GMAT Prep Stocks

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moneyman: Master | Next Rank: 500 Posts; Posts: 468; Joined: Sat Mar 03, 2007 10:17 pm; Thanked: 5 times

by moneyman » Sun Oct 28, 2007 2:29 am

All of the stocks on the over the counter market are designated by either a 4 letter or a 5 letter code that is created by using the 26 letters of the alphabet.Which of the following gives the maximum number of different stocks that can be designated with these codes??

2(26^5)
26(26^4)
27(26^4)
26(26^5)

Maxx

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Source: Beat The GMAT — Problem Solving | Sun Oct 28, 2007 2:29 am

me4mba: Junior | Next Rank: 30 Posts; Posts: 26; Joined: Wed Apr 11, 2007 10:33 am; Thanked: 8 times

by me4mba » Sun Oct 28, 2007 12:36 pm

There are 26 alphabets to choose from.

1) 4-letter code: the number of possible combinations are 26*26*26*26 or 26^4

2) 5-letter code: the number of possible combinations are 26*26*26*26*26 or 26^5

The number of possible combinations, combining the 4-letter and 5-letter options, are 26^4 + 26^5

Factor out 26^4, and you'll get 26^4(1+26) which is 27*26^4.

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