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CEMC Fermat, 2022 Difficulty 1.2 Junior Find the answer Canada
The expression ( 1 + 2 + 3 ) ( 1 + 1 2 + 1 3 ) (1+2+3)(1+\frac{1}{2}+\frac{1}{3}) ( 1 + 2 + 3 ) ( 1 + 2 1 + 3 1 )
Pick one
A 3 3 3 B 11 11 11 C 6 6 6 D 11 6 \dfrac{11}{6} 6 11 E 12 12 12
Solution Evaluating, ( 1 + 2 + 3 ) ( 1 + 1 2 + 1 3 ) = 6 ( 1 + 1 2 + 1 3 ) = 6 + 6 2 + 6 3 = 6 + 3 + 2 = 11 (1+2+3)(1 + \frac{1}{2} + \frac{1}{3}) = 6(1 + \frac{1}{2} + \frac{1}{3}) = 6 + \frac{6}{2} + \frac{6}{3} = 6 + 3 + 2 = 11 ( 1 + 2 + 3 ) ( 1 + 2 1 + 3 1 ) = 6 ( 1 + 2 1 + 3 1 ) = 6 + 2 6 + 3 6 = 6 + 3 + 2 = 11
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