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