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Alphabet codes - gmatprep

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arocks: Master | Next Rank: 500 Posts; Posts: 127; Joined: Tue Oct 02, 2007 9:35 am; Thanked: 1 times

by arocks » Thu Oct 18, 2007 3:33 am

A certain stock exchange designates each stock with a one, two or three letter code, where each letter is selected from the 26 alphabets. If the letters may be replaced 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. 2,951
B. 8,125
C. 15,600
D. 16,302
E. 18,278

Pls explain. Thanks.

OA- E

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Source: Beat The GMAT — Problem Solving | Thu Oct 18, 2007 3:33 am

gmatrant: Master | Next Rank: 500 Posts; Posts: 416; Joined: Wed Oct 03, 2007 9:08 amFollowed by: 1 member; Thanked: 10 times

Re: Alphabet codes - gmatprep

by gmatrant » Thu Oct 18, 2007 5:26 am

arocks wrote:A certain stock exchange designates each stock with a one, two or three letter code, where each letter is selected from the 26 alphabets. If the letters may be replaced 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. 2,951
B. 8,125
C. 15,600
D. 16,302
E. 18,278

Pls explain. Thanks.

OA- E

There are 3 possible codes
One letter Code - This can be created in 26 ways as there are 26 alphabets

Two letter Code- This can be created in 26 * 26 ways i.e 676 ways because there are two letters to be used and each letter can be chosen in 26 ways

Three letter Code - Same as above 26 * 26 *26 = 17576
Total =18278

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dingo001: Junior | Next Rank: 30 Posts; Posts: 24; Joined: Tue Sep 18, 2007 6:27 pm

by dingo001 » Thu Oct 18, 2007 7:27 am

Thanks - nice explanation

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arocks: Master | Next Rank: 500 Posts; Posts: 127; Joined: Tue Oct 02, 2007 9:35 am; Thanked: 1 times

by arocks » Thu Oct 18, 2007 7:28 am

Thanks...i guess i didn't apply the basics and made it seem more complicated.

So it is 26+26^2+26^3. On that a minor suggestion...I know you would have thought of it...still...

last digit would be 6+6+6=18
The only choice with 8 at the end is E. So without calculations we can say it is E.

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rackbar: Junior | Next Rank: 30 Posts; Posts: 22; Joined: Sun Aug 17, 2008 9:33 pm; GMAT Score:770

by rackbar » Sat Nov 29, 2008 9:58 am

What about symbols such as AAA, BBB and COC, which can be arranged and still have the same ticker, do you have to subtract those?

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