AAPL wrote:e-GMAT
Is the perimeter of triangle ABC greater than 12 cm?
1) One side of triangle ABC measures 6 cm.
2) The lengths of the three sides of triangle ABC are consecutive positive even integers.
All lengths are measured in centimeters.
$$a + b + c\,\,\mathop > \limits^? \,\,12$$
$$\left( 1 \right)\,\,{\rm{WLOG}}\,\left( * \right)\,\,\,a = 6\,\,\,\,\,\mathop \Rightarrow \limits^{\Delta \,\,{\rm{exists!}}} \,\,\,\,6 = a < b + c\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\,\,$$
(*) WLOG = without loss of generality
$$\eqalign{
& \left( 2 \right)\,\,a + b + c = 2M + 2M + 2 + 2M + 4 = 6M + 6\,\,,\,\,\,M \ge 2\,\,{\mathop{\rm int}} \,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \cr
& \left( {M = 1\,\,\, \Rightarrow \,\,\,\,2,4,6\,\,{\rm{is}}\,\,{\rm{not}}\,\,{\rm{a}}\,\,{\rm{triangle!}}} \right) \cr} $$
(We have NOT said that a, b and c are respectively equal to 2M, 2M+2 and 2M+4 ... be careful!)
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
