1982 AHSME Problems/Problem 7
Problem
If the operation is defined by , then which one of the following is FALSE?
Solution
(A) is true because multiplication is commutative.
(B) is false because we have and which does not match with the previous expression.
(C) is true because for all .
(D) is true because for all .
(E) is true because multiplication is associative (and the plus-ones inside the parentheses and the minus-ones outside cancel out).
Therefore, our answer is , and we are done.
See also
1982 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 6 |
Followed by Problem 8 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
All AHSME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.