a 33.33% decrease followed by a 50% increase, is the final result greater than the original value, less than the original value, or the same as the original value?

-33.33+50= 16.67
it is the original amount plus 16.67%... so it is greater that the original value

Well let's try and see what happens...

Let's start with any number. We'll do 100 to make it easy..

A 33.33% decrease would be

.3333 × 100 = 33.33 (this is the amount of decrease). Subtract from the original amount...

100 - 33.33 = 66.67

Now let's increase by 50%...

66.67 × .50 = 33.335 (this is the amount of increase so add it to 66.67...

66.67 + 33.335 = 100.005

Rounded to the nearest hundredth it would be 100.01

Technically there is a slight increase from the original value. This is because the decrease is a repeating decimal that was rounded to the nearest hundredth, while the increase was a whole number... but I don't know how technical you want to get :)