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

_________________

Brent Hanneson – Founder of gmatprepnow.com