2023 AMC 10B Problems/Problem 18: Difference between revisions

Latest revision as of 19:45, 15 November 2023

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-== Solution (Guess and check + Contrapositive)==
+#redirect[[2023 AMC 12B Problems/Problem 15]]
-<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.
-<math>II.</math> A => B or C. equiv. ~B AND ~C => ~A.
-Let a = 14, b=15 (statisfying ~B and ~C). => C = 2*210. which is ~A.
-<math>II</math> is true.
-So the answer is E.
-<math>\boxed{\textbf{(E) } II \text{ and } III \text{only}.}</math>
-~Technodoggo