Difference between revisions of "1969 AHSME Problems/Problem 4"
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== Solution == | == Solution == | ||
| − | <math>\ | + | Performing the operation based on the definition, <math>(3,3)\star(0,0) = (3,3)</math> and <math>(x,y)\star(3,2)=(x-3,y+2)</math>. Because the outputs are identical pairs, they must equal each other, so <math>3 = x-3</math>. Solving for x yields <math>x = 6</math>, which is answer choice <math>\boxed{\textbf{(E)}}</math>. |
== See also == | == See also == | ||
Latest revision as of 02:13, 7 June 2018
Problem
Let a binary operation 
on ordered pairs of integers be defined by 
. Then, if 
and 
represent identical pairs, 
equals:
Solution
Performing the operation based on the definition, 
and 
. Because the outputs are identical pairs, they must equal each other, so 
. Solving for x yields 
, which is answer choice 
.
See also
| 1969 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 3 |
Followed by Problem 5 | |
| 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 • 31 • 32 • 33 • 34 • 35 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
