Problem:
What is the value of
(1−321)(1−521)(1−721)(1+31)(1+51)(1+71)?
Answer Choices:
A. 3
B. 2
C. 15
D. 4
E. 105
Solution:
Let x be the displayed expression. Then
x2=(1−321)(1−521)(1−721)(1+31)2(1+51)2(1+71)2=(1+31)(1+31)⋅(1−31)(1+31)⋅(1+51)(1+51)⋅(1−51)(1+51)⋅(1+71)(1+71)⋅(1−71)(1+71)=(1−31)(1+31)⋅(1−51)(1+51)⋅(1−71)(1+71)=24⋅46⋅68=4.
Therefore x=(B)2.
The problems on this page are the property of the MAA's American Mathematics Competitions