The longest side of a triangle is twice the shortest side and the third side is $2 \text{ cm}$ longer than the shortest side. If the perimeter of the triangle is more than $166 \text{ cm}$, then find the minimum length of the shortest side. (in $\text{ cm}$)

Find all pairs of consecutive even positive integers,both of which are larger than $5$,such that their sum is less than $23$.

Solve the following inequality: $\frac{|x-1|}{x+2} < 1$.

The $I.Q.$ of a person is given by the formula $I.Q. = \frac{MA}{CA} \times 100$,where $MA$ is mental age and $CA$ is chronological age. If $75 < I.Q. < 125$ for a group of $16$ year old children,find the range of their mental age.

There are $30$ questions in a multiple-choice test. $A$ student gets $1$ mark for each unattempted question,$0$ mark for each wrong answer,and $4$ marks for each correct answer. If a student answered $x$ questions correctly and scored $60$,then the number of possible values of $x$ is:

$A$ manufacturer has $600 \text{ litres}$ of a $12 \%$ solution of acid. How many litres of a $30 \%$ acid solution must be added to it so that the acid content in the resulting mixture will be more than $15 \%$ but less than $18 \%$?