Bunuel wrote:

Is the integer b divisible by 3 ?

(1) 8b is divisible by 6.

(2) 9b is divisible by 12.

\(b\,\,\operatorname{int}\)

\(\frac{b}{3}\,\,\mathop = \limits^? \,\,\operatorname{int}\)

\(\left( 1 \right)\,\,\frac{{4b}}{3}\,\, = \,\,\,\operatorname{int} \,\,\,\,\mathop \Rightarrow \limits^{GCD\left( {3,4} \right)\,\, = \,\,1} \,\,\,\frac{b}{3} = \operatorname{int} \,\,\,\, \Rightarrow \,\,\,\left\langle {{\text{YES}}} \right\rangle\)

\(\left( 2 \right)\,\,\frac{{3b}}{4}\,\, = \,\,\,\operatorname{int} \,\,\,\,\left\{ \begin{gathered}

\,{\text{Take}}\,\,b = 0\,\,\,\, \Rightarrow \,\,\,\left\langle {{\text{YES}}} \right\rangle \hfill \\

\,{\text{Take}}\,\,b = 4\,\,\,\, \Rightarrow \,\,\,\left\langle {{\text{NO}}} \right\rangle \hfill \\

\end{gathered} \right.\)

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

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Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or GMATH.com.br (Portuguese version)

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