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:
We can regroup all the numbers as follows:
1⋅(2⋅33⋅2)(3⋅44⋅3)…(98⋅9999⋅98)⋅99100
From this representation, we can see that all the middle terms cancel, leaving only
21⋅99100=9950.
Thus, the correct answer is B.
Answer: B.
The problems on this page are the property of the MAA's American Mathematics Competitions