BTGmoderatorDC wrote:If x and y are integers, is the product xy odd?

(1) x = -5
(2) x and y are consecutive integers

Source: Magoosh

\[x,y\,\,{\text{ints}}\,\,\,\left( * \right)\]
\[{\text{xy}}\,\,\mathop = \limits^? \,\,{\text{odd}}\,\,\,\,\,\,\,\,\mathop \Leftrightarrow \limits^{\left( * \right)} \,\,\,\,\,\,\,?\,\,:\,\,\,x,y\,\,\,{\text{odd}}\]
\[\left( 1 \right)\,\,\,\left\{ \begin{gathered}
\,{\text{Take}}\,\,\left( {x,y} \right) = \left( { - 5,0} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\text{NO}}} \right\rangle \hfill \\
\,{\text{Take}}\,\,\left( {x,y} \right) = \left( { - 5,1} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \hfill \\
\end{gathered} \right.\]
\[\left( 2 \right)\,\,\,{\text{one}}\,\,{\text{odd}}{\text{,}}\,\,{\text{another}}\,\,{\text{even}}\,\, \Rightarrow \,\,\,\left\langle {{\text{NO}}} \right\rangle \]

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.