Problem:
The product of the 9 factors (1−21​)(1−31​)(1−41​)…(1−101​)=
Answer Choices:
A. 101​
B. 91​
C. 21​
D. 1110​
E. 211​
Solution:
The desired product equals 21​×32​×43​×…×98​×109​=101​ Notice that since 21​×32​=31​, the product is less than 31​ so (C),(D) and (E) are easily eliminated.
Answer: A​.
The problems on this page are the property of the MAA's American Mathematics Competitions