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A certain stock exchange designates each stock with a 1, 2

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A certain stock exchange designates each stock with a 1, 2 [#permalink] New post 26 Oct 2009, 12:25
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72% (02:17) correct 28% (01:27) wrong based on 79 sessions
A certain stock exchange designates each stock with a 1, 2 or 3 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 diff stocks is it possible to designate with these codes?

A: 2,951
B: 8,125
C: 15,600
D: 16,302
E: 18,278

[Reveal] Spoiler:
They say that QA is E, however I am not sure how to get there.

I have C 26 taken by 3 = 2,600
C of 26 taken by 2 = 325
C of 26 taken by 1 = 26.
If I add these, I get answer A. Not sure what I am doing wrong.

Thank you,
Andreea
[Reveal] Spoiler: OA
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Re: Combinations - Powerprep [#permalink] New post 26 Oct 2009, 12:40
I think that I should be using permutations as order does matter here, but I am still not getting the answer:
P of 26 taken by 3 = 15,600
P of 26 taken by 2 = 650
P of 26 taken by 1 = 26
adding them does not give me the right answer still.
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Re: Combinations - Powerprep [#permalink] New post 26 Oct 2009, 12:57
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Pretty simple actually
Number of 1 letter symbols = 26
Number of 2 letter symbols = 26*26
Number of 3 letter symbols = 26*26*26

The answer is sum of the 3. However if you are a real GMAT club member and confident about your approach you won't calculate any further.

The answer choices have their units digits unique. All 3 of the above end in 6 (6 to the power of anything ends in 6) so 6+6+6 = 18 i.e. ends with 8.

So the answer is E.
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Last edited by atish on 26 Oct 2009, 13:13, edited 1 time in total.
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Re: Combinations - Powerprep [#permalink] New post 26 Oct 2009, 13:08
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Expert's post
ralucaroman wrote:
HI,

Can smb please help me to understand the below problem?

A certain stock exchange designates each stock with a 1, 2 or 3 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 diff stocks is it possible to designate with these codes?
A: 2,951
B: 8,125
C:15,600
D: 16,302
E: 18,278

They say that QA is E, however I am not sure how to get there.

I have C 26 taken by 3 = 2,600
C of 26 taken by 2 = 325
C of 26 taken by 1 = 26.
If I add these, I get answer A. Not sure what I am doing wrong.

Thank you,
Andreea


1 letter code - 26 (or you can write 26C1)
2 letter code - 26*26=26^2 (or you can write 26C1*26C1=26^2)
3 letter code - 26*26*26=26^3 (or you can write 26C1*26C1*26C1=26^3)

(For 2 letter, for example, you have 26 choices per each letter, it's 26^2 and not 26C2 or 26P2.)

Total =26+26^2+26^3 =18,278
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Re: Combinations - Powerprep [#permalink] New post 26 Oct 2009, 13:20
Thank you, guys. I understand now. Appreciate your help.
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Re: A certain stock exchange designates each stock with a 1, 2 [#permalink] New post 02 Dec 2013, 00:01
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Re: Combinations - Powerprep [#permalink] New post 02 Dec 2013, 00:47
Expert's post
Bunuel wrote:
ralucaroman wrote:
HI,

Can smb please help me to understand the below problem?

A certain stock exchange designates each stock with a 1, 2 or 3 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 diff stocks is it possible to designate with these codes?
A: 2,951
B: 8,125
C:15,600
D: 16,302
E: 18,278

They say that QA is E, however I am not sure how to get there.

I have C 26 taken by 3 = 2,600
C of 26 taken by 2 = 325
C of 26 taken by 1 = 26.
If I add these, I get answer A. Not sure what I am doing wrong.

Thank you,
Andreea


1 letter code - 26 (or you can write 26C1)
2 letter code - 26*26=26^2 (or you can write 26C1*26C1=26^2)
3 letter code - 26*26*26=26^3 (or you can write 26C1*26C1*26C1=26^3)

(For 2 letter, for example, you have 26 choices per each letter, it's 26^2 and not 26C2 or 26P2.)

Total =26+26^2+26^3 =18,278


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Hope this helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Combinations - Powerprep   [#permalink] 02 Dec 2013, 00:47
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