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

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Intern
Joined: 17 Aug 2009
Posts: 10
A certain stock exchange designates each stock with a one-,  [#permalink]

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Updated on: 15 Sep 2013, 12:14
1
12
00:00

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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Joined: 04 Jan 2008
Posts: 803
Re: Ticker Designation: GMAT PREP  [#permalink]

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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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Intern
Joined: 09 Jul 2012
Posts: 10
Re: Ticker Designation: GMAT PREP  [#permalink]

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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.
Math Expert
Joined: 02 Sep 2009
Posts: 49496
Re: A certain stock exchange designates each stock with a one-,  [#permalink]

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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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15 Jul 2018, 23:51
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: A certain stock exchange designates each stock with a one-, &nbs [#permalink] 15 Jul 2018, 23:51
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