For an integer n greater than 1, the set Sn={ kn | k is an integer gre

\(n \geqslant 2\,\,\,\operatorname{int}\)

\({S_n} = \left\{ {\,k \cdot n\,\left. {} \right|\,\,\,k \geqslant 1\,\,\operatorname{int} } \right\}\)

\(? = n\)


Let´s understand what each S_n means:

\({S_2} = \left\{ {\,2k\,\,\left. {} \right|\,\,\,k \geqslant 1\,\,\operatorname{int} } \right\} = \left\{ {2,4,6,8, \ldots } \right\}\,\,{\text{ = }}\,\,{\text{positive}}\,\,{\text{even}}\,\,{\text{integers}}\)

\({S_3} = \left\{ {\,3k\,\,\left. {} \right|\,\,\,k \geqslant 1\,\operatorname{int} } \right\} = \left\{ {3,6,9,12, \ldots } \right\}\,\,{\text{ = }}\,\,{\text{positive}}\,\,{\text{multiples}}\,\,{\text{of}}\,\,3\)

\({S_4} = \left\{ {\,4k\,\left. {} \right|\,\,\,k \geqslant 1\,\operatorname{int} } \right\} = \left\{ {4,8,12,16, \ldots } \right\}\,\,{\text{ = }}\,\,{\text{positive}}\,\,{\text{multiples}}\,\,{\text{of}}\,\,4\)

and so on...


\(\left( 1 \right)\,\,\,2 \in {S_n}\,\,\, \Rightarrow \,\,\,\,n = 2\,\, \Rightarrow \,\,\,\,{\text{SUFF}}.\)

\(\left( 2 \right)\,\,\,4 \in {S_n}\,\,\, \Rightarrow \,\,\,\,n = 2\,\,\,{\text{or}}\,\,\,n = 4\,\,\,\, \Rightarrow \,\,\,\,{\text{INSUFF}}.\)


The right answer is therefore (A).



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

Regards,
Fabio.