GMAT Question

[ngbrian85]

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.

[seal4913]

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

[ngbrian85]

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

[seal4913]

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

[Bill@VeritasPrep]

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.

[seal4913]

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

[Bill@VeritasPrep]

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.