Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized for You
we will pick new questions that match your level based on your Timer History
Track Your Progress
every week, we’ll send you an estimated GRE score based on your performance
Practice Pays
we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
Your score will improve and your results will be more realistic
Is there something wrong with our timer?Let us know!
Wondering if you should waive the GMAT/GRE? In this quick tips video, Personal MBA Coach Founder, Scott Edinburgh, discusses when it may be a good idea to waive the GMAT/GRE
Starting at $975 and offering up to $545 of savings, our new Amplify Hourly Packages offer structure and support in certain high-value areas (story development, resume, essays, interviewing) to help get your applications across the finish line.
Join our Sia Admissions founder, Susan Berishaj, on March 31st to learn 3 steps for crafting admission committee-proof goals. Top-ranked business schools seek leaders with impactful and achievable goals. Let Susan help you make your dreams a reality.
The average of (x-1)^2 and (x+3)^2 or 3
[#permalink]
02 Jun 2020, 02:30
1
Expert Reply
3
Bookmarks
00:00
Question Stats:
57% (01:34) correct
42% (01:09) wrong based on 114 sessions
HideShow
timer Statistics
Quantity A
Quantity B
The average of \((x-1)^2\) and \((x+3)^2\)
3
A) Quantity A is greater. B) Quantity B is greater. C) The two quantities are equal. D) The relationship cannot be determined from the information given.
The average of (x-1)^2 and (x+3)^2 or 3
[#permalink]
02 Jun 2020, 05:06
5
1
Bookmarks
Carcass wrote:
Quantity A
Quantity B
The average of \((x-1)^2\) and \((x+3)^2\)
3
A) Quantity A is greater. B) Quantity B is greater. C) The two quantities are equal. D) The relationship cannot be determined from the information given.
Tricky!!!
Start with: Average \(= \frac{(x-1)^2 + (x+3)^2}{2}\)
Simplify numerator: Average \(= \frac{2x^2 + 4x + 10}{2}\)
Simplify numerator: Average \(= x^2 + 2x + 5\)
This is where it gets tricky!!! You may notice that we kind of have a perfect square hiding in our algebraic expression. We know that \(= x^2 + 2x + 1\) is a perfect square because we can rewrite it as \((x + 1)^2\)
So let's take: \(= x^2 + 2x + 5\) And rewrite it as: \(= x^2 + 2x + 1 + 4\) Now factor the first part to get: \(= (x + 1)^2 + 4\)
So, the average \(= (x + 1)^2 + 4\)
Since \((x + 1)^2 ≥ 0\) for all values of x, we can conclude that \((x + 1)^2 + 4 ≥ 4\) for all values of x
In other words: QUANTITY A: Some number greater than or equal to 4 QUANTITY B: 3