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# Here's a challenge. Can anyone sovle A certain stock

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Manager
Joined: 14 May 2006
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Here's a challenge. Can anyone sovle A certain stock [#permalink]  24 Dec 2006, 17:07
Here's a challenge. Can anyone sovle

A certain stock exchnage designates each stock with 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 constitue a different code, how many different stocks is it possible to unique designate with these codes

a) 2,951
b) 8,125
c) 15,600
d) 16,302
e) 18,278

Dan
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[#permalink]  24 Dec 2006, 17:34
Answer is E (discussed before)

26 + 26^2 + 26^3
Director
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[#permalink]  24 Dec 2006, 18:03
There are 26 one letter stocks
There are 26X26 two letter stocks
There are 26X26X26 three letter stocks

Total =26+26^2+26^3=18278
E !

Problem would have been more interesting with some constrains ...
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"Education is what remains when one has forgotten everything he learned in school."

Manager
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Thanks guys [#permalink]  24 Dec 2006, 18:06
Wow! this problem turns out to be easier than expected

Dan
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[#permalink]  25 Dec 2006, 04:57
E is indeed the right answer, and of course the formula that led to it is correct....
i'd like to add a minor comment on calculations... (i.e some may ask if GMAT really expect us to compute 26^3+26^2+26 in 1.5 minutes or so....)

in many gmat questions that seem to require lots of calculation there is usually a simple way to avoid it. it usually employs one of two methods:
a) rough estimation of result
b) calculating part of the answer, usually the digit unit, or the two last digits.

in this case, once you know the formula 26+26^2+26^3, you can find out that each of the three parts has last digit 6 (all exponents of 6 end with 6). because of that... adding three of them must end with 8 (6+6+6=18).
there is only one answer that ends with 8 and this is E. you don't have to actually calculate 26^3.

estimation in this case helps just a little:
26^3=26^2*26>650*25 = 16000, so you can safely eliminate a,b,c.
a closer estimation will also eliminate d.

my rule for real gmat questions is: never work too hard. there is always a simple way to solve questions.
Manager
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[#permalink]  25 Dec 2006, 05:14
Nice method, Hobbit.
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[#permalink] 25 Dec 2006, 05:14
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# Here's a challenge. Can anyone sovle A certain stock

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