Prep Exam 1 - #24

[Guest]

Hello:

Can someone please walk me through this problem (ie. using the method in the Manhattan GMAT "Word Translations" Guide).

Thanks

[RonPurewal]

An interesting problem, which mixes the 'word translations' stuff with good old factoring.

As with many problems, note that you can't classify every problem neatly into one little box; this one is half factoring and half 'word translations,' with each half being the more difficult half for different students.

In any case:
As specified in the word translations book, you can use multiplication to determine how many codes are possible for each of the different situations.
4 letters: 26 x 26 x 26 x 26 = 26^4 codes
5 letters: 26 x 26 x 26 x 26 x 26 = 26^5 codes. However, here's the trick: We're going to write this as 26(26^4) instead of 26^5, so that it will add to the # of codes in the first part.
Thus:
Total # codes = 26^4 + 26(26^4) = 27(26^4) codes

Answer: C

[Guest]

Ron,

Thanks for the help.