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by albema » Wed Dec 10, 2008 2:39 pm
A researcher plans to identify each participant in a certain medical experiment with a code consisting of either a single letter 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

B
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by dmateer25 » Wed Dec 10, 2008 2:50 pm
If we had 4 letters:

A
B
C
D
AB
AC
AD
BC
BD
CD

Only 10 distinct possibilities.

5 Letters
A
B
C
D
E
AB
AC
AD
AE
BC
BD
BE
CD
CE
DE

15 Distinct Possibilities.


Another approach would be:

4 single letters + 4C2
4 + 6 = 10

Not enough

5 single letters + 5C2
5 + 10 = 15

This would be enough.
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by cramya » Wed Dec 10, 2008 6:00 pm
Since it doesnt take much time listing out the possibiltiies would be a safe approach.

I think Dmateer has explained it quite well!
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by canuckclint » Wed Dec 10, 2008 6:18 pm
It is unclear if order matters.
ie AB and BA are different.

Given order does not matter and want to do it automatically take

(x c 2) + x for a quicker solution.
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by shafeek » Thu Dec 11, 2008 4:32 am
Hi all, this is my first post in this wonderful site that i discovered yesterday. With only 2 weeks left for my GMAT exam i am trying to cover as much as ground as possible in this site. Pray for me guys..

canuckclint order matters.. the question states that: a pair of distinct letters written in alphabetical order
so AB is correct but you cant consider BA
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