VyDinh wrote:A certain stock exchange designates each stock with a one-, two- or three-letter code, where each letter is selected from the 26 letters of the alphabets. If the letter maybe repeated and if the same letters used in different order constitude a different code, how many different stock is it possible to uniquely designate with these codes?
A. 2,951
B. 8,125
C. 15,600
D. 16,302
E. 18,278
1-letter codes
26 letters, so there are 26 possible codes
2-letter codes
There are 26 options for the 1st letter, and 26 options for the 2nd letter.
So, the number of 2-letter codes = (26)(26) = 26^2
3-letter codes
There are 26 options for the 1st letter, 26 options for the 2nd letter, and 26 options for the 3rd letter.
So, the number of 3-letter codes = (26)(26)(26) = 26^3
So, the TOTAL number of codes = 26 + 26^2 + 26^3
IMPORTANT: Before we perform ANY calculations, we should first look at the answer choices, because we know that the GMAT test-makers are very reasonable, and they don't care if we're able make long, tedious calculations. Instead, the test-makers will create the question (or answer choices) so that there's an alternative approach.
The alternative approach here is to recognize that:
26 has
6 as its units digit
26^2 has
6 as its units digit
26^3 has
6 as its units digit
So, (26)+(26x26)+(26x26x26) = (2
6)+(___
6)+(____
6) = _____
8
Since only
E has
8 as its units digit, the answer must be
E
Cheers,
Brent
