BTGmoderatorDC wrote:How many factors does the number X have?

1) X is divisible by 47
2) X lies between 100 and 150, inclusive.

Source: e-GMAT

\[?\,\,:\,\,\,\,\# \,\,{\text{of}}\,\,{\text{factors}}\,\,{\text{of}}\,\,{\text{X}}\]
\[\left( 1 \right)\,\,\,\,\,\frac{X}{{47}} = \operatorname{int} \,\,\,\,\left\{ \begin{gathered}
\,{\text{Take}}\,\,X = 0\,\,\,\, \Rightarrow \,\,\,{\text{?}}\,\,{\text{ = }}\,\,{\text{infinite}}\,\,\,\,\,\,\left[ {\,{\text{every}}\,\,{\text{nonzero}}\,\,{\text{integer}}\,} \right]\, \hfill \\
\,{\text{Take}}\,\,X = 47\,\,\,\,\left( {{\text{prime}}} \right)\,\,\,\, \Rightarrow \,\,\,{\text{?}}\,\,{\text{ = }}\,\,4\,\,\,\,\,\,\,\,\left[ {\, - 47\,,\, - 1\,,\,\,1\,,\,\,47\,} \right] \hfill \\
\end{gathered} \right.\]
\[\left( 2 \right)\,\,\,100 \leqslant X \leqslant 150\,\,\,\,\,\left\{ \begin{gathered}
\,{\text{Take}}\,\,X = 101\,\,\,\left( {{\text{prime}}} \right)\,\,\,\, \Rightarrow \,\,\,{\text{?}}\,\,{\text{ = }}\,\,4\,\,\,\,\,\,\,\,\left[ {\, - 101\,,\, - 1\,,\,\,1\,\,,\,\,101\,} \right] \hfill \\
\,{\text{Take}}\,\,X = 100\,\,\,\, \Rightarrow \,\,\,?\,\, > \,\,4\, \hfill \\
\end{gathered} \right.\]
\[\left( {1 + 2} \right)\,\,\,\,X = 47 \cdot 3\,\,\,\,\,\, \Rightarrow \,\,\,\,\,?\,\,\,{\text{unique}}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,{\text{SUFF}}.\,\]

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

Regards,
Fabio.

P.S.: -47 is a factor of 47, because both are integers and 47/(-47) is an integer.
This is not only mathematically perfect, but also GMAT-definition-of-factor accepted.