List of top General Aptitude Questions on mathematical reasoning

Consider an art gallery whose walkways are shown as lines in the diagram. A black dot represents a junction of two walkways. A guard may be placed at a junction to watch over the walkways that join at that junction. The minimum number of guards needed to watch all the walkways is ________.

Consider the following inequalities: \[ p^2 - 4q < 4, 3p + 2q < 6 \] where \(p\) and \(q\) are positive integers. The value of \((p+q)\) is \underline{\hspace{1cm}}.