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# All the stocks on the over-the-counter market are designated

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All the stocks on the over-the-counter market are designated [#permalink]

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20 Aug 2005, 08:28
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All the stocks on the over-the-counter market are designated by either a 4 letter or 5 letter codes 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 designated 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

Last edited by Bunuel on 31 Jul 2012, 03:31, edited 1 time in total.
Edited the question and added the OA.
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30 Sep 2008, 10:13
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C.

4 letter code can be designed in 26*26*26*26 ways that is 26^4 ways.
5 letter code can be designed in 26^5 ways.

Adding the two, it will be 26^4(1 + 26) = 26^4 * 27 ways.
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20 Aug 2005, 09:22
with 4 letters: 26^4
with 5 letters: 26^5

26^4 + 26^5 = 27*(26^4)

C
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20 Aug 2005, 10:01
qpoo wrote:
with 4 letters: 26^4
with 5 letters: 26^5

26^4 + 26^5 = 27*(26^4)

C

gpoo,

quick thot, why 26^4 and 26 ^5 and not 26P4 and 26P5?
Isn't this a permutation problem?
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20 Aug 2005, 20:27
the question did not say the letters have to be different.
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07 May 2006, 14:22
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 sotcks that can be designated with these codes?

a) 2(26^5)
b) 26(26^4)
c) 27(26^4)
d) 26(26^5)
e) 27(26^5)
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07 May 2006, 14:36
john2005 wrote:
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 sotcks that can be designated with these codes?

a) 2(26^5)
b) 26(26^4)
c) 27(26^4)
d) 26(26^5)
e) 27(26^5)

it is unclear whether repetition is allowed or not.

if allowed c) 27(26^4) = 26^4 + 26^5 = 26^4 (1+26)
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07 May 2006, 16:49
yes it should be 27(26^4)

26 ^4 + 26 ^ 5 = 26^4 *( 1 + 26) = 27(26^4)

yes the repetition is allowed . It's a GMATPREP question .
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19 Aug 2007, 10:13
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 designated with these codes?

a. 2(26^5)
b. 26(26^4)
c. 27(26^4)
d. 26(26^5)
e. 27(26^5)
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Re: Gmatprep PS - Stocks [#permalink]

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19 Aug 2007, 10:21
Piter wrote:
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 designated with these codes?

a. 2(26^5)
b. 26(26^4)
c. 27(26^4)
d. 26(26^5)
e. 27(26^5)

C.

Four letters have total of = 26*26*26*26 = 26^4
Five letters have total of = 26*26*26*26*26 = 26^5
Together, Total = 26^4 + 26^5 = 26^4 * (1+26) = 26^4 * 27
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30 Sep 2008, 09:34
all the stocks on the over-the-counter market are designed 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 designed with these codes?
a) 2(26^5)
b) 26(26^4)
c) 27(26^4)
d) 26(26^5)
e) 27(26^5)
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22 Oct 2008, 11:49
All stocks on over the counter medication is designtaed by either 4 or 5 letter code created by using 26 letters of the alphabet. Which of the following gives the maximum number of different stocks that can be designated using these codes.

A) 2(26 ^5)
B)26(26^4)
C)27(26^4)
D)26(26^5)
E)27(26^5)
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22 Oct 2008, 11:52
rishi2377 wrote:
All stocks on over the counter medication is designtaed by either 4 or 5 letter code created by using 26 letters of the alphabet. Which of the following gives the maximum number of different stocks that can be designated using these codes.

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

4 letter code OR 5 letter code (OR means ADD)

ie 26*26*26*26 + 26*26*26*26*26

====> 26*26*26*26(26+1)

(26^4)(27)

C ??
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22 Oct 2008, 12:30
Another C. repetition is allowed and hence 26 ^ 4 + 26 ^ 5
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22 Oct 2008, 12:35
amitdgr wrote:
rishi2377 wrote:
All stocks on over the counter medication is designtaed by either 4 or 5 letter code created by using 26 letters of the alphabet. Which of the following gives the maximum number of different stocks that can be designated using these codes.

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

4 letter code OR 5 letter code (OR means ADD)

ie 26*26*26*26 + 26*26*26*26*26

====> 26*26*26*26(26+1)

(26^4)(27)

C ??

Yup. OA is C. I got the wording wrong. i thought that some numbers were codified with 2-letter code and some by 5-letter code. Idiotic mistake.

Amit, how true the GMAT Perp scores can be? I mean in math section, I got 14 wrong ( time constrain), though in first 20 only 3 were incorrect and in verbal I got 8 incorrect ( 3 wrongs in first 20 ) yet I got 690. and my verbal score were low and math scores were high in that prep test.
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22 Oct 2008, 22:47
rishi2377 wrote:
amitdgr wrote:
rishi2377 wrote:
All stocks on over the counter medication is designtaed by either 4 or 5 letter code created by using 26 letters of the alphabet. Which of the following gives the maximum number of different stocks that can be designated using these codes.

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

4 letter code OR 5 letter code (OR means ADD)

ie 26*26*26*26 + 26*26*26*26*26

====> 26*26*26*26(26+1)

(26^4)(27)

C ??

Yup. OA is C. I got the wording wrong. i thought that some numbers were codified with 2-letter code and some by 5-letter code. Idiotic mistake.

Amit, how true the GMAT Perp scores can be? I mean in math section, I got 14 wrong ( time constrain), though in first 20 only 3 were incorrect and in verbal I got 8 incorrect ( 3 wrongs in first 20 ) yet I got 690. and my verbal score were low and math scores were high in that prep test.

GMATPrep scores are the closest. It uses the same algorithm as the real one ... I guess you got the tough ones wrong and had a string of wrongs .....
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22 Oct 2008, 23:01
Yup..initial questions were right. I was let with 12 min. for last 10 questions and I answered 8 of those 10 questions wrong. *blushes sweet me.
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10 Apr 2009, 10:53
Can you explain why the four and five letter code has 26^4 and 25^5 different permutations? I thought I would have to work out a very complicated permutations formula on this problem in order to figure it out...
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12 Apr 2009, 04:41
Manbehindthecurtain wrote:
Can you explain why the four and five letter code has 26^4 and 25^5 different permutations? I thought I would have to work out a very complicated permutations formula on this problem in order to figure it out...

Coming to 4 letter code, each letter can be any one of the 26 alphabets. So total number ways of choosing 4 letters will be 26 x 26 x 26 x 26 = 26^4

Similarly 5 letter code we will have = 26^5

Total = 26^5+26^4 = 26^4(26+1) = 27 (26^4)

In case if no two letters of the code are same, then the first letter of the 4 letter code can be chosen in 26 ways, the second letter of the code can be chosen in 25 ways, third letter in 24 ways and the 4 letter in 23 ways. Hence in this case the total number of 4 letter codes will be 26 x 25 x 24 x 23

Hope this is clear
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02 Sep 2009, 11:04
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GMATPrep Permutations   [#permalink] 02 Sep 2009, 11:04

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