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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
29% (01:50) correct
71%
(01:56)
wrong
based on 255
sessions
History
Date
Time
Result
Not Attempted Yet
GMATH practice exercise (Quant Class 12)
The alternative choices are tricky... the official answer is NOT wrong, and you can find it in 3 SECONDS, using LOGIC only!
27 Mar 2019, 13:30
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fskilnik
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.
General Discussion
27 Mar 2019, 12:56
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subhadeep13
Excellent! I have edited my "hint" to mention the possibility of finding the right answer in less than a few seconds. Congrats!
Now I suggest you answer the question in the "traditional way"...
P.S.: if we take into account that GMAT asks the candidate to find the BEST answer, someone could argue that it is very "risky" to adopt the 3-seconds approach... think about that!
