Difference between revisions of "1969 AHSME Problems/Problem 4"
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== Solution == | == Solution == | ||
− | 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>. | + | 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 | |
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All AHSME Problems and Solutions |
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