alexandrabiorka wrote:What is the average of 101² and 99²?
a) √101 + √99
b) 100
c) 100² - 1
d) 100²
e) 100² + 1
I have doubts about the "GMAT-ness" of this question, since the answer choices seem to force us into a certain approach. For example, the correct answer could also be written as
99² + 200 or
100² - 200, which might force a different approach.
Here's an alternate approach that would favor the other 2 options:
First recognize that the average of 2 values will be HALFWAY between those 2 values.
For example, 10 is the average of 7 and 13, and 10 is HALFWAY between 7 and 13.
So, to determine the average of 101² and 99², let's first determine the DISTANCE between these two values:
The distance between the two values = 101² - 99²
[we can factor this difference of squares]
= (101 + 99)(101 - 99)
= (200)(2)
= 400
Since 101² is 400 more than 99², the HALFWAY point between 99² and 101² will be 200 more than 99².
So the average will be
99² + 200
Or we can say that the HALFWAY point between 99² and 101² will be 200 less than 101², which means the average will
101² - 200
Having said all of that, we can still make these two answer choices resemble answer choice
E.
99² + 200 = (100 - 1)² +
200
= 100² - 200 + 1 +
200
= 100² + 1
=
E
We can use similar algebra to make
101² - 200 resemble answer choice
E as well.
Cheers,
Brent
