stock code

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dreamv: Senior | Next Rank: 100 Posts; Posts: 85; Joined: Thu Jan 12, 2012 7:18 pm; Thanked: 1 times

by dreamv » Sat Jan 14, 2012 10:28 pm

A certain stock exchange designates each stock with one-, two-, or three- letter code, where each letter is selected from 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 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

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Source: Beat The GMAT — Problem Solving | Sat Jan 14, 2012 10:28 pm

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Sat Jan 14, 2012 10:35 pm

dreamv wrote:A certain stock exchange designates each stock with one-, two-, or three- letter code, where each letter is selected from 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 different stocks is it possible to uniquely designate with these codes?

Number of possible one-letter codes = 26
Number of possible two-letter codes = 26*26
Number of possible three-letter codes = 26*26*26

Hence, total number of possible codes = 26 + 26*26 + 26*26*26

No need to calculate the above. Just notice that unit's digit of all the underlined term ends with 6. Hence, unit's digit of the correct answer will be unit's digit of (6 + 6 + 6) = unit's digit of 18 = 8.

Only option E has 8 as unit's digit.

Hence, the correct answer is E.

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ArunangsuSahu: Master | Next Rank: 500 Posts; Posts: 382; Joined: Thu Mar 31, 2011 5:47 pm; Thanked: 15 times

by ArunangsuSahu » Sat Jan 14, 2012 10:47 pm

The answer has to be greater than (26C1+26C2*2!+26C3*3!) as repetition is allowed

(E) is the choice

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ronnie1985: Legendary Member; Posts: 626; Joined: Fri Dec 23, 2011 2:50 amFollowed by: 10 members; Location: Ahmedabad; Thanked: 31 times

by ronnie1985 » Sun Jan 15, 2012 8:45 pm

18278 = 26+26^2+26^3

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