Find all School-related info fast with the new School-Specific MBA Forum

It is currently 30 Jul 2016, 06:59
GMAT Club Tests

Close

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
Your Progress

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Is x > y^2? (1) x > y+5 (2) x^2-y^2 = 0

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

Hide Tags

1 KUDOS received
Manager
Manager
User avatar
Status: Current MBA Student
Joined: 19 Nov 2009
Posts: 127
Concentration: Finance, General Management
GMAT 1: 720 Q49 V40
Followers: 12

Kudos [?]: 261 [1] , given: 210

Is x > y^2? (1) x > y+5 (2) x^2-y^2 = 0 [#permalink]

Show Tags

New post 12 Jul 2010, 17:53
1
This post received
KUDOS
4
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

38% (02:36) correct 62% (01:33) wrong based on 270 sessions

HideShow timer Statistics

Is x > y^2?

(1) x > y+5

(2) x^2-y^2 = 0

Hello,

I was wondering if someone can help with providing a detailed explanation as to how they arrived at correct answer . The explanation on the test (GMAT Club Test m2#19) review is a bit brief. Thanks
[Reveal] Spoiler: OA
Expert Post
5 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 34120
Followers: 6109

Kudos [?]: 76924 [5] , given: 9992

Re: Is x > y^2? (1) x > y+5 (2) x^2-y^2 = 0 [#permalink]

Show Tags

New post 12 Jul 2010, 19:39
5
This post received
KUDOS
Expert's post
2
This post was
BOOKMARKED
tonebeeze wrote:
Hello,

I was wondering if someone can help with providing a detailed explanation as to how they arrived at (c). The explanation on the test review is a bit brief. Thanks


Is x>y^2?

(1) x>y+5

(2) x^2-y^2 = 0


Is \(x>y^2\)?

(1) \(x>y+5\) --> \(x-y>5\). Clearly insufficient, for example: if \(x=1\) and \(y=-10\) then the answer is NO, but if \(x=10\) and \(y=1\) then the answer is YES. Two different answers, hence not sufficient.

(2) \(x^2-y^2=0\) --> \((x-y)(x+y)=0\) --> so either \(x-y=0\) or \(x+y=0\). Also insufficient: if \(x=1\) and \(y=1\), then answer is NO, buy if \(x=\frac{1}{2}\) and \(y=\frac{1}{2}\), then the answer is YES. Two different answers, hence not sufficient.

(1)+(2) As from (1) \(x-y>5\neq{0}\), then from (2) must be true that \(x+y=0\) --> so \(x=-y\) --> substitute \(x\) in (1) --> \(-y-y>5\) --> \(y<-\frac{5}{2}<0\), as \(x=-y\), then \(x>\frac{5}{2}>0\), so \(y^2\) (or which is the same \(x^2\)) will always be more than \(x\), thus the answer to the question "Is \(x>y^2\)" is NO. Sufficient.

To elaborate more as \(x=-y>0\), the only chance for \(x>y^2\) to hold true (or which is the same for \(x>x^2\) to hold true) would be if \(x\) is fraction (\(0<x<1\)). For example if \(x=\frac{1}{2}\) and \(y=-\frac{1}{2}\) then \(x=\frac{1}{2}>y^2=\frac{1}{4}\). But the fact that \(x>\frac{5}{2}>0\) rules out this option.

Answer: C.

Hope it's clear.
_________________

New to the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
User avatar
Status: Current MBA Student
Joined: 19 Nov 2009
Posts: 127
Concentration: Finance, General Management
GMAT 1: 720 Q49 V40
Followers: 12

Kudos [?]: 261 [0], given: 210

Re: Is x > y^2? (1) x > y+5 (2) x^2-y^2 = 0 [#permalink]

Show Tags

New post 12 Jul 2010, 20:13
Thanks! That was a much clear explanation.

Last problem of the day:

What is the best approach to solve problems such as this:


"How many times will the digit 7 be written when listing the integers from 1 to 1000?"

