BTGModeratorVI wrote: ↑Thu Dec 03, 2020 2:43 pm
Set T consists of 82 consecutive odd integers. If the sum of the integers is 3^8 - 165, what is the median of set T?
A) 78
B) 79
C) 80
D) 81
E) 82
Answer:
A
Source: GMAT Prep Now
There's a nice rule that says,
"In a set where the numbers are equally spaced, the mean will equal the median."
For example, in each of the following sets, the mean and median are equal:
{7, 9, 11, 13, 15}
{-1, 4, 9, 14}
{3, 4, 5, 6}
Since set T consists of 82
consecutive odd integers (e.g., 5, 7, 9, 11, etc), we can see that these values are equally spaced.
So, the mean and median of set T are equal.
So, to find the answer,
we need only find the mean of set T.
Median = mean = (3⁸ - 165)/82
= (
3⁸ - 1 -
164)/82
[you'll see why I did this shortly]
= (
3⁸ - 1)/82 -
164/82
= (
3⁸ - 1)/82 - 2
[PERFECT!! 164/82 simplified to 2]
Now let's do some factoring
[since 3⁸ - 1 is a DIFFERENCE OF SQUARES]
=
(3⁴ + 1)(3⁴ - 1)/82 - 2
=
(81 + 1)(81 - 1)/82 - 2
=
(82)(80)/82 - 2
= 80 - 2
= 78
Answer: A
Cheers,
Brent
