• NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    Hundreds of Questions Highly Detailed Reporting Expert Explanations TAKE A FREE GMAT QUIZ
  • 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

Is (y-10)^2>(x+10)^2? ----Veritas

This topic has 2 expert replies and 0 member replies

Top Member

Is (y-10)^2>(x+10)^2? ----Veritas

Post

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Difficult



Is (y-10)^2>(x+10)^2 ?

(1) -y>x+5

(2) x>y

OA: C

Source: Veritas

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Top Reply
Post
Mo2men wrote:
Is (y-10)^2>(x+10)^2 ?

(1) -y>x+5

(2) x>y
x² < y² can be rephrased as follows:
|x| < |y|
Thus, the question stem can be rephrased as follows:
Is |x+10| < |y-10|?

|a-b| = the distance between a and b
|a+b| = |a-(-b)| = the distance between a and -b
Thus, the question stem can be further rephrased as follows:
Is the distance between x and -10 less than the distance between y and 10?

Statement 1, rephrased: x+y < -5
Case 1: y=-20 and x=-10
y= -20..........x=-10..........0..........10
In this case, the distance between x and -10 is less than the distance between y and 10, so the answer to the rephrased question stem is YES.

Case 2: x=-20 and y=10
x=-20..........-10..........0.........y=10
In this case, the distance between x and -10 is NOT less than the distance between y and 10, so the answer to the rephrased question stem is NO.

Since the answer is YES in Case 1 but NO in Case 2, INSUFFICIENT.

Statement 2: y < x
Case 1 also satisfies Statement 2,
In Case 1, the answer to the rephrased question stem is YES.

Case 3: y=10 and x=20
-10..........0..........y=10..........x=20
In this case, the distance between x and -10 is NOT less than the distance between y and 10, so the answer to the rephrased question stem is NO.

Since the answer is YES in Case 1 but NO in Case 3, INSUFFICIENT.

Statements combined:
Adding together x+y < -5 and y < x, we get:
x+y+y < x-5
2y < -5
y < -2.5

Case 4: y=-3 and x=-2.5, with the result that x+y < -5 and y < x
-10........y=-3.......x=-2.5......0..........10
In this case, the distance between x and -10 is less than the distance between y and 10, so the answer to the rephrased question stem is YES.

Case 5: y=-10 and x=4, with the result that x+y < -5 and y < x
y=-10............0...........x=4............10
In this case, the distance between x and -10 is less than the distance between y and 10, so the answer to the rephrased question stem is YES.

The cases above illustrate that -- when the two statements are combined -- the distance between x and -10 must be less than the distance between y and 10.
Thus, the answer to the rephrased question stem is YES.
SUFFICIENT.

The correct answer is C.

_________________
Mitch Hunt
Private Tutor for the GMAT and GRE
GMATGuruNY@gmail.com

If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.

Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.
Student Review #1
Student Review #2
Student Review #3

  • +1 Upvote Post
  • Quote
  • Flag
Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.

GMAT/MBA Expert

GMAT Instructor
Joined
09 Oct 2010
Posted:
1449 messages
Followed by:
32 members
Upvotes:
59
Post
Mo2men wrote:
Is (y-10)^2>(x+10)^2 ?

(1) -y>x+5

(2) x>y
Source: Veritas
VERY nice problem. Please note we will use two different rephrasings (one for each (1) and (2) alone, the other for (1+2)):
$${\left( {y - 10} \right)^2}\,\,\mathop > \limits^? \,\,{\left( {x + 10} \right)^2}\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\left\{ \matrix{
\,\left| {y - 10} \right|\,\,\,\mathop > \limits^? \,\,\,\left| {x + 10} \right|\,\,\,\,\,\,\,\,\left( {\rm{I}} \right) \hfill \cr
\,\,\,{\rm{OR}} \hfill \cr
\,\left( {x + y} \right)\left( {y - x - 20} \right)\,\,\,\mathop > \limits^? \,\,\,0\,\,\,\,\,\,\,\,\left( {{\rm{II}}} \right)\,\,\,\,\,\left( * \right) \hfill \cr} \right.$$
$$\left( * \right)\,\,\,\left\{ \matrix{
{\left( {y - 10} \right)^2}\,\,\mathop > \limits^? \,\,{\left( {x + 10} \right)^2}\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,{\left( {y - 10} \right)^2} - \,{\left( {x + 10} \right)^2}\,\,\mathop > \limits^? \,\,\,0 \hfill \cr
\,{\left( {y - 10} \right)^2} - \,{\left( {x + 10} \right)^2} = \left[ {\left( {y - 10} \right) + \left( {x + 10} \right)} \right]\left[ {\left( {y - 10} \right) - \left( {x + 10} \right)} \right] = \left( {x + y} \right)\left( {y - x - 20} \right)\,\,\,\mathop > \limits^? \,\,\,0 \hfill \cr} \right.$$

$$\left( 1 \right)\,\,\,x + y < - 5\,\,\,\,\left( {\rm{I}} \right)\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {0, - 6} \right)\,\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr
\,{\rm{Take}}\,\,\left( {x,y} \right) = \left( { - 16,10} \right)\,\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr} \right.$$

$$\left( 2 \right)\,\,x > y\,\,\,\,\left( {\rm{I}} \right)\,\,\,\,\,\,\left\{ \matrix{
\,\left( {{\mathop{\rm Re}\nolimits} } \right){\rm{Take}}\,\,\left( {x,y} \right) = \left( {0, - 6} \right)\,\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr
\,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {1,0} \right)\,\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr} \right.$$

$$\left( {1 + 2} \right)\,\,\,\,\,\,\left( {{\rm{II}}} \right)\,\,\,\left\{ \matrix{
\,x + y < 0\,\,\,{\rm{by}}\,\,\,\left( 1 \right) \hfill \cr
\,y - x - 20 = \left( {y - x} \right) - 20\mathop < \limits^{{\rm{by}}\,\,\left( 2 \right)} - 20\, < 0 \hfill \cr} \right.\,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\left( {\rm{C}} \right)\,\,\,\,$$


This solution follows 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

  • +1 Upvote Post
  • Quote
  • Flag
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep

Top First Responders*

1 Ian Stewart 57 first replies
2 Brent@GMATPrepNow 31 first replies
3 Jay@ManhattanReview 29 first replies
4 GMATGuruNY 21 first replies
5 ceilidh.erickson 15 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description Scott@TargetTestPrep

Target Test Prep

199 posts
2 image description Max@Math Revolution

Math Revolution

84 posts
3 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

69 posts
4 image description Ian Stewart

GMATiX Teacher

65 posts
5 image description GMATGuruNY

The Princeton Review Teacher

40 posts
See More Top Beat The GMAT Experts