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