# Thread: GMATPREP - Over the counter stocks...Need help!

1. Good post? |

## GMATPREP - Over the counter stocks...Need help!

All of the stock on the over the counter market are designated by either a 4 letter code or 5 letter code that is created by using the 26 letters of the alphabet. Which of the following gives 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)

SPOILER - Official Answer is C

I understand it is 25^4 + 25^5, but how does that become 27(26^4)??

Any help is much appreciated!

2. Good post? |
4 letter code = 26.26.26.26=26^4 possible (since the second letter can have repetition SINCE IT WILL FORM UNIQUE CODE )
5 letter code = 26.26.26.26.26=26^5

SO Max number of stocks - 26^4+26^5=26^4(1+26)=27(26^4)

3. Good post? |
Okay gotcha...
So when you factor 26^4 out of (26^4 + 26^5) you get 26^4(1 + 26) = 27(26^4). I missed that factoring step for some reason, thanks for the reply!

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