Set T consists of 82 CONSECUTIVE ODD integers. If the sum of the integers is 3� - 1, what is the median of set T?
A) 41
B) 42
C) 80
D) 82
E) 164
Nice work, nipunranjan!
Here's my full solution (with a minor shortcut at the end)
There's a nice rule that says,
"In a set where the numbers are equally spaced, the mean will equal the median."
Since the consecutive odd integers are equally spaced, the mean = median.
So, let's find the mean.
The mean = (SUM of all 82 integers)/82
= (3� - 1)/82
= (3� - 1)(3� + 1)/82
[factored the difference of squares]
= (81 - 1)(81 + 1)/82
= (80)(82)/82
=
80
=
C
Cheers,
Brent