A certain stock exchange designates each stock with a one-, : GMAT Problem Solving (PS)
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# A certain stock exchange designates each stock with a one-,

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

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30 May 2008, 05:19
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Question Stats:

69% (02:03) correct 31% (01:32) wrong based on 452 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
[Reveal] Spoiler: OA

Last edited by Bunuel on 20 Jul 2013, 09:43, edited 1 time in total.
Edited the question.
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30 May 2008, 07:12
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Remember that Numbers can be repeated.

Number of 1 Digit Codes = 26
Number of 2 Digit Codes = 26 * 26 = 676
Number of 2 Digit Codes = 26 * 26 * 26 = 17576

Total = 26 + 676 + 17576 = 18278

In future do not put OA with the question. As people might solve it back wards to reach the solution.
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30 May 2008, 07:13
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You have 3 different sets of Permutations available.

First set is of stocks that have only 1 letter, or 26 possibilities

Second set is of stocks with 2 letters, or 26 * 26 possibilities

Third set is of stocks with 3 letters, or 26 * 26 * 26 possibilities.

This equal 26 +676 + 17576 = 18,278.
japped187 wrote:
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

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30 May 2008, 07:42
abhijit_sen wrote:

In future do not put OA with the question. As people might solve it back wards to reach the solution.

I think the moderator/owner of the forum should add a "spoiler" function on the forum. That function is the perfect fit for this type of forum, but this forum does not have it.
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Re: A certain stock exchange designates each stock with a one-, [#permalink]

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20 Jul 2013, 09:12
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japped187 wrote:
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

As discussed above, the solution is indeed 26 + 26*26 + 26*26*26. I noticed that all the digits were different in the options.
So I simply calculated the unit digit of each product. 6 +6 + 6. = 18 = Unit digit of answer = 8. Hence, E.
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Re: A certain stock exchange designates each stock with a one-, [#permalink]

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20 Jul 2013, 09:45
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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

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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02 Aug 2014, 23:39
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Re: A certain stock exchange designates each stock with a one-, [#permalink]

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11 Aug 2015, 23:27
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-,   [#permalink] 11 Aug 2015, 23:27
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