Sorry, just to clarify, the answer is E.

What's potentially confusing here is the wording of the question. I think it should read "1, 2, OR 3 letter codes".

Because letters can be repeated, looking at the three letter codes, we have: 26*26*26. For the two letter codes: 26*26. For the one letter code: 26. Then, sum them up.

You don't have to do all of that. Cube 26 is 17576. You know the answer must be greater than that.

Quickest way (no messy multiplying): Because 6*6 is 36, all powers of 6 have 6 as their last digit. So, for 26^3 the last digit is 6; same for 26^2; same for 26. When we sum these up, the sum of our units digits will be 6 + 6 + 6 = 18. Thus, the last digit of our final result has to be 8....choose E.

an ah-ha moment just hit

I understand what you are saying Testluv, but what if you make a mistake in your calculation to begin with, and are not on target for the estimation. Don't you find it useful to confirm values? I understand that Data Sufficiency is amenable to estimation, but problem solving seems more absolute. Feelings?

artistocrat wrote:I understand what you are saying Testluv, but what if you make a mistake in your calculation to begin with, and are not on target for the estimation. Don't you find it useful to confirm values? I understand that Data Sufficiency is amenable to estimation, but problem solving seems more absolute. Feelings?

In PS, we should use estimation in those questions that ask us to find "approximate" values.

However, in PS, we should always use reasoning. In general, in PS we should be open to alternative approaches such as using logic, using the answer choices + logic, picking numbers, etc. Here, I used knowledge of bases and powers and logic, and it certainly would save me time, thereby raising my score.