Problem:
Suppose nβ means n1β, the reciprocal of n. For example, 5β=51β. How many of the following statements are true?
(i)3β+6β=9β(ii)6ββ4β=2β(iii)2ββ6β=12β(iv)10βΓ·2β=5β
Answer Choices:
A. 0
B. 1
C. 2
D. 3
E. 4
Solution:
Statements i and ii are false; iii and iv are true.
i.iii.β3β+6β=31β+61βξ =91β2ββ
6β=21ββ
61β=121β=12ββ
Answer: Cβ.
The problems on this page are the property of the MAA's American Mathematics Competitions