Set T consists of 82 CONSECUTIVE ODD integers. If the sum of the integers is 3â�¸ - 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

= (3â�¸ - 1)/82

= (3â�´ - 1)(3â�´ + 1)/82

*[factored the difference of squares]*
= (81 - 1)(81 + 1)/82

= (80)(82)/82

=

80
=

C
Cheers,

Brent