Problem Solving

Max@Math Revolution wrote:[Math Revolution GMAT math practice question]
If x and y are integers, what is the least possible positive value of 21x+35y?
A. 1
B. 3
C. 5
D. 7
E. 9

Nice problem, in which STRUCTURE does the most part of it, as we see below!
\[x,y\,\,{\text{ints}}\,\,\left( * \right)\]
\[{\text{?}}\,\,{\text{ = }}\,\,{\left( {21x + 35y} \right)_{\,\min \, > \,0}} = \,\,\,{\left[ {7\left( {3x + 5y} \right)} \right]_{\,\min \, > \,0}}\,\,\,\mathop = \limits^{\left( * \right)} \,\,\,{\left[ {7\left( {3x + 5y} \right)} \right]_{\,\min \, \geqslant \,1}}\]
\[{?_{{\text{temporary}}}}\,\, = \,\,{\left[ {3x + 5y\,\,\mathop = \limits^{\left( * \right)} \,\,\operatorname{int} } \right]_{\,\min \, \geqslant \,1}} \geqslant 1\]
\[{\text{Take}}\,\,\left( {x,y} \right) = \left( { - 3,2} \right)\,\,\, \Rightarrow 3x + 5y = 1 = {\left[ {3x + 5y} \right]_{\,\min \, \geqslant \,1}}\]
\[? = 7\]

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

Regards,
fskilnik.