GMAT Question

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ngbrian85: Newbie | Next Rank: 10 Posts; Posts: 6; Joined: Tue Feb 08, 2011 7:58 pm; Thanked: 1 times

by ngbrian85 » Mon Apr 02, 2012 5:16 pm

A researcher plans to identify each participant in a certain medical experiment with a code consisting of either a single litter or a pair of distinct letters written in alphabetical order. What is the least number of letters that can be used if there are 12 participants, and each participant is to receive a different code ?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

Please help guru's! I'm looking for a way to solve this in 1.5 minutes tops.

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Source: Beat The GMAT — Problem Solving | Mon Apr 02, 2012 5:16 pm

seal4913: Master | Next Rank: 500 Posts; Posts: 106; Joined: Wed Mar 23, 2011 4:56 pm; Thanked: 8 times

by seal4913 » Mon Apr 02, 2012 5:22 pm

I think it's B

a, b, c, d, e and then with those you can pair it ab ac ad ae bc bd de cd de. if you use 4 you can only make 10 pairs

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ngbrian85: Newbie | Next Rank: 10 Posts; Posts: 6; Joined: Tue Feb 08, 2011 7:58 pm; Thanked: 1 times

by ngbrian85 » Mon Apr 02, 2012 5:28 pm

Blah, that was an oversight on my behalf, I was using combo's. I don't have the solution just the question unfortunately.

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seal4913: Master | Next Rank: 500 Posts; Posts: 106; Joined: Wed Mar 23, 2011 4:56 pm; Thanked: 8 times

by seal4913 » Mon Apr 02, 2012 5:30 pm

Its okay, but I'm positive what I said is correct.

Using 4 letters you get a b c d and then the combos of ab ac ad bc bd cd

So you have to go up to 5 to cover at least 12

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Bill@VeritasPrep: GMAT Instructor; Posts: 1248; Joined: Thu Mar 29, 2012 2:57 pmFollowed by: 192 members; Location: Everywhere; Thanked: 503 times; GMAT Score:780

by Bill@VeritasPrep » Mon Apr 02, 2012 8:06 pm

Seal's got it.

With 4 letters, we have 4 single letter codes and 4C2=6 two-letter codes, for a total of 10. Since we have 12 participants, this isn't enough.

With 5 letters, we have 5 single letter codes and 5C2 =10 two-letter codes, for a total of 15. This means we have enough for our 12 participants.

The key wording that might be easy to overlook here is "in alphabetical order." If that weren't there (i.e. BA is a valid code), then 4 letters would be enough.

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seal4913: Master | Next Rank: 500 Posts; Posts: 106; Joined: Wed Mar 23, 2011 4:56 pm; Thanked: 8 times

by seal4913 » Mon Apr 02, 2012 8:10 pm

I didn't even think of using combinations. Bill great work and reading all your post you make the hardest problem easy. Thanks!

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Bill@VeritasPrep: GMAT Instructor; Posts: 1248; Joined: Thu Mar 29, 2012 2:57 pmFollowed by: 192 members; Location: Everywhere; Thanked: 503 times; GMAT Score:780

by Bill@VeritasPrep » Mon Apr 02, 2012 8:13 pm

Thanks! I'm glad I can help.

The fact that we're looking for codes, which are combinations of letters/numbers/etc, is a big indicator that combinatorics is probably the way to go.

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