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A certain stock exchange designates each stock with a one-,

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Intern
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A certain stock exchange designates each stock with a one-,  [#permalink]

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New post Updated on: 15 Sep 2013, 12:14
1
12
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

76% (00:29) correct 24% (01:06) wrong based on 222 sessions

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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. 2951
B. 8125
C. 15600
D. 16302
E. 18278

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-certain-stock-exchange-designates-each-stock-with-a-86656.html

Originally posted by konayuki on 21 Sep 2009, 18:02.
Last edited by Bunuel on 15 Sep 2013, 12:14, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: Ticker Designation: GMAT PREP  [#permalink]

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New post 23 Sep 2009, 03:34
permutations-s-79747.html

konayuki wrote:
A certain stock exchange designates with a one-two-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 letter, and in a different order constitute a different cosde, how may different stock is it possible to uniquely designate with this codes?

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Re: Ticker Designation: GMAT PREP  [#permalink]

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New post 15 Sep 2013, 12:08
1
1
With one letter, 26 stocks can be designated.
With two letters, 26*26 stocks can be designated.
With three letters, 26*26*26 stocks can be designated.
So, 26+262+263, the units digit is 8.
Answer is E
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Re: A certain stock exchange designates each stock with a one-,  [#permalink]

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New post 15 Sep 2013, 12:15
9
13
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. 2951
B. 8125
C. 15600
D. 16302
E. 18278

1 letter codes = 26
2 letter codes =2 6^2
3 letter codes = 26^3

Total=26+26^2+26^3

The problem we are faced now is how to get the answer quickly. Note that the units digit of 26+26^2+26^3 would be (6+6+6=18) 8. Only one answer choice has 8 as unit digit: E (18,278). So I believe, even not calculating 26+26^2+26^3, that answer is E.

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OPEN DISCUSSION OF THIS QUESTION IS HERE: a-certain-stock-exchange-designates-each-stock-with-a-86656.html
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Re: A certain stock exchange designates each stock with a one-,  [#permalink]

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New post 15 Jul 2018, 23:51
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