GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 15 Oct 2018, 01:41

GMAT Club Daily Prep

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

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Is x^2>y^2?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6361
GMAT 1: 760 Q51 V42
GPA: 3.82

Show Tags

18 May 2017, 01:07
1
11
00:00

Difficulty:

65% (hard)

Question Stats:

50% (01:36) correct 50% (01:29) wrong based on 174 sessions

HideShow timer Statistics

Is $$x^2>y^2$$?

1) |x|>y
2) x>|y|

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" CEO Joined: 08 Jul 2010 Posts: 2531 Location: India GMAT: INSIGHT WE: Education (Education) Re: Is x^2>y^2? [#permalink] Show Tags 18 May 2017, 07:12 MathRevolution wrote: Is $$x^2>y^2$$? 1) |x|>y 2) x>|y| Question : Is $$x^2>y^2$$? Statement : 1) |x|>y @y = -4, x=2, $$x^2<y^2$$ @y = -4, x=5, $$x^2>y^2$$ NOT SUFFICIENT Statement : 2) x>|y| i.e. value of x is positive and absolute value of x is greater than absolute value of y. hence, squaring both sides of the inequation we get $$x^2>y^2$$ SUFFICIENT Answer: Option B _________________ Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772 Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6361 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Is x^2>y^2? [#permalink] Show Tags 21 May 2017, 17:58 ==> In the original condition, there are 2 variables (x,y), and in order to match the number of variables to the number of equations, there must be 2 variables. Since there is 1 for con 1) and 1 for con 2), C is most likely to be the answer. By solving con 1) and con 2), from x>|y|≥0, it is x>0, so from x>|y|, it is |x|>|y|, which becomes $$x^2>y^2$$, hence yes, it is sufficient. The answer is C. However, this is an absolute value question, one of the key questions, so you apply CMT 4 (A: if you get C too easily, consider A or B). For con 1), you get (x,y)=(2,1) yes (2,-3) no, hence not sufficient. For con 2), from x>|y|≥0, you get x>0, which becomes |x|>|y|, then $$x^2>y^2$$, it is always yes and sufficient. Therefore, the answer is B. Answer: B _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

DS Forum Moderator
Joined: 22 Aug 2013
Posts: 1348
Location: India
Re: Is x^2>y^2?  [#permalink]

Show Tags

21 May 2017, 23:05
x^2 > y^2 if and only if |x|>|y|

Statement 1. |x|>y.
So absolute value of x is greater than y. But we don't know whether |x|>|y| or not.

Eg, take x = 4, y = 3. Here |x| > y and |x| is also > |y|. So x^2 > y^2
Now take x= -4, y= -5. Here |x| > y But |x| < |y|. Here x^2 < y^2
So Insufficient.

Statement 2. x > |y|
If x > |y| then obviously |x| will also be > |y|.
(Because absolute value of x must be either greater than x if x is negative, or equal to x if x is non-negative)

Thus definitely x^2 > y^2. Statement is Sufficient

Hence answer is B
Intern
Joined: 27 Apr 2015
Posts: 41
GMAT 1: 370 Q29 V13
Re: Is x^2>y^2?  [#permalink]

Show Tags

19 Feb 2018, 06:56
1
MathRevolution wrote:
Is $$x^2>y^2$$?

1) |x|>y
2) x>|y|

To Find Is $$x^2>y^2$$ ?
=> OR $$x^2-y^2>0$$
=> OR $$(x-y)(x+y)>0$$
Thus $$x^2>y^2$$ is possible if both $$(x-y)(x+y)$$ are of same sign

PL. NOTE Now IF $$a>b$$----(1) and
=> Case 1 IF $$(a+b)>0$$ then SQUARING both the side of the inequality (1) the inequality sign (here '>') remains SAME i.e (2) becomes $$a^2>b^2$$
=> Case 2 IF $$(a+b)<0$$ then SQUARING both the side of the inequality (1) the inequality sign (here '>') REVERSE. i.e (2) becomes $$a^2<b^2$$
One can verify the above OUTCOMES by plugging values

Stat 1 $$|x|>y$$ ---(2)
So from (2)we have LHS '|x|' is ALWAYS +ve and RHS 'y' is less than |x|
=> Therefore 'y'can be +ve OR -ve and SO $$(|x|+y)$$ can be >0 OR <0. Thus SQUARING both the side of the inequality (2) will give 2 OUTCOMES i.e
=> Case 1 $$(|x|+y)>0$$ then $$|x|^2>y^2$$ or $$x^2>y^2$$
=> Case 2 $$(|x|+y)<0$$ then $$|x|^2<y^2$$ or $$x^2<y^2$$
Since no unique answer, therefore NOT SUFFICIENT

Stat 2 $$x>|y|$$
Since RHS '|y| is ALWAYS +ve and LHS 'x' is greater than |y|
=> Therefore 'x' is ALSO +ve and SO $$(x+|y|)$$ is >0. Thus SQUARING both the side of the inequality (2) will give ONLY 1 OUTCOMES
=> Case 1 $$(x+|y|)>0$$ then $$x^2>|y|^2$$ or $$x^2>y^2$$
Since unique answer, therefore SUFFICIENT

Thus Option "B"

Regards
Dinesh
Re: Is x^2>y^2? &nbs [#permalink] 19 Feb 2018, 06:56
Display posts from previous: Sort by

Is x^2>y^2?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.