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

 It is currently 23 Oct 2019, 21:35 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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  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 V
Joined: 16 Aug 2015
Posts: 8033
GMAT 1: 760 Q51 V42 GPA: 3.82

Show Tags

1
13 00:00

Difficulty:   65% (hard)

Question Stats: 52% (01:35) correct 48% (01:27) wrong based on 161 sessions

HideShow timer Statistics

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

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

_________________
CEO  D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2978
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Re: Is x^2>y^2?  [#permalink]

Show Tags

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

_________________
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 V
Joined: 16 Aug 2015
Posts: 8033
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Is x^2>y^2?  [#permalink]

Show Tags

==> 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.
_________________
Retired Moderator P
Joined: 22 Aug 2013
Posts: 1428
Location: India
Re: Is x^2>y^2?  [#permalink]

Show Tags

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  B
Joined: 27 Apr 2015
Posts: 39
GMAT 1: 370 Q29 V13 Re: Is x^2>y^2?  [#permalink]

Show Tags

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
Non-Human User Joined: 09 Sep 2013
Posts: 13418
Re: Is x^2>y^2?  [#permalink]

Show Tags

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________ Re: Is x^2>y^2?   [#permalink] 21 Jul 2019, 04:35
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  