Problem:
What is the value of the product below?
(2⋅21⋅3)(3⋅32⋅4)(4⋅43⋅5)⋯(98⋅9897⋅99)(99⋅9998⋅100)
Answer Choices:
A. 21
B. 9950
C. 98019800
D. 99100
E. 50
Solution:
The product may be rewritten as
(21)(2⋅33⋅2)(3⋅44⋅3)(4⋅55⋅4)...(98⋅9999⋅98)(99100)=21⋅99100=9950.
Answer: B.
The problems on this page are the property of the MAA's American Mathematics Competitions