All of the stocks on the over-the-counter market are

[jd3518]

This a question from Practice Test 1 of the MBA.com GMAT tests.

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?

A. 2(26^5)
B. 26(26^4)
C. 27(26^4)
D. 26(26^5)
E. 27(26^5)

Any help would be much appreciated.

Thank you.

[anadi]

4 letter possibilities 26^4, and 5 letter possibilities 26^5.

Add them,

26^4 + 26^5 = (26^4) * (1+26) = 27*(26^4), C is the answer.

[jd3518]

I appreciate the prompt reply. Very helpful.

Is it possible to elaborate a little more on the underlying math. Why is a 4 letter possibility 26^4. My instinct was leading me towards combinations and picking 4 letters from a group of 26 letters.

Thanks again.

[GMAT 2007]

It has not been mentioned that the 4 letter codes must have different letters. So, for every letter there are 26 choices to pick from.

Therefore for 4 letters possible ways = 26^4 similarly for 5 letters possible ways = 26^5.

Hope it helps

GMAT 2007

[StaceyKoprince]

Nice, GMAT2007

Also see givemeanid's response in this thread: http://www.manhattangmat.com/forums/gmac-practice-test-1-problem-24-t721.html?highlight=letters%20alphabet

It's worth doing a search when you have a question now - a lot of questions with responses are now floating around in past threads! :)