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# Combinatorics, kaplan, 700 level, PS - unique 2 latter code

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Manager
Joined: 10 Jan 2011
Posts: 244
Location: India
GMAT Date: 07-16-2012
GPA: 3.4
WE: Consulting (Consulting)
Followers: 0

Kudos [?]: 57 [1] , given: 25

Combinatorics, kaplan, 700 level, PS - unique 2 latter code [#permalink]

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16 Oct 2011, 10:03
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Question Stats:

38% (01:24) correct 63% (00:29) wrong based on 17 sessions

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Each runner during a race is labeled with a unique one-letter code or a unique two-letter code, where the two letters are different. The codes use the 26-letter English alphabet, and if a given two letter code is used then the reverse code is not used. What is the maximum number of runners that can receive unique codes for the race?

A 325
B 351
C 677
D 650
E 676

guys please explain your answer I will provide OA after discussion
_________________

-------Analyze why option A in SC wrong-------

Last edited by 144144 on 17 Oct 2011, 00:39, edited 1 time in total.
Moved to the right place
Manager
Joined: 21 Aug 2010
Posts: 189
Location: United States
GMAT 1: 700 Q49 V35
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Kudos [?]: 98 [1] , given: 141

Re: Combinatorics, kaplan, 700 level, PS - unique 2 latter code [#permalink]

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19 Oct 2011, 10:53
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nishtil wrote:
Each runner during a race is labeled with a unique one-letter code or a unique two-letter code, where the two letters are different. The codes use the 26-letter English alphabet, and if a given two letter code is used then the reverse code is not used. What is the maximum number of runners that can receive unique codes for the race?

A 325
B 351
C 677
D 650
E 676

guys please explain your answer I will provide OA after discussion

1. 26 one letter code can be given(equal to number of alphabets)
2. Two letter codes

Number of possible 2 letter codes is equal to the sum of all the numbers between 25 and 1 (sum first 25 digits)

i.e, n(n+1)/2 = 325

Maximum number of runners that can receive unique codes = 325+26 =351
Ans B
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Re: Combinatorics, kaplan, 700 level, PS - unique 2 latter code   [#permalink] 19 Oct 2011, 10:53
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# Combinatorics, kaplan, 700 level, PS - unique 2 latter code

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