Every day, the value of a stock rises by exactly two dollars in the morning, and
then falls by exactly one dollar in the afternoon. If the stock's value at the start of the first
day is $100, on what day will the stock's value first reach $200?
Choose the correct option:
A) 50  B) 99  C) 100  D) 101  E) 200

Rationale: note that each day the stock is worth $ 1 more than on the previous day , and that on the first day it rises to $ 102 and then falls to $ 101 . therefore , on the nth day , the stock ' s value rises to n + 101 dollars in the morning and falls to n + 100 dollars in the afternoon . the solution is therefore the smallest n for which n + 101 = 200 , or n = 99 . in particular , the stock will be $ 200 in the middle of day 99 , although not at the end of this day . correct answer b
Answer: B