2024 AMC 8 Problems/Problem 8
Problem
On Monday Taye has $2. Every day, he either gains $3 or doubles the amount of money he had on the previous day. How many different dollar amounts could Taye have on Thursday, 3 days later?
Solution 1 (BRUTE FORCE)
How many values could be on the first day? Only dollars. On the second day, you can either add
dollars, or double so that you can have
dollars, or
. For each of these values, you have
values for each. For
dollars, you have
dollars or
, and for
dollars, you have
dollars or $
. Now, you have
values for each of these. For
dollars, you have
dollars or
, for
dollars, you have
dollars or
, for
dollars, you have
dollars or
, and for
dollars, you have
dollars or
.
There is a total of 2*2=8
11
16
8-2 = \boxed{\textbf{(C)} 6}$ different values.
~cxsmi (minor formatting edits)