CoachErf wrote:If X is a set of consecutive integers in which 9 is the greatest number, how many integers are in set X?
1. The average (arithmetic mean) of all the integers in set X is 6
2. The average (arithmetic mean) of set X equals its range.
Key point is we are dealing with consecutive integers i.e. 1,2,3,4,5,etc.
Statement 1.
If the average is 6 and the greatest number is 9, it means that from the midpoint to the max we have 7,8,9.
At the average, there is a symmetric distribution of number of points, therefore we need 3 points from the average which becomes 3,4,5.
Therefore set x is 3,4,5,6,7,8,9. No. of points is 7. statement is sufficient.
Statement 2.
Since we are dealing with integers, we know the range has to be an integer (integer - integer = integer)
Therefore the number of points has to be an odd number
For example the average of 1 and 2 = 1.5 -> even number of points
the average of 1,2,3 = 2 -> odd number of points
with 9 being the highest value, here are the possibilities
7 8 9 -> range = 9-7=2; average =8
5 6 7 8 9 -> range = 9-5=4; average =7
3 4 5 6 7 8 9 -> range = 9-3=6; average =6
1 2 3 4 5 6 7 8 9 -> range = 9-1=8; average =5
There is only 1 choice where the range and the average are the same
This statement is sufficient.
