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# All of the stocks on the over the counter market are

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Manager
Joined: 30 Apr 2009
Posts: 134
All of the stocks on the over the counter market are [#permalink]

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30 Aug 2009, 13:36
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Difficulty:

55% (hard)

Question Stats:

71% (01:58) correct 29% (01:30) wrong based on 89 sessions

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All of the stocks on the over the counter market are designated by either a 4 letter or a 5 letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different stocks that can be desgnated with these codes?

A. 2 (26)^5
B. 26(26)^4
C. 27(26)^4
D. 26(26)^5
E. 27(26)^5

OPEN DISCUSSION OF THIS QUESTION IS HERE: all-of-the-stocks-on-the-over-the-counter-market-are-126630.html
[Reveal] Spoiler: OA

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Last edited by Bunuel on 07 Jun 2012, 12:44, edited 4 times in total.
Edited the question and added the OA. Topic is locked.
Manager
Joined: 10 Aug 2009
Posts: 130
Re: GMAT Prep 2 - Prob [#permalink]

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30 Aug 2009, 16:14
I am getting the number of possibilities $$27\times 26^4$$

$$26^4+26^5=26^4\times (1+26)=27\times 26^4$$

Manager
Joined: 18 Jul 2009
Posts: 169
Location: India
Schools: South Asian B-schools
Re: GMAT Prep 2 - Prob [#permalink]

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31 Aug 2009, 00:20
I agree with above explination 27(26^4)
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Manager
Joined: 30 Apr 2009
Posts: 134
Re: GMAT Prep 2 - Prob [#permalink]

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31 Aug 2009, 06:24
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Senior Manager
Joined: 27 May 2012
Posts: 291
Re: GMAT Prep 2 - Prob [#permalink]

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07 Jun 2012, 04:23
LenaA wrote:
I am getting the number of possibilities $$27\times 26^4$$

$$26^4+26^5=26^4\times (1+26)=27\times 26^4$$

can some please explain this , why 26^4 and 26 ^5 ?

explanation should be provided while solving , so that others can understand the solution, simply solving for oneself
does no good to others
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- Stne

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7452
Location: Pune, India
Re: GMAT Prep 2 - Prob [#permalink]

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07 Jun 2012, 04:56
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KUDOS
Expert's post
kt00381n wrote:

There are two slightly different ways of doing this question:

No of different four letter codes:
26*26*26*26 = 26^4

No of different five letter codes:
26*26*26*26*26 = 26^5

Total number of codes = 26^4 + 26^5 = 27*26^4

or

Total no of different four or five letter codes:
26*26*26*26*27 = 27*26^4
(you multiply by 27 because for the last letter, you have 27 different possibilities - the 26 letters and null i.e. no letter which takes care of including all the 4 letter codes)
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Senior Manager
Joined: 27 May 2012
Posts: 291
Re: GMAT Prep 2 - Prob [#permalink]

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07 Jun 2012, 12:38
VeritasPrepKarishma wrote:
kt00381n wrote:

There are two slightly different ways of doing this question:

No of different four letter codes:
26*26*26*26 = 26^4

No of different five letter codes:
26*26*26*26*26 = 26^5

Total number of codes = 26^4 + 26^5 = 27*26^4

or

Total no of different four or five letter codes:
26*26*26*26*27 = 27*26^4
(you multiply by 27 because for the last letter, you have 27 different possibilities - the 26 letters and null i.e. no letter which takes care of including all the 4 letter codes)

Thank you karishma

I guess some assumptions in the question are that letters can be repeated

so we can have a code like AAAA and BBBBB or AAAA and AAAAA

looking forward to more assistance from you , thank you
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- Stne

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Joined: 02 Sep 2009
Posts: 39756
Re: All of the stocks on the over the counter market are [#permalink]

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07 Jun 2012, 12:43
All of the stocks on the over the counter market are designated by either a 4 letter or a 5 letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different stocks that can be desgnated with these codes?
A. 2 (26)^5
B. 26(26)^4
C. 27(26)^4
D. 26(26)^5
E. 27(26)^5

In 4-digit code {XXXX} each digit can take 26 values (as there are 26 letters), so total # of 4-digits code possible is 26^4;

The same for 5-digit code {XXXXX} again each digit can take 26 values (26 letters), so total # of 5-digits code possible is 26^5;

Total: $$26^4+26^5=26^4(1+26)=27*26^4$$.

OPEN DISCUSSION OF THIS QUESTION IS HERE: all-of-the-stocks-on-the-over-the-counter-market-are-126630.html

In case of any questions please post there.
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Re: All of the stocks on the over the counter market are   [#permalink] 07 Jun 2012, 12:43
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