DS questions about MEDIANS are relatively common. The best strategy is often to test cases.
What is the median of set A {-8, 15, -9, 4, N}?
First, put the known terms in order: [-9, -8, 4, 15]. There are several possibilities for what the median could be:
- if N</= -8, then -8 will be the median: [N, -9, -8, 4, 15]
- if N >/= 4, then 4 will be the median: [-9, -8, 4, N, 15]
- if N is between -8 and 4, N itself will be the median: [-9, -8, N, 4, 15]
In the first 2 cases, knowing either the value of N or simply the range of N would be sufficient to tell us the value of the median. In the 3rd case, we would have to know the value of N itself.
(1) N is a prime and N^6 is even
If some power of N is even, then N itself must be even. If it is also prime, then N = 2 (the only even prime). This is sufficient: the median must be 2.
(2) 2N + 14 < 20
Simplify:
2N < 6
N < 3
If N < 3, it might also be less than -8, making -8 the median. Or it might be the -8 < N < 3, in which case N is the median (of unknown value). This is insufficient to tell us the value of the median.
The answer is A.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
