GMAT Math

All of the stocks on the over-the counter market are designated by either a 4 -letter or 5-letter code that is created by using the 26 letters of tthe alphabet. Which of the following gives the maximum number of different stocks that can be designated with these codes?
A. 2 (26^5)
B. 26 (26^4)
C. 27 (26^4)
D. 26 (26^5)
E. 27 (26^5)

4-letter codes = 26*26*26*26 (assumes repeating letters are allowed) = 26^4
5-letter codes = 26*26*26*26*26 = 26^5

adding them 26^4 + 26^5 = 26^4 (1 + 26) = 27* 26^4 = C

Just to add: Make sure when you add in the final step you don't add the exponents. We can only add the exponents during multiplication. Tricky!

Also, this question was nice because it told us the number of options for each digit (26, since it was alphabetical). Sometimes for a numerical code, you will be required to know that each digit has 10 options (the numbers 0 through 9).

Good point, Vivian - even more complicated, IF they ask for a four digit number, the first digit only has nine options since 0123 counts as a three-digit, not a four digit number.