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A researcher plans to identify each participant in a certain medical experiment with a code consisting of either a

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A researcher plans to identify each participant in a certain medical experiment with a code consisting of either a

by BTGmoderatorDC » Thu May 14, 2020 4:53 pm

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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

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Re: A researcher plans to identify each participant in a certain medical experiment with a code consisting of either a

by Jay@ManhattanReview » Thu May 14, 2020 10:19 pm
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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