Quote:
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
My approach is similar to that of Bhoopendra, with a TWIST at the end.
1-letter codes26 letters, so there are 26 possible codes
2-letter codesThere are 26 options for the 1st letter, and 26 options for the 2nd letter.
So, the number of 2-letter codes = (26)(26) = 26²
3-letter codesThere 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) = 26³
So, the TOTAL number of codes = 26 + 26² + 26³
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 whether 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
26² has
6 as its units digit
26³ has
6 as its units digit
So, (26)+(26²)+(26³) = (2
6)+(___
6)+(____
6) = _____
8 Since only E has
8 as its units digit, the answer must be E
Cheers,
Brent
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