Problem Solving

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

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.

Since it doesnt take much time listing out the possibiltiies would be a safe approach.

I think Dmateer has explained it quite well!

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.

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