theCodeToGMAT wrote:What is the average (arithmetic mean) height of the n people of a certain group?
(1) The average height of the n/3 tallest people in the group is 6 feet 2.5 inches, and the average height of the rest of the people in the group is 5 feet 10 inches
(2) The sum of the heights of the n people is 178 feet 9 inches
OA [spoiler][A][/spoiler]
Statement 1:
Test TWO CASES.
If the average height is the same in each case, the statement is SUFFICIENT.
If the average height is NOT the same in each case, the statement is INSUFFICIENT.
To simplify the math, plug in easier values for the heights:
The average height of the n/3 tallest people in the group is 1 FOOT, and the average height of the rest of the people in the group is 2 FEET.
Case 1: n=3
Here, n/3 = 3/3 = 1, so 1 person is 1 foot tall, while the other 2 people are each 2 feet tall.
Average height for all 3 people = (1*1 + 2*2)/3 = 5/3.
Case 2: n=6
Here, n/3 = 6/3 = 2, so 2 people are each 1 foot tall, while the other 4 people are each 2 feet tall.
Average height for all 6 people = (2*1+ 4*2)/6 = 10/6 = 5/3.
Since the average height is the same in each case, SUFFICIENT.
Statement 2:
Without knowing the value of n, we cannot determine the average height.
INSUFFICIENT.
The correct answer is
A.
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