Bunuel wrote:
teal wrote:
Is the median of set \(S\) even?
1. Set \(S\) is composed of consecutive odd integers
2. The mean of set \(S\) is even
Can someone please explain the correct approach for this one?
Is the median of set S even?(1) Set S is composed of consecutive odd integers --> set S is evenly spaced --> for any every evenly spaced set
mean=median. But still insufficient.
(2) The mean of set S is even. Insufficient on its own.
(1)+(2) From (1)
mean=median and from (2)
mean=even -->
mean=median=even. Sufficient.
Answer: C.
Hope it helps.
Bunuel wrote:
teal wrote:
can you please give me an example of a set in which mean is even and median is odd for statement 2?
Sure: {1, 1, 4} --> mean=(1+1+4)/3=2=even and median=1=odd.
If you tested cases for stmt 2 instead of using theory, then you'll need to consider the 3 cases mentioned below:
3 Cases
1) When list just has one item: Mean = Median
2) When list has even # of items:
(x + y)/2 = even
x + y = even
So x & y could be both even or both odd.
In either case, median = even.
3) When list has odd # of items:
(x + y + z)/3 = even
(x + y + z) = even
If x & z are both even or odd, then (x + z) = even and y = even.
If x & z are opposite, then (x + z) = odd and y = odd.