Is there any combinationatorics shortcuts? The GMTClub test approached seemed very time consuming.
Manager
Manager
avatar
Joined: 22 Jun 2010
Posts: 57
Followers: 1

Kudos [?]: 41 [0], given: 10

Re: Is x > y^2? (1) x > y+5 (2) x^2-y^2 = 0 [#permalink]

Show Tags

New post 15 Jul 2010, 08:33
tonebeeze wrote:
Thanks! That was a much clear explanation.

Last problem of the day:

What is the best approach to solve problems such as this:


"How many times will the digit 7 be written when listing the integers from 1 to 1000?"

Is there any combinationatorics shortcuts? The GMTClub test approached seemed very time consuming.


digits-problem-difficulty-in-gmat-club-test-97153.html
Expert Post
3 KUDOS received
Magoosh GMAT Instructor
User avatar
Joined: 28 Dec 2011
Posts: 3262
Followers: 1098

Kudos [?]: 4797 [3] , given: 53

Re: Is x > y^2? (1) x > y+5 (2) x^2-y^2 = 0 [#permalink]

Show Tags

New post 08 Jan 2012, 22:58
3
This post received
KUDOS
Expert's post
Hi, there! I'm happy to help with this. :)

The question: is x > y^2

Statement #1: x > y + 5

This doesn't necessarily tell us anything. If y = 1, and x = 7, then x > y^2, but if y = -6 and x = 0, then x < y^2. But itself, Statement #1 is not sufficient.

Statement #2: x^2 - y^2 = 0

This means that x^2 = y^2, which means that x = ±y. Same absolute value, but both could be positive, both could be negative, or either one could be positive and the other negative. We know that y^2 will be positive, but the x can be positive or negative, so by itself, Statement #2 is insufficient.

Combined
Now, we know that x^2 - y^2 = 0 ---> x = ±y, AND we know that x > y + 5. This leads immediate to a few conclusions
(a) x is positive and y is negative --- that's the only way they could have the same absolute value, but with x bigger than y + 5
(b) x and y must have an absolute value greater than 2.5, so that the different between positive x and negative y is more than 5

So we are comparing a positive number x, greater than 2.5, to the square of the negative number with the same absolute value. Of course, x^2 and y^2 are equal, so the question really boils down to: given that x > 2.5, is x > x^2?

For all x greater than one, the square of x is greater than x. That's because, squaring is multiplying a number by itself, and when you multiply anything by a number greater than one, it gets bigger.

Thus, if x > 2.5, when we square it, it will get bigger. Therefore, x^2 = y^2 > x for all values of x > 2.5.

Thus, combined, the statements are sufficient together. Answer = C

Does that make sense? Please let me know if you have any questions.

Mike :)
_________________

Mike McGarry
Magoosh Test Prep

Image

Image

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 34120
Followers: 6109

Kudos [?]: 76924 [0], given: 9992

Re: Is x > y^2? (1) x > y+5 (2) x^2-y^2 = 0 [#permalink]

Show Tags

New post 17 Jul 2013, 00:22
Expert's post
Manager
Manager
avatar
Status: How easy it is?
Joined: 09 Nov 2012
Posts: 122
Location: India
Concentration: Operations, General Management
GMAT 1: 650 Q50 V27
GMAT 2: 710 Q49 V37
GPA: 3.5
WE: Operations (Other)
Followers: 2

Kudos [?]: 81 [0], given: 171

GMAT ToolKit User Reviews Badge
Re: Is x > y^2? (1) x > y+5 (2) x^2-y^2 = 0 [#permalink]

Show Tags

New post 18 Jul 2013, 19:33
Bunnel, can you please provide a graphical solution to this particular problem?
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 34120
Followers: 6109

Kudos [?]: 76924 [0], given: 9992

Re: Is x > y^2? (1) x > y+5 (2) x^2-y^2 = 0 [#permalink]

Show Tags

New post 18 Jul 2013, 22:41
Expert's post
Intern
Intern
avatar
Joined: 11 Aug 2013
Posts: 6
Schools: ISB '15 (S)
Followers: 0

Kudos [?]: 2 [0], given: 7

Re: Is x > y^2? (1) x > y+5 (2) x^2-y^2 = 0 [#permalink]

Show Tags

New post 07 Oct 2013, 12:06
Hi i had a question.

