GMAT Focus Edition Section Quantitative

Which of the following options always equates to sqrt(xexp2 – 4x +4)?

A. x – 2

B. 2 + x

C.| 2 – x |

D. |2 + x|

E. 2 -x

ANSWER C.

Unraveling the Mysteries of GMAT Quant: Your Path to Success

Dear GMAT Focus Edition Aspirant,

Welcome to the realm of GMAT Quant, where numbers dance, patterns emerge, and solutions await those who dare to embark on this thrilling journey. I’m Claudio Hurtado, your guide through the intricacies of the GMAT Quantitative Reasoning section and the Data Insight Section. Within these domains lie the keys to unlocking your potential and achieving mastery over the quantifiable aspects of the GMAT Focus Edition.

Picture this: you’re seated at your desk, pencil poised, mind buzzing with anticipation. The clock is ticking, and each moment brings you closer to your goal. But fear not, for I am here to equip you with the knowledge, strategies, and confidence you need to conquer the challenges that lie ahead.

Let’s delve into the question posed: “Which of the following options always equates to sqrt(x^2 – 4x +4)?” This question, like many others you’ll encounter on your GMAT journey, may seem daunting at first glance. But fear not, for I’m about to unravel its mysteries and empower you with the tools to tackle it head-on.

Firstly, let’s break down the expression sqrt(x^2 – 4x +4). Notice that it resembles a quadratic equation in the form of (x – a)^2, where ‘a’ represents the constant term. In this case, ‘a’ is 2, as evidenced by the equation (x – 2)^2. Now, recall that the square root of a squared term yields the absolute value of the expression within the square root. Hence, the expression simplifies to |x – 2|.

Now, armed with this insight, let’s examine the options provided:

A. x – 2
B. 2 + x
C. |2 – x|
D. |2 + x|
E. 2 – x

To determine which option always equates to |x – 2|, we must consider the scenarios in which each option holds true.

Let’s start with option A, x – 2. While this expression appears similar to |x – 2|, it fails to account for negative values of (x – 2), thus rendering it inadequate.

Moving on to option B, 2 + x. We cannot take this expression to the form, |2-x|, therefore we must discard option B.

Now, let’s scrutinize option C, |2 – x|. While this expression seems reminiscent of |x – 2|, it crucially differs in its arrangement of terms. Option C represents the absolute value of (2 – x), not (x – 2). But we must keep in mind that |x-2| is the same as |2-x|.

Next, we turn our attention to option D, |2 + x|. This expression deviates from our target expression, |x – 2|, by incorporating different terms within the absolute value brackets. Consequently, option D does not satisfy the given criteria and can be eliminated.

Finally, let’s assess option E, 2 – x. Upon squaring this expression, we do not obtain |x – 2| but rather |-(x – 2)|. Hence, option E does not consistently equate to the desired expression and is thus invalidated.

In conclusion, after careful evaluation, we deduce that option C, |2 – x|, always equates to sqrt(x^2 – 4x +4) or |x – 2|.

ANSWER C.

By understanding the underlying principles and strategically analysing the given options, you can navigate even the most perplexing GMAT Quant questions with confidence and precision.

Remember, the GMAT Focus Edition is not merely a test of mathematical aptitude; it’s a testament to your perseverance, adaptability, and problem-solving prowess. With the right guidance and preparation, you can rise above any challenge and emerge victorious.

If you’re ready to embark on this transformative journey and elevate your GMAT Quantitative Reasoning skills to new heights, I invite you to reach out to me. Whether you prefer one-on-one tutoring sessions, comprehensive courses, or tailored strategies to suit your unique needs, I’m here to support you every step of the way.

Don’t let uncertainty hold you back; seize this opportunity to unleash your full potential and chart a course towards success. Together, we’ll turn your GMAT aspirations into reality.

To connect with me and embark on your GMAT Focus Edition journey, reach out via WhatsApp at +56 945 517 215 or email me at clasesgmatchile@gmail.com.

For more information about my services and testimonials from satisfied students, visit my website at https://gmatchile.cl  and https://clasesgmat.es .

Let’s embark on this adventure together and transform your GMAT dreams into a tangible reality. Your success awaits.

Warm regards,

Claudio Hurtado
GMAT Quant Expert
GMAT Focus Edition Strategist