BTGmoderatorDC wrote: ↑Thu May 14, 2020 4:53 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
OA
B
Source: Official Guide
Say the least no. of letters used is n.
Thus, the total no. of single-letter codes = n; and
the total no. of single-letter codes = nC2 = n(n – 1)/1.2
Total no. of codes = n + n(n – 1)/2
Thus, n + n(n – 1)/2 ≥ 12
Instead of solving above for n, it's better that we plug-in values from options.
A. n = 4. At n = 4, we have n + n(n – 1)/2 = 10 < 12. Incorrect.
B. n = 5. At n = 5, we have n + n(n – 1)/2 = 15 ≥ 12. Correct.
The correct answer:
B
Hope this helps!
-Jay
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