Problem:
(2×3×4)(21+31+41)=
Answer Choices:
A. 1
B. 3
C. 9
D. 24
E. 26
Solution:
Using the distributive law, the product equals
(2×3×4)×(21)+(2×3×4)×(31)+(2×3×4)×(41)=(3×4)+(2×4)+(2×3)=12+8+6=26.
Although it is more tedious, one can perform the operations within each set of parentheses to obtain:
24(126+124+123)=24(1213)=26.
Answer: E.
The problems on this page are the property of the MAA's American Mathematics Competitions