BTGmoderatorDC wrote:Is x an integer?

(1) x/2 is an integer
(2) 2x is an integer

Statement 1:
x/2 = 1, 2, 3, 4, 5...
Multiplying every value by 2, we get:
x = 2, 4, 6, 8, 10...
In every case, x is an integer.
SUFFICIENT.

Statement 2:
2x = 1, 2, 3, 4, 5...
Dividing every value by 2, we get:
x = 1/2, 1, 3/2, 2, 5/2...
If x=1/2, then x is not an integer.
If x=1, then x is an integer.
INSUFFICIENT.

The correct answer is A.

BTGmoderatorDC wrote:Is x an integer?

(1) x/2 is an integer
(2) 2x is an integer

\[x\,\,\mathop = \limits^? \,\,\operatorname{int} \]
\[\left( 1 \right)\,\,\frac{x}{2} = \operatorname{int} \,\,\,\,\mathop \Rightarrow \limits^{f{\text{ocus}}\,:\,\,\left( { \cdot \,\,2} \right)} \,\,\,\,\,\,2\left( {\frac{x}{2}} \right) = 2\operatorname{int} = \operatorname{int} \,\,\,\,\,\,\, \Rightarrow \,\,\,\,x = \operatorname{int} \,\,\,\,\,\, \Rightarrow \,\,\left\langle {{\text{YES}}} \right\rangle \]
\[\left( 2 \right)\,\,2x = \operatorname{int} \,\,\,\left\{ \begin{gathered}
\,{\text{Take}}\,\,x = 0\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \,\,\, \hfill \\
\,{\text{Take}}\,\,x = \frac{1}{2}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\text{NO}}} \right\rangle \,\,\, \hfill \\
\end{gathered} \right.\,\,\,\,\]

The above follows the notations and rationale taught in the GMATH method.