My current age is two more than thrice the age of one of my

vishwash wrote:My current age is two more than thrice the age of one of my two sisters named Richa. After N years, I will be two more than thrice the age of my other sister named Mamita. What is the minimum possible integral difference (in years) between the age of my two mentioned sisters? (N is a natural number)

(A) 10
(B) 6
(C) 4
(D) 2
(E) 5

source: cl gmat homework book 800 level questions

$$? = \left| {M - R} \right|\,\,{\mathop{\rm int}} \,\,{\rm{minimum}}$$
$$\left\{ \matrix{
A = 3R + 2 \hfill \cr
A + N = 3\left( {M + N} \right) + 2 \hfill \cr} \right.\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( - \right)} \,\,\,\,\,\, - N = 3\left( {R - M} \right) - 3N\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,2N = 3\left( {R - M} \right)$$
$$2N = 3\left( {R - M} \right)\,\,\,\, \Rightarrow \,\,\,\,\left\{ \matrix{
\,N\,\,{\rm{multiple}}\,\,{\rm{of}}\,\,3\,\,\,\,\left[ {\,\left( {R - M} \right)\,\,{\mathop{\rm int}} \,} \right]\,\,\,\,\,\,\mathop \Rightarrow \limits^{N\,\, \ge \,1} \,\,\,\,\,\,N \ge 3 \hfill \cr
\,R - M\,\,{\rm{even}}\,\,\,\, \Rightarrow \,\,\,? = 2\,\,\,\,\,\left( {{\rm{for}}\,\,N = 3} \right) \hfill \cr} \right.\,\,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\,\left( {\rm{D}} \right)$$


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

Regards,
Fabio.