fskilnik wrote:
GMATH practice exercise (Quant Class 12)
Hi, Ian! Thanks for joining, for your kind words and for all your important comments related to the "theme"!
Let me add the following observation:
In each question, the GMAT asks the test taker to find the BEST answer (among the 5 alternative choices offered), therefore if you were given the following alternative choices:
(A) x < 3
(B) x
< 2
(C) ---
(D) ---
(E) ---
You would be supposed to consider (B) the "proper" right answer (it is more "restrictive"), although (as explained by Ian) alternative choice (A) is also true. (If x
< 2 then x<3, of course!)
The fact is that I did NOT offer two right answers (to have to deal with the "best" one to be chosen, something I personally dislike), therefore the official answer is (A) without any mess!
Okay... I hope this comment is a good complement to Ian´s discussion!
Now let´s go to "the official solution":
\(?\,\,\,:\,\,\,\,x\,\,{\rm{must}}\,\,{\rm{be}}\,\,\, \ldots\)
\(x + \sqrt {{x^2} - 4x + 4} \,\,\, = \,\,\,2\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\sqrt {{{\left( {x - 2} \right)}^2}} = 2 - x\)
\(\,\,\,\, \Leftrightarrow \,\,\,\,\,\left| {x - 2} \right| = - \left( {x - 2} \right)\,\,\,\,\, \Leftrightarrow \,\,\,\,\,x - 2 \le 0\,\,\,\,\, \Leftrightarrow \,\,\,\,\,x \le 2\)
\(x \le 2\,\,\,\, \Rightarrow \,\,\,\left( A \right)\,\,{\rm{is}}\,\,{\rm{true}}\,\,\,\,\left[ {{\rm{and}}\,\,\left( B \right),\left( C \right),\left( D \right),\left( E \right)\,\,{\rm{are}}\,\,{\rm{false}}} \right]\)
We follow the notations and rationale taught in the
GMATH method.
Regards,
Fabio.