GMAT PREP I ARRANGEMENTS / PERMUTATION

[pkw209]

Hi all,

Couldn't figure this one out. I got to 16,302 but couldn't figure out how to also account for those 3 letter codes that multiple letters. A brief explanation would be appreciated. FYI, I took this directly from Zuleron's list of 198 gmat prep questions. Thanks!

93) Each stack is designated with a 1, 2, and 3 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 constitutes a different code, how many different stocks is it possible to uniquely designate with these codes?

a. 2951
b. 8125
c. 15600
d. 16302
e. 18278

[pkw209]

Sorry, just to clarify, the answer is E.

[Testluv]

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.

[pkw209]

an ah-ha moment just hit

[artistocrat]

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?

[Testluv]

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.