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