient.
Answer: A.
Hope it helps.
Hi Bunuel,
I don't understand why this is the case. I think there might be a small error in the question or in my understanding of the question.
So lets assume there are 10 people. Heights are as follows: {20,19,18,7,6,5,4,3,2,1}. Then we need to know the average height of 6 people. so n=6.
1st tells us that average height of 2 tallest people is 19.5. and the average of other 8 people is 5.75. How can you find out the average height of 6 people from this group? and by the way, which 6 people are we talking about?
I feel that the question confuses language a little bit. Instead of "the average height of the rest of the people in the group is 5 feet 10 inches" it probably should say "the average height of the rest of the people in the group
n is 5 feet 10 inches".
Your response would be highly appreciated.