GmatKiss wrote: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 desgnated with these codes?

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

Hi!

At first glance this may look like a permutations question, but it's actually an exponent question with a tiny bit of permutations thrown in.

Since there's no restriction on how many times we use each letter in each code, the number of possible 5 letter codes is simply 26^5 and the number of possible 4 letter codes is 26^4. Since we want the total number of possible codes, we sum those two numbers.

So, the question is really asking:

Which of the following is equivalent to 26^5 + 26^4?

There are simple rules for multiplying and dividing exponents, but no easy way to add or subtract them. The only time you can add or subtract exponents is when both the base and the power are the same - in that case, you simply add or subtract the coefficients.

For example: 3(x^4) + 7(x^4) = 10(x^4).

Accordingly, if we want to add or subtract exponents with the same base but different powers, we need to equalize the powers. We do so by factoring down to the smaller power.

Let's leave 26^4 alone and rewrite 26^5 as a multiple of 26^4:

26^5 = 26^1 * 26^4 = 26(26^4)

Now we can do our sum:

26^5 + 26^4 = 26(26^4) + 1(26^4) = 27(26^4)... choose C!