How to solve this very quickly? 
A number leaves a remainder $2$ when
  divided by $9$.Which of the following
  could not be the remainder when it is
  divided by $45$?



*

*$20$

*$30$

*$29$

*$38$


How could we solve this under a minute? Please explain your approach.

It's easy: $\rm \ 45\ k + n\ =\ 9\ m + 2\ \Rightarrow\ 9\:$ divides $\rm\: n-2\:,\: $ which fails only for the 2nd choice $\rm\:n = 30\:. $
