2. You have a list of real numbers, whose sum is 40 . If you replace every number $x$ on the list by $1-x$, the sum of the new numbers will be 20 . If instead you had replaced every number $x$ by $1+x$, what would the sum then be?
Solution: 100
Let $n$ be the number of numbers on the list. If each initial number is replaced by its negative, the sum will then be -40 , and adding 1 to every number on this list increases the sum by $n$, so $n-40=20 \Rightarrow n=60$. Then, if we had simply added 1 to each of the initial numbers (without negating first), the sum would increase to $40+n=40+60=100$.