benejo wrote:
A set of 13 integers has a median of 10 and an average of 15. If the highest term in the set is a unique, non-repeating integer, what is the lowest possible value of the highest integer in the set?
A. 81
B. 25
C. 22
D. 21
E. 20
Source:
ExpertsGlobalTo make X- the last 13th member of the set, we have to maximize other values in the set.
1) Median (7th member) = 10, then we can max 1-6th values also to 10
2) Numbers in the set are integers, so X will be unique min, when 8-12th numbers = X-1
3) Sum of the set = avarage*number of set members = 15*13
We got an uquality:
10*7 +
5*(x-1) + x =
13*153x=65
x= 21.7
Since x- is integer we can say it is 21 or 22,
so 3x=66 or 3x=63. In second case (63) we have to give extra 2 points to any number/numbers of the set which will a)move median b) will make other numbers = or > than the X. So the only scenario is possible to "take" extra 1 point from any other number of the set. Hence Answer is 22 (C)