If x+sqrt(x^2-4x+4)=2, then:

Expert replies

Previous Topic Next Topic

fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

by fskilnik@GMATH » Wed Mar 27, 2019 11:57 am

Timer

00:00

Answers

Stats

Difficulty—

GMATH practice exercise (Quant Class 12)

Answer: [spoiler]______ (A)__[/spoiler]

Hint: [spoiler]The alternative choices are tricky... the official answer is NOT wrong... and you can find it in 3 SECONDS, using LOGIC only!
Obs.: someone could argue that GMAT asks you to find the BEST answer, therefore the 3-seconds approach may be considered "risky"... [/spoiler]

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

Like this post

Source: Beat The GMAT — Problem Solving | Wed Mar 27, 2019 11:57 am

fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

If x+sqrt(x^2-4x+4)=2, then:

by fskilnik@GMATH » Wed Mar 27, 2019 12:39 pm

fskilnik@GMATH wrote:GMATH practice exercise (Quant Class 12)

Answer: [spoiler]______ (A)__[/spoiler]

Important: Have you realized (looking at the alternative choices carefully) that the answer MUST BE (A)?
Reason: if (B), (C), (D), or (E) is true, then (A) is also true!

On the other hand, the GMAT asks you to find the BEST answer, therefore this approach could be considered "risky"... let me explain why:

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 choice (A) is also true.

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... now letÂ´s go to "the official solution":

$$?\,\,\,:\,\,\,\,x\,\,{\rm{must}}\,\,{\rm{be}}\,\,\, \ldots $$
$$x + \sqrt {{x^2} - 4x + 4} \,\,\, = \,\,\,2\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\sqrt {{{\left( {x - 2} \right)}^2}} = 2 - x$$
$$\,\,\,\, \Leftrightarrow \,\,\,\,\,\left| {x - 2} \right| = - \left( {x - 2} \right)\,\,\,\,\, \Leftrightarrow \,\,\,\,\,x - 2 \le 0\,\,\,\,\, \Leftrightarrow \,\,\,\,\,x \le 2$$
$$x \le 2\,\,\,\, \Rightarrow \,\,\,\left( A \right)\,\,{\rm{is}}\,\,{\rm{true}}\,\,\,\,\left[ {{\rm{and}}\,\,\left( B \right),\left( C \right),\left( D \right),\left( E \right)\,\,{\rm{are}}\,\,{\rm{false}}} \right]$$

The correct answer is (A).

We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

563 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (563 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review