MathRevolution wrote:
[
Math Revolution GMAT math practice question]
(number properties) \(n\) is a \(3\) digit integer of the form \(ab6\). Is \(n\) divisible by \(4\)?
1) \(a+b\) is an even integer
2) \(ab\) is an odd integer.
\(n = \left\langle {ab6} \right\rangle \,\,\,\, \Rightarrow \left\{ \matrix{
\,n > 0\,\,\,\left( {{\rm{implicitly}}} \right) \hfill \cr
\,a \in \left\{ {1,2,3, \ldots ,9} \right\} \hfill \cr
\,b \in \left\{ {0,1,2,3, \ldots ,9} \right\} \hfill \cr} \right.\)
\({{\left\langle {ab6} \right\rangle } \over 4}\,\,\mathop = \limits^? \,\,{\mathop{\rm int}}\)
\(\left( 1 \right)\,\,\,a + b = {\rm{even}}\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {a,b} \right) = \left( {1,1} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr
\,{\rm{Take}}\,\,\left( {a,b} \right) = \left( {2,2} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr} \right.\)
\(\left( 2 \right)\,\,ab = {\rm{odd}}\,\,\, \Rightarrow \,\,\,b = {\rm{odd}}\,\,\, \Rightarrow \,\,\,\left\langle {b6} \right\rangle \in \left\{ {16,36,56,76,96} \right\}\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\,\)
The correct answer is therefore (B).
We follow the notations and rationale taught in the GMATH method.
Regards,
Fabio.
_________________
Fabio Skilnik ::
GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here:
https://gmath.net