Question : What is the value of $\left[\frac{1}{5}+\left\{\frac{1}{6}\right.\right.$ of $\left.\left.\left(\frac{42}{35} \div \frac{6}{25}\right)–\left(\frac{2}{7} \times \frac{6}{5} \div \frac{18}{42}\right)\right\}+\frac{19}{30}\right]$?
Option 1: $\frac{17}{15}$
Option 2: $\frac{13}{15}$
Option 3: $\frac{14}{15}$
Option 4: $\frac{11}{15}$
Correct Answer: $\frac{13}{15}$
Solution :
$\left[\frac{1}{5}+\left\{\frac{1}{6}\right.\right.$ of $\left.\left.\left(\frac{42}{35} \div \frac{6}{25}\right)–\left(\frac{2}{7} \times \frac{6}{5} \div \frac{18}{42}\right)\right\}+\frac{19}{30}\right]$
$=\left[\frac{1}{5}+\left\{\frac{1}{6}\right.\right.$ of $\left.\left.\left(\frac{42}{35} \times \frac{25}{6}\right)–\left(\frac{2}{7} \times \frac{6}{5} \times \frac{42}{18}\right)\right\}+\frac{19}{30}\right]$
$=[\frac{1}{5}+(\frac{1}{6}\times 5–\frac{4}{5})+\frac{19}{30}]$
$=[\frac{1}{5}+(\frac{5}{6}–\frac{4}{5})+\frac{19}{30}]$
$=[\frac{1}{5}+\frac{1}{30}+\frac{19}{30}]$
$=\frac{26}{30}$
$=\frac{13}{15}$
Hence, the correct answer is $\frac{13}{15}$.
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