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 alphabet. If the letters may be repeated and if the same letters used in a different order constitute a different code, how many different stocks is it possible to uniquely designate with these codes?
a) 2,951
b) 8,125
c) 15,600
d) 16,302
e) 18,278
Since letters can be reused, there are 26 options for each letter in the code:
Total possible 1-letter codes = 26
Total possible 2-letter codes = 26*26
Total possible 3-letter codes = 26*26*26
Now look at the answer choices.
We need to determine which answer choice represents the sum of the results above.
Each of the results above will have a units digit of 6.
6+6+6 = 18.
Thus, the correct answer must have a units digit of 8.
The correct answer is
E.
I suspect that the GMAT writers purposefully included only one answer choice with a units digit of 8.
The GMAT is not an arithmetic test. Always look at the answer choices to see whether the correct answer can be determined without performing unnecessary -- and time-wasting -- arithmetic.
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