Statement two provides us with equation x^2=y^2

Doesn't that answer our question for x>y^2 as No always ?

For example if x=-2 and y=2 then -2 is not greater than y^2..
Or x=2 and y=2; 2 is not greater than 4 ?

Am i missing something here ? :?:

P.S: Thanks in advance for the help !
1 KUDOS received
Manager
Manager
avatar
Joined: 29 Aug 2013
Posts: 78
Location: United States
Concentration: Finance, International Business
GMAT 1: 590 Q41 V29
GMAT 2: 540 Q44 V20
GPA: 3.5
WE: Programming (Computer Software)
Followers: 0

Kudos [?]: 52 [1] , given: 24

Re: Is x > y^2? (1) x > y+5 (2) x^2-y^2 = 0 [#permalink]

Show Tags

New post 07 Oct 2013, 23:15
1
This post received
KUDOS
priyankakhosla wrote:
Hi i had a question.

Statement two provides us with equation x^2=y^2

Doesn't that answer our question for x>y^2 as No always ?

For example if x=-2 and y=2 then -2 is not greater than y^2..
Or x=2 and y=2; 2 is not greater than 4 ?

Am i missing something here ? :?:

P.S: Thanks in advance for the help !


If x and y are fractions for eg. x=1/2 and y=1/2
then 1/2 > 1/4 ; i.e. x > y^2 - Hence you get a YES answer here and statement 2 becomes Insufficient.

Consider Kudos if it helped.
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 10667
Followers: 496

Kudos [?]: 131 [0], given: 0

Premium Member
Re: Is x > y^2? (1) x > y+5 (2) x^2-y^2 = 0 [#permalink]

Show Tags

New post 23 Nov 2014, 23:03
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Manager
Manager
avatar
Joined: 30 Mar 2013
Posts: 137
Followers: 0

Kudos [?]: 38 [0], given: 196

GMAT ToolKit User
Re: Is x > y^2? (1) x > y+5 (2) x^2-y^2 = 0 [#permalink]

Show Tags

New post 07 Dec 2014, 01:29
Bunuel wrote:
tonebeeze wrote:
Hello,

I was wondering if someone can help with providing a detailed explanation as to how they arrived at (c). The explanation on the test review is a bit brief. Thanks


Is x>y^2?

(1) x>y+5

(2) x^2-y^2 = 0


Is \(x>y^2\)?

(1) \(x>y+5\) --> \(x-y>5\). Clearly insufficient, for example: if \(x=1\) and \(y=-10\) then the answer is NO, but if \(x=10\) and \(y=1\) then the answer is YES. Two different answers, hence not sufficient.

(2) \(x^2-y^2=0\) --> \((x-y)(x+y)=0\) --> so either \(x-y=0\) or \(x+y=0\). Also insufficient: if \(x=1\) and \(y=1\), then answer is NO, buy if \(x=\frac{1}{2}\) and \(y=\frac{1}{2}\), then the answer is YES. Two different answers, hence not sufficient.

(1)+(2) As from (1) \(x-y>5\neq{0}\), then from (2) must be true that \(x+y=0\) --> so \(x=-y\) --> substitute \(x\) in (1) --> \(-y-y>5\) --> \(y<-\frac{5}{2}<0\), as \(x=-y\), then \(x>\frac{5}{2}>0\), so \(y^2\) (or which is the same \(x^2\)) will always be more than \(x\), thus the answer to the question "Is \(x>y^2\)" is NO. Sufficient.

To elaborate more as \(x=-y>0\), the only chance for \(x>y^2\) to hold true (or which is the same for \(x>x^2\) to hold true) would be if \(x\) is fraction (\(0<x<1\)). For example if \(x=\frac{1}{2}\) and \(y=-\frac{1}{2}\) then \(x=\frac{1}{2}>y^2=\frac{1}{4}\). But the fact that \(x>\frac{5}{2}>0\) rules out this option.

Answer: C.

Hope it's clear.


Hello, could someone please remove the highlighted part from the original post? (also from my post now, I suppose).
Also, I just wanted to know, if we could also write \(x^2-y^2=0\) as \(x^2=y^2\) which is the same as \(|x|=|y|\).
Just asking because I've become slightly comfortable with solving with absolute values. So is this ok?
1 KUDOS received
Senior Manager
Senior Manager
User avatar
Joined: 13 Jun 2013
Posts: 279
Followers: 14

Kudos [?]: 300 [1] , given: 13

Premium Member
Re: Is x > y^2? (1) x > y+5 (2) x^2-y^2 = 0 [#permalink]

Show Tags

New post 07 Dec 2014, 02:18
1
This post received
KUDOS
usre123 wrote:
Hello, could someone please remove the highlighted part from the original post? (also from my post now, I suppose).
Also, I just wanted to know, if we could also write \(x^2-y^2=0\) as \(x^2=y^2\) which is the same as \(|x|=|y|\).
Just asking because I've become slightly comfortable with solving with absolute values. So is this ok?


yes, you can use \(x^2-y^2=0\) as \(x^2=y^2\) or \(|x|=|y|\)
Manager
Manager
avatar
Joined: 30 Mar 2013
Posts: 137
Followers: 0

Kudos [?]: 38 [0], given: 196

GMAT ToolKit User
Re: Is x > y^2? (1) x > y+5 (2) x^2-y^2 = 0 [#permalink]

Show Tags

New post 07 Dec 2014, 04:20
thank you, and thank you for editing the questions I pointed out.
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 10667
Followers: 496

Kudos [?]: 131 [0], given: 0

Premium Member
Re: Is x > y^2? (1) x > y+5 (2) x^2-y^2 = 0 [#permalink]

Show Tags

New post 11 Dec 2015, 01:22
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Expert Post
Math Revolution GMAT Instructor
User avatar
Joined: 16 Aug 2015
Posts: 1574
GPA: 3.82
Followers: 106

Kudos [?]: 836 [0], given: 0

Re: Is x > y^2? (1) x > y+5 (2) x^2-y^2 = 0 [#permalink]

Show Tags

New post 13 Dec 2015, 04:29
Expert's post
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.


Is x > y^2?

(1) x > y+5

(2) x^2-y^2 = 0

-> In the original condition, there are 2 variables(x, y), which should match with the number of equations. So, you need 2 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make C the answer. In 1) & 2), it is x-y>5 for 1). In case of 2), x=y, x=-y. When x=y, it is 0>5 from x-y>5, which is impossible and becomes x=-y. Thus, x>y^2? --> -y>y^2? --> 0>y^2+y? --> 0>y(y+1)? --> -1<y<0?. In 1), -y>y+5, -5>2y, -5/2>y, -2.5>y, which is no and sufficient. Therefore, the answer is C.

During the exam, it is better to choose C since there are 2 variables.

-> For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
_________________

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.
Find a 10% off coupon code for GMAT Club members.
Unlimited Access to over 120 free video lessons - try it yourself
See our Youtube demo

Re: Is x > y^2? (1) x > y+5 (2) x^2-y^2 = 0   [#permalink] 13 Dec 2015, 04:29
    Similar topics Author Replies Last post
Similar
Topics:
3 Experts publish their posts in the topic Is x^2-y^2>x+y? MathRevolution 2 13 Jun 2016, 09:59
11 Experts publish their posts in the topic Is (x^-1-y^-1)/(x^-2-y^-2)>1? excelingmat 12 10 Oct 2015, 08:03
16 Experts publish their posts in the topic Is |x^2 + y^2| > |x^2 - y^2|? makhija1 21 04 Jun 2013, 20:45
43 Experts publish their posts in the topic If x^2 = y^2, is true that x>0? burnttwinky 45 20 May 2012, 19:02
13 Experts publish their posts in the topic Is x > y^2? 1. x > y + 5 2. x^2 - y^2 = 0 sset009 8 02 Sep 2008, 07:41
Display posts from previous: Sort by

Is x > y^2? (1) x > y+5 (2) x^2-y^2 = 0

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


cron

GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

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®.