jmc

Question

On the first day, Barry Sotter used his magic wand to make an object's length increase by 12, meaning that if the length of the object was originally x, then it is now x + 12 x. On the second day he increased the object's longer length by 13; on the third day he increased the object's new length by 14; and so on. On the n^th day of performing this trick, Barry will make the object's length exactly 100 times its original length. What is the value of n?

Accepted Answer

On day n, Barry increases the length of the object by a factor of n+2n+1. Thus, the overall increase through day n is by a factor of ( 32 ) ( 43) ( n+1n) ( n+2n+1). Canceling, we see that this expression equals n+22. Thus we have n+22=100, and so n=198.