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Difference between revisions of "2023 AMC 10B Problems/Problem 18"
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== Solution ==
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== Solution (Guess and check + Contrapositive)==
 
<math>I.</math>  Try <math>a=3,b=5 => c = 17\cdot15</math> which makes <math>\textbf{I}</math> false.
 
<math>I.</math>  Try <math>a=3,b=5 => c = 17\cdot15</math> which makes <math>\textbf{I}</math> false.
 
At this point, we can rule out answer A,B,C.
 
At this point, we can rule out answer A,B,C.

Revision as of 15:24, 15 November 2023

Solution (Guess and check + Contrapositive)

$I.$ Try $a=3,b=5 => c = 17\cdot15$ which makes $\textbf{I}$ false. At this point, we can rule out answer A,B,C.

$II.$ A => B or C. equiv. ~B AND ~C => ~A. Let a = 14, b=15 (statisfying ~B and ~C). => C = 2*210. which is ~A.

$II$ is true.

So the answer is E. $\boxed{\textbf{(E) } II \text{ and } III \text{only}.}$ ~Technodoggo

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