jack0997 wrote:A botanist plans to code each experimental plant used in an experiment with a code that consists of either a single letter or a pair of distinct letters written in an alphabetic order. What is the least number of letters that can be used if there are 15 plants, and each plant is to get a different code?
(A) 3 (B) 4 (C) 5 (D) 7 (E) 14
We can PLUG IN THE ANSWERS, which represent the least number of letters required to make 15 codes.
Start with the smallest answer choice.
A: 3
The following codes are possible for letters A, B and C:
A, B, C, AB, AC, BC.
6 codes.
Since the number of codes is too small, eliminate A.
B: 4
The following codes are possible for letters A, B, C and D:
A, B, C, D, AB, AC, AD, BC, BD, CD.
10 codes.
Since the number of codes is too small, eliminate B.
C: 5
The following codes are possible for letters A, B, C, D and E:
A, B, C, D, E, AB, AC, AD, AE, BC, BD, BE, CD, CE, DE.
15 codes.
Success!
The correct answer is
C.
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Corrected my post.
