bagdbmba wrote:
A company assigns product codes consisting of all the letters in the alphabet.How many product codes are possible if the company uses at most 3 letters in its codes, and all letters can be repeated in any one code?
A.15600
B.16226
C.17576
D.18278
E.28572
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 D has
8 as its units digit, the answer must be D
Cheers,
Brent
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