2021 JMPSC Sprint Problems/Problem 1

Problem

Compute $\left(\frac{1}{3}+\frac{1}{6}+\frac{1}{9}\right)(3+6+9)$ .

Solution

Solving the right side gives $3 + 6 + 9 = 18$ . Distributing into the left side gives $\frac{18}{3}+\frac{18}{6}+\frac{18}{9}$ , so the answer is $6 + 3 + 2 = \boxed{11}$ .

Solution 2

$\frac{1}{3}+\frac{1}{6}+\frac{1}{9}=\frac{6}{18}+\frac{3}{18}+\frac{2}{18}=\frac{11}{18}$ and $3+6+9=18$ , so the answer is $\frac{11}{18}\cdot18=\boxed{11}$ .

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2021 JMPSC Sprint Problems/Problem 1

Problem

Solution

Solution 2