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Senior | Next Rank: 100 Posts
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by vertigo05 » Mon Apr 13, 2009 11:43 pm
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(65^5)
B) 26(26^4)
C) 27(26^4)
D) 26(26^5)
E) 27(26^5)
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by bluementor » Tue Apr 14, 2009 12:11 am
No. of possibilities for a 4-letter code:

26 x 26 x 26 x 26 = 26^4

No. of possibilities for a 5-letter code:

26 x 26 x 26 x 26 x 26 = 26^5

Maximum no. of codes possible:

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

Choose C.

-BM-
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by vittalgmat » Tue Apr 14, 2009 12:17 am
I was about to explain when I saw BM's explanation.

Some small clarifications.
The question says either 4 letter code or a 5 letter code.
So we have to add the permutations for 4 letter code and 5 letter code.

The rest is BM's excellent explanation.
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by vertigo05 » Tue Apr 14, 2009 4:15 am
thanx.
OA is C.
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by brotherwo » Tue Apr 14, 2009 10:26 am
bluementor wrote:No. of possibilities for a 4-letter code:

26 x 26 x 26 x 26 = 26^4

No. of possibilities for a 5-letter code:

26 x 26 x 26 x 26 x 26 = 26^5

Maximum no. of codes possible:

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

Choose C.

-BM-
Just so I can wrap my head around this concept...
what if it was 26^4 + 26^7 ??
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by brotherwo » Tue Apr 14, 2009 10:31 am
bluementor wrote:No. of possibilities for a 4-letter code:

26 x 26 x 26 x 26 = 26^4

No. of possibilities for a 5-letter code:

26 x 26 x 26 x 26 x 26 = 26^5

Maximum no. of codes possible:

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

Choose C.

-BM-
Just so I can wrap my head around this concept...
what if it was 26^4 + 26^7 ??
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by VP_Jim » Tue Apr 14, 2009 11:14 am
Just factor out 26^4 --

(26^4 + 26^7) = 26^4 (1 + 26^3)

Don't forget to leave a 1 as a placeholder where the 26^4 was!

You can test your answer by multipling the 26^4 back into the parentheses.
brotherwo wrote:
bluementor wrote:No. of possibilities for a 4-letter code:

26 x 26 x 26 x 26 = 26^4

No. of possibilities for a 5-letter code:

26 x 26 x 26 x 26 x 26 = 26^5

Maximum no. of codes possible:

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

Choose C.

-BM-
Just so I can wrap my head around this concept...
what if it was 26^4 + 26^7 ??
Jim S. | GMAT Instructor | Veritas Prep